text:
## 17 in 17: Efficient 17-bit synthesis project

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### Re: 17 in 17: Efficient 17-bit synthesis project

Sokwe wrote:That's not quite #239, but with a little modification it can be made to work. The cis-hook with tail can be added with the hook with tail already in place. Further, the final step can be done with just 2 gliders. The final cost is 11:
And that naturally suggests reductions to related SLs of different sizes:

Code: Select all

x = 64, y = 86, rule = B3/S23
13bo$3bobo6bo$4b2o6b3o$4bo$54bo$54bobo$13b2o39b2o$12b2o44b2o$3o11bo43b
o3b2o$2bo49bo6bo2bo$bo50b2o6bobo$51bobo7bo$7bo49bo$7b3o47b3o$10bo5b2o
42bo$9b2o4b2o42b2o$17bo7$13bo$3bobo6bo$4b2o6b3o$4bo$54bo$54bobo$13b2o 39b2o$12b2o44b2o$3o11bo43bo3b2o$2bo49bo6bo2bo$bo50b2o6bobo$51bobo7bo$7bo49bo$7b3o47b3o$10bo5b2o42bo$9bo5b2o42bo$9b2o6bo41b2o7$13bo$3bobo6bo$4b2o6b3o$4bo$54bo$54bobo$13b2o39b2o$12b2o44b2o$3o11bo43bo3b2o$2bo49bo 6bo2bo$bo50b2o6bobo$51bobo7bo$7bo49bo$7b3o47b3o$10bo5b2o42bo$7b3o5b2o 40b3o$7bo9bo39bo7$13bo$3bobo6bo$4b2o6b3o$4bo$54bo$54bobo$13b2o39b2o$
12b2o44b2o$3o11bo43bo3b2o$2bo49bo6bo2bo$bo50b2o6bobo$51bobo7bo$7bo49bo$7b3o47b3o$10bo5b2o42bo$7b2obo4b2o40b2obo$7bobo7bo39bobo! The 16-bitter thus goes down to 9 gliders. It does not reduce any further 17-bitters, though. Princess of Science, Parcly Taxel Kazyan Posts: 867 Joined: February 6th, 2014, 11:02 pm ### Re: 17 in 17: Efficient 17-bit synthesis project Good catch, Sokwe. #61 in 15G: Code: Select all x = 128, y = 48, rule = B3/S23 124bo$123bo$123b3o2$119b2o$119bobo$120bo4$bo$2b2o42bo$b2o44bo17bo55bo$
45b3o15bobo55bo4bo$bo62b2o55bo3bo$b2o39bo5b3o22bo51b3o$obo39bo7bo21bo$
42bo6bo6bobo13b3o36b2o$57b2o47bo3bo2bo6b3o$57bo48b3o2b3o$109b2o$60b3o
45bo2bo$62bo46b2o$39b3o19bo$41bo27b2o$40bo28bobo$44b3o22bo$44bo$45bo2$
112bo4b2o$111bobo2b2o$111bobo4bo$112bo12$42b2o$41bobo$43bo!
Tanner Jacobi

Posts: 1907
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: 17 in 17: Efficient 17-bit synthesis project

Kazyan wrote:Good catch, Sokwe.

#61 in 15G:

Code: Select all

rle
Reducible to 14, two (EDIT: three) different ways:

Code: Select all

x = 253, y = 70, rule = B3/S23
251bo$250bo$250b3o2$150bo$148b2o$149b2o12$150bo$149bo$149b3o6$7bo$8bo
17bo$6b3o15bobo$25b2o$3bo5b3o22bo175bo$3bo7bo21bo177bo$3bo6bo6bobo13b 3o173b3o$18b2o90bo$18bo92bo94bo5b3o$109b3o94bo7bo$21b3o182bo6bo6bobo 10bo$23bo82bo5b3o106b2o9bo$3o19bo83bo7bo106bo10b3o$2bo27b2o74bo6bo6bob
o10bo$bo28bobo88b2o9bo91b3o$5b3o22bo90bo10b3o91bo$5bo197b3o19bo$6bo
117b3o78bo$126bo77bo$103b3o19bo82b3o24b3o$105bo102bo26bo$104bo104bo26b
o$108b3o24b3o$108bo26bo$109bo26bo3$250bo$249b2o$249bobo5$3b2o$2bobo46b
2o$4bo45b2o$52bo$206b2o$205bobo$207bo$106b2o$105bobo$107bo!

LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Sokwe
Moderator
Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: 17 in 17: Efficient 17-bit synthesis project

Kazyan wrote:#61 in 15G
Reducible to 14
Down to 13 by synthesising the block and blinker on the left in 3:

Code: Select all

x = 122, y = 58, rule = B3/S23
3bo$bobo$2b2o5$31bo$32b2o$31b2o$16bo$17b2o34bobo$16b2o7bo27b2o$23bobo 28bo$24b2o5$115b2o$19b2o89bo3bo2bo$20b2o88b3o2b3o$19bo93b2o$112bo2bo$
113b2o5$28bo$28b2o$27bobo$116bo$50b2o63bobo$30b2o17b2o64bobo$30bobo18b o64bo$30bo$119b2o$119bobo$3o116bo$2bo$bo13$9b2o$10b2o58b3o$9bo60bo$71b o! -Matthias Merzenich Sokwe Moderator Posts: 1480 Joined: July 9th, 2009, 2:44 pm ### Re: 17 in 17: Efficient 17-bit synthesis project #92, #93, and #94 in 14 each: Code: Select all x = 238, y = 164, rule = B3/S23 bo$2bo$3o7$110bo$109bo$109b3o2$107bo$106bobo$106bobo$107bo13$178bo$
104bo59bo12bo$103bobo57bobo11b3o$37b2o64bobo57bobo$36bobo22b2o41bob2o 56bob2o$38bo22bobo38bobobobo53bobobobo$61bo39bobo3b2o52bobo3b2o4bobo$
102bo59bo10b2o$174bo3$51bo123b3o$45bobo2bo124bo$46b2o2b3o109bo13bo$46b o115b2o$33bo127bobo$33b2o$32bobo138bo$173b2o$172bobo10$23b2o$22bobo$24bo10$4b2o$5b2o$4bo16$177bo$175b2o$164bo11b2o$163bobo$163bobo$164bob
2o$162bobobobo$161bobo3b2o$162bo3$181bo$168b2o9b2o$169b2o9b2o$168bo4b 2o$173bobo$163b2o8bo$162bobo$164bo43$235b2o$164bo59bo4bobo3bobo$163bob
o57bobo4b2o3bo$163bobo57bobo4bo$164bob2o56bob2o$162bobobobo53bobobobo$
161bobo3b2o52bobo3b2o$162bo59bo$173bo$173bobo56bo$173b2o52bo3bobo$227b 2o2bobo$176b2o48bobo3bo$176bobo$176bo!
-Matthias Merzenich

Extrementhusiast
Posts: 1797
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 17 in 17: Efficient 17-bit synthesis project

Sokwe wrote:#92, #93, and #94 in 14 each:

Code: Select all

RLE
Ship-to-carrier transition in one less:

Code: Select all

x = 12, y = 11, rule = B3/S23
9bo$7b2o$b2o5b2o$bobo$2b2o$10bo$5b2o2b2o$6b2obobo$bo3bo$b2o$obo!

EDIT: #104 in fourteen gliders:

Code: Select all

x = 107, y = 28, rule = B3/S23
64bo$64bobo$64b2o9$7bo$8bo37bo$6b3o36bo$13bobo29b3o13bo36bo$13b2o45bob o29b2o3bobo$14bo45bo2bo29bo3bo2bo$46b3o9b2obobo29bob2obobo$bo4bo39bo
10bobob2o25bo5bobob2o$b2ob2o41bo10bo30b2o4bo$obo2b2o81b2o12bo$16b2o84b obo$16bobo73b2o3b3o2b2o$16bo74bobo3bo$93bo4bo5b3o$5bo98bo$5b2o98bo$4bo bo!  EDIT 2: #269 in twelve (and #207 by the same method): Code: Select all x = 139, y = 54, rule = B3/S23 obo$b2o$bo3$12bo$11bo$11b3o$44bob2o26bob2o57bob2o$44b2obo26b2obo57b2ob
o$8b2o32b2o28b2o59b2o$8bobo30bobo27bobo58bobo$4b2o2bo32b2o28b2o59b2o$
5b2o$4bo$45b2o$45b2o2$47b3o$47bo$48bo$68bobo59b3o$69b2o$69bo2$69b2o$70b2o46bo$69bo46bobo5b3o$117b2o5bo$125bo$119bo$119b2o$118bobo7$118b3o$120bo$119bo10$90b2o$89bobo$91bo!  I Like My Heisenburps! (and others) Freywa Posts: 589 Joined: June 23rd, 2011, 3:20 am Location: Singapore Contact: ### Re: 17 in 17: Efficient 17-bit synthesis project Can the following sparks or subpatterns be synthed at the stated times so as to knock out two of the remaining xs17s? Code: Select all x = 62, y = 20, rule = LifeHistory 18.A5.A$19.2A.A.A36.A$18.2A3.2A26.2A8.A$4.3D43.A2.A7.A$3.D3.D43.2A3. 2A$3.D3.D6.D42.2A$.2D5.2D3.D.D31.2D8.A$D4.D4.D.D2.D30.4D$D3.D.D3.D2.D .D8.A24.2D$D4.D4.D3.D9.2A24.2D$.2D5.2D9.A3.A.A24.2D$3.D3.D11.2A29.D$3.D3.D10.A.A$4.3D2$10.3D.3D27.D.3D$12.D3.D27.D.D$10.3D.3D27.D.3D$10.D
5.D27.D3.D$10.3D.3D27.D.3D! Edit: #55 in 13 from its only soup: Code: Select all x = 124, y = 70, rule = B3/S23 108bo$107bo$107b3o16$90bo$79bo9bo$80b2o7b3o$79b2o3bobo$85b2o$85bo 5$41bobo$42b2o40bo$42bo3b3o34bobo23bo$46bo37b2o22bo$47bo60b3o4$2bo 103bobo$obo103b2o$b2o44bo39bo19bo$47bo39bo$4b2o41bo39bo$4bobo$4bo 2$47bo39bo$8b3o36bo39bo$8bo38bo39bo$9bo10$106b2o$106bobo$106bo8$121b3o$121bo$122bo! This also knocks out #56, so 168 stills remain. There are already two "rivers" flowing top-to-bottom. Code: Select all x = 603, y = 217, rule = B3/S23 218bo198b3o$217b2o197bo3bo$218bo201bo$218bo200bo$218bo199bo$218bo198bo
$217b3o196b5o4$17b3o17bo19b3o17b3o19bo16b5o16b3o16b5o16b3o17b3o17b3o
17bo19b3o17b3o19bo16b5o16b3o16b5o16b3o17b3o17b3o17bo19b3o17b3o19bo16b
5o16b3o16b5o16b3o17b3o$16bo3bo15b2o18bo3bo15bo3bo17b2o16bo19bo3bo19bo 15bo3bo15bo3bo15bo3bo15b2o18bo3bo15bo3bo17b2o16bo19bo3bo19bo15bo3bo15b o3bo15bo3bo15b2o18bo3bo15bo3bo17b2o16bo19bo3bo19bo15bo3bo15bo3bo$16bo
3bo16bo22bo19bo16bobo16bo19bo22bo16bo3bo15bo3bo15bo3bo16bo22bo19bo16bo
bo16bo19bo22bo16bo3bo15bo3bo15bo3bo16bo22bo19bo16bobo16bo19bo22bo16bo
3bo15bo3bo$16bobobo16bo21bo18b2o16bo2bo17b3o16b4o19bo17b3o17b4o15bobob o16bo21bo18b2o16bo2bo17b3o16b4o19bo17b3o17b4o15bobobo16bo21bo18b2o16bo 2bo17b3o16b4o19bo17b3o17b4o$16bo3bo16bo20bo21bo15b5o19bo15bo3bo17bo17b
o3bo19bo15bo3bo16bo20bo21bo15b5o19bo15bo3bo17bo17bo3bo19bo15bo3bo16bo
20bo21bo15b5o19bo15bo3bo17bo17bo3bo19bo$16bo3bo16bo19bo18bo3bo18bo16bo 3bo15bo3bo17bo17bo3bo15bo3bo15bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3bo 17bo17bo3bo15bo3bo15bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3bo17bo17bo3bo 15bo3bo$17b3o16b3o17b5o16b3o19bo17b3o17b3o18bo18b3o17b3o17b3o16b3o17b
5o16b3o19bo17b3o17b3o18bo18b3o17b3o17b3o16b3o17b5o16b3o19bo17b3o17b3o
18bo18b3o17b3o9$36b2o38b2o58b2o18b2obo15b2o19bo58bo3b2o34b2o2b2o14b2ob ob2o35b2o40bo18bo17b2o2b2o35b2o56b2o20bo18bo$b3o32bobob2o34bo60bo18bob
2o16bo18bobo2b2o53b3o2bo34bo3bobo13bob2obo2bo32bo2bo35b2obobo16bobo15b
o2bo2bo34bobo56bobo19b3o15bobo2b2o$o3bo33b2obo35bo59bob2o19b2o14bobo 17bo2bo2bo55b2o37bobobo17bo2b2o31bobo2bo34bob2o2bo14bobobo15bobobo34bo bo60bo16b2o3bo14bo2bo2bo$o3bo32bo38b2o2bo57bobo16b2o2bo15bobo17b3obo
55bo38b2o2bo15b3o37bob3o38b2o14bo2bobo14b2o2bo35bo2b3o55b2o18bo2bobo
14bob2o$obobo32bo40b3o55bobo17bob2o19bo20bo56bo39bo18bo40bo38b2o18b2ob o16bo39b2o2bo54bo19bo4bo14b2o$o3bo30b2o39b2o57bobobo16bo22b2o18bo58b2o
36bo61bo37bo20bo17bo41bo57bob3o15bobo18bo$o3bo30bo39bo2bo56bo2bo16b2o 20b2o2bo16bo60bo36b2o57b3o39bo17bobo17b2o38bo60bobo17bobo16bo$b3o32bo
39bobo57b2o39bo2bo17b2o58bo96bo40b2o17b2o58b2o63bo16bo17b2o$35b2o40bo 100b2o78b2o279b2o12$36b2ob2o19b2o16b2o38b2o41b2o12b2o19bo98b2o2b2o14b
2obo38b2o18b2o21b2o55b2o18bo57b2o21bo17bo24b2o$bo34bob2o16b2o3bo17bo 39bo2b2o33b2o2bo14bo2b2o14bobo4b2o91bo3bobo13bob2o37bo2bo15bo2bo16b2o 2bobo54bo2bo16bobo56bobo18b3o16bobo20bobobo$2o39bo14bo2bo16b3o40bobobo
32bo2bobo14bobo2bo14bo2bo2bo94bobobo17b2o34bobobo15b2obob2o13bobo2bo
54bo2bobo14bo2bo59bo16bo19bo2bob2o15bob2o$bo35b2ob2o15bob2o15bo2b3o35b obo2bo34bob2o16bob2o16b2obobo93b2o2bo15b2obo2bo33bo2b2o16bobobo16b2o 55b2obo2bo13bobob2o55b2o18bo19bob2obo15bo3bo$bo35bo20bo19bo2bo34bob2o
36b2o21bo19bobo95bo18bobo2b2o34b2o18bo18b2o59bob2o15b2o2bo54bo19b2o18b
2o21bob2o$bo33bobo18bobo17bobo37bo40bo19bobo19bo95bo21bo40bo19bo18bo 59bo20bo56bo19bo4bo15bo18b3o$bo33b2o18bobo17bobo37b2o38bo20bobo19b2o
95b2o58b3o21bo16bo59b2o17bobo58b2o2b2o14bo2bobo13bo19bo$3o52b2o19bo78b 2o20bo177bo22b2o16b2o77b2o61bo2bo15bo2bo14b2o$538b2o18b2o12$38b2o40b2o 59b2o14bo77b2o3b2o13b2o2b2o14b2o18b2o2b2o14b2o40b2o18b2ob2o18b2o16b2o 78b2o19bo15b2o23b2o$b3o33bobo41bo54b2o2bobo13bobo2b2o72bo2bo2bo13bo2bo
2bo13bo2bobo14bo3bo15bo40bo2bo15bo2bobo14b2o2bobo15bo2bo76bo2bo17bobo
14bobo18b2o2bo$o3bo31bo39bo2bo57bo2bo15bo2bo2bo74b2obo15bobob2o14b2ob 2o16bobobo15bo4bo32bobo2bo14b2obo2bo13bo3bo16bo2bobo76bo2bo15bobobo16b o16bo2bobo$4bo32b2o37b5o56bob2o16bob2o77bob2o15bobo17bo18b2o2b2o14b2o
3bobo32bo4bo15bob2o16bob2o14bo4bo75bob2obo15bobobo14b2o18bob2o$3bo35bo 96b2o18b2o79bo21bo17bo19bo18bo3bobo34b4o16bo18b2o18b4o75bobo2bo14b2o3b o14bo19b2o$2bo32b4o39bo58bo19bo78bo21bo19b2o15bo21bo2bo37bo17b2o19bo
19bo77bo2bo16bo19bo20bo$bo33bo40b3o56bo19bo80b2o20b2o19bo15b2o21bobo 35bo38bo19bo80b2o18bo19b2o17bo$5o31bo38bo59b2o18b2o121bo40bo36b2o37b2o
18b2o100bo20bob2o13b2o$37bo37b2o201b2o236b2o20b2obo$36b2o11$17bo21b2o 95b2o19bo17b2ob2o55b2o18b2o3bo14b2o2bo120bo58b2o14b2o58b2o21bo41bo$b3o
12bobo2b2o14bo2bo95bo19bobo17bobo56bo2bob2o13bo3bobo13bo2bobo114b2o2bo
bo54b2o2bo15bo58bo3b2o14bobobo39bobo$o3bo12bobo2bo13bob2o97bo18bo2bob 2o13bo2b3o55b2obo15bo2bo2bo13b2obo115bo3bobo53bo2b2o15bo61bo2bo14b2obo bo38bo2bo$4bo14b2o16bo2b3o95bo18bob2obo14b2o2bo56bo2bo15bob3o15bo119bo
b2o54bobo2b3o12b2o59b2obo18bobo36b2obobo$2b2o14bo19bo3bo93bobo17b2o20b o58bo2b2o16bo18bo118b2o58bobo3bo14bo57bo3b2o14b2o2bo37bo2b2o$4bo11b3o
16b3o97bobob2o16bo18bo59bo22bo15b2o120bo59bo17b2o59b3o16bo42bo$o3bo10b o19bo99bobo2bo14bo20b2o58b2o20b2o15bo119bo79bo3b2o57bo18bo37b3o$b3o11b
2o119bobo16b2o119bo118b2o79bo2bo76b2o37bo$137bo137b2o200bobo$478bo11$60bo16b2o57b2o22b2o73b2o2b2o14b2o3b2o33b2obob2o13b2o21b2o18bobo57b2o 15b2o2b2o78bo38bo$3bo54b3o17bo57bo19b2o3bo73bo2bo2bo13bo2bo2bo33bob3ob
o13bobo18b3obo15b4obo56bo16bo3bo78bobo34bobobo$2b2o53bo18bo2b2o57bo17b o2bo77b2obo15bob3o56b3o15bo5bo13bo5bo54b2o2bo15bo3bo76bobo35b2obobo$bo
bo52bo2b2o15b2obo2bo54b2o18bob2o77bob2o15bo41b2o15bo3bo15bo5bo13b2o3b
2o52bo2b3o14b2o2b2o76bobobo36bobo$o2bo53b2obo17bo2b2o53bo19b2o2bo76bo 20bo37bobobo15b3obo16bo3b2o14bo58b2o18bobo76b2o3b2o33b2o2bo$5o53bo16bo
bo57bo2b3o14bo2bo77bo18b3o38b2o21bo18bobo15bo61bo17bobo76bo39bo$3bo52b obo16b2o59b2obo16b2o78b2o17bo62bo20b2o15b2o57bobo19bo78bo39bo$3bo51bob
o83bo176b2o95b2o100bo37b2o$56bo83b2o374b2o12$16b2o23b2o15bo77b2o21bo
36bo21b2o15b2o3b2o33b2o18bo3b2o16b2o3bo15bob2o55bo79b2obo54b2o21bo42bo
$5o11bo3b2o15b2o2bo15bobobo74bo21bobo34bobo2b2o13b2o2bo15bo2bo2bo33bo 19b3o2bo15bo2bobobo12b3obo55bobo78bob2o54bo19bobobo39b3o$o17bo2bo14bo
2bobo15bob2obo75bo19bo2bo34bobo2bo14bobo18b2obo36bob2o17b2o15bobo2b2o
2bo10bo5bo54bo2bo81b2o54bo17b2obo39bo$o16b2obo16b2obo15b2o4bo74b2o17b 2o2b2o36b2o16bob4o17bo36b3o2bo15bo2b3o13bo5bobo11bo5bo52b2ob2o78b2o2bo 53b2o20bobo38bo$b3o14bob2o16bo18bo4b2o72bo19bo40bo19bo3bo15b2o41bo15bo
bo3bo19b2o13bob3o55bo77bobob2o54bo19b2o2b2o37b2o$4bo10b3o18bobo16bo79b o2b3o16bo40b2o18bo18bo40b2o17bo40b2o57bo77b2o58bo4b2o13bo41bo$o3bo10bo
19bobo17b2o79b2o2bo17bo40bo17b2o19bo39bo116b2o139b2o2bo16bo39bo$b3o32b o101bo17bobo38bo39b2o40bo115bo142bobo15b2o37b2o$138b2o15bobo39b2o79b2o
116bo141b2o55bo$156bo238b2o199bo$597bo$596b2o9$16b2o22b2o36b2o16b2o98b
o38bo2bo16b2o2bo15b2o3b2o35bo20bo16b2ob2o38b2o39bo17bo38bo38b2o3b2o16b
o40b2o$b3o12bobo17b2o3bo35bobo17bo97bobo2b2o33b6o14bo2bobo14bo4bo35bob ob2o14b3o2b2o13bobo2bo36bo39bobo15bobo37b3o36bo2bo2bo13bobobo39bobo$o
3bo14bo16bo2bo36bo19bo99bobo2bo39bo14bobo2bo15bo3bo33bo2b2obo13bo5bo
13bo4b2o34b2o2bo34b2o2bo15bobobo39bo37b2obo14b2obo43bo$o19bo17b3o35bob 4o14b2o100b2o37b4o16bob2o15b5o35b2o18bo5bo13b2o37bo2b3o34bob2o16bobo2b o35b2o2bo37bob2o16bobo39b2o$4o13b4o56bo3bo15bo99bo40bo19bo60b2o16bo3b
2o15bo37bo40bo18bob3o34bo2b2o35b3o17b2o2b2o38bo$o3bo12bo18b3o39bo17bo 3b2o96b2o36bo19bobo19bo41bo17bobo14bobo39b2o38bo19bo38b2o37bo19bo43bo$
o3bo13bo16bo2bo36b3o18bobo2bo97bo36b2o18b2o19bobo38bo20b2o14b2o41bo36b
2o21bo38bo58bo40b2o$b3o12bobo17b2o37bo19b2ob2o98bo79bo39b2o77bo37bo21b 2o36bo59b2o40bo$15bobo180b2o197b2o37bo58b2o101bo$16bo418b2o158b3o$595b
o10$16b2o2b2o18b2o14b2o20bo17b2o22b2o37bo16b2o2b2o53bo59b2o44bo34bo62b o20b2o17bo16b2o37b2o21b2o$5o11bobo2bo14b2o3bo15bo19bobo17bo19b2o2bo36b
obo14bo2bo2bo53b3o2b2o53bo40b2o2bobo32bobo60bobo15bo2bobo16bobo15bo38b
o2bob2o13bo2bobo$4bo13b2o16bo2bo17bob2o15bo2bo16bo21bobo36bo2bo15bob3o 57bo2bo54bo38bo2bo2bo33bo2bo2b2o52bo2bobo14bobo2bo17bo2bo15bo39b2obo 14b3o2bo$3bo13bo20b3o15b2o2bo15bob2obo14b2o20bob2o34bo3bob2o13bo59b2ob
o56bo38bo2b2o35b2obo2bo52b3obo15bo2b2o16b2o2b2o14b2o40bo2bo16b2o$3bo 13bo40bo18bo2b2o15bo18b2o38b2o3bobo14bo59bob2o54b2o39b2o38bob2o57bo17b 2o17bo19bo39b3o2b2o13b2o$2bo12b2o19b3o17b2o20bo17bo18bo41bo17b3o58bo
58bo2b2o38bo36bo59b2o20bo17bo19bob3o35bo19bo$2bo12bo19bo2bo16bo19b3o 18bobob2o14bobo36bo19bo60b2o57bobo2bo36bo37b2o58bo19bo20b2o18bobobo56b o$2bo14bo17b2o19bobo16bo19b2ob2obo15b2o36b2o139bo2bo37b2o97bo18b2o20bo
22bo55b2o$16b2o39b2o238b2o136b2o39bo23b2o$476b2o11$16b2o2b2o35b2obo17b 2o96b2o2b2o53bo3b2o14b2o18b2o40b2o22b2o16b2o38bo38b2o39bo16b2o18b2o17b 2o2b2o$b3o12bobo2bo34bo2b2o16bo2bo94bo2bo2bo53b3o2bo14bo2b2o15bo3b2o
35bobo17bo3bobo12b2o3bo36b3o38bo39bobo15bo18bo2bobo14bo2bo2bo$o3bo13b 2o37bo18bobo2bo94bob2o58b2o16bobo2bo15bo2bo34bo19bobo2bo14bo2bo37bo3b 2o33bo3b3o36bo2bo15bo18bob2obo15b2obo$o3bo12bo38b2ob2o15bo2b2o96bo59bo
19bo2b2o14b2obo36b2o18bo2b2o16b3o35bob2o2bo33b4o2bo34b2o2b2o14b2o19bo
3bo16bob2o$b3o13bo40bobo16b2o99b2o57bo20b2o18bo39bo18b2o57bo2b2o37bo 36bo19bo19bobo3b2o12b3o$o3bo10b2o38bobo20bo100bo55b2o22bo16b2o40bo19bo
16b3o40bo38bo37bo19bo4b2o13b2o18bo$o3bo10bo39b2o18b3o100bo56bo22bo17bo 40b2obo16bo17bo2bo38b2o37bo39b2o18b2o2bo$b3o12bo58bo102b2o57bo20b2o17b
o41bobo15b2o18b2o77b2o39bo20bobo$15b2o219b2o38b2o41bobo153bo22b2o$320b
o154b2o11$16b2o38b2o39b2ob2o34b2obo15b2o19bo4b2o13bo18b2obo16bo3b2o14b 2o60bo21b2o18b2o55b2o18b2o58b2o17b2o40b2o20b2o$b3o12bobob2o34bo2b2o37b
obo35bob2o16bo18bobo4bo12bobo2b2o13bob4o14b3o2bo14bo2b2o56bobo17bo2bo
15b2o3bo54bo2bo18bo58bo18bo2bobo34bo2bo19bo2bo$o3bo13b2obo35bobo2bo34b o3bo54bob2o16bo3bo15bobo2bo19bo16b2o16bobobo54bo2b3o14bobobo15bo2bo57b ob3o14bo61bo18bob2obo33b3o20bobo$o3bo12bo38b2o3b2o35b2obo35b5o15bobo
17b5o16b3o18bo2bo14bo19bo3bo54b2o3bo14bo2b2o16b3o55b2o4bo13b2o59b2o19b
o3bo36b3o16b2o2b3o$b4o12bo40bo37bobobo35bobo2bo18b2o35bo20bob2o15bo20b 3o57bob2o15b2o77bo3b2o15bo57bo19bobo3b2o32b2o3bo17bo4bo$4bo10b2o38bobo
37bobo38bo25bo16bo18bo19bo16b2o19bobo56bobo20bo16b3o57bo21bo58bobo16b
2o38bo19b3o$o3bo10bo39b2o39bo38b2o25b3o13bobo14b3o19b2o16bo20b2o57b2o 18b3o17bo2bo56b2o21b2o55b2ob3o55bo18bo$b3o13bo147bo13bo15bo40bo98bo20b
2o82bo60bo53b2o$16b2o146b2o69b2o201b2o60b2o$438bo$439bo$438b2o!
Princess of Science, Parcly Taxel

Goldtiger997
Posts: 547
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 17 in 17: Efficient 17-bit synthesis project

#277 in 16G:

Code: Select all

x = 159, y = 63, rule = B3/S23
55bo$53b2o$54b2o12$139bo$140bo5bo3bobo$138b3o6bo3b2o3bo$145b3o3bo4bobo
$156b2o6$146b2o$86b2o49b2o7bo$86bo49bobo8bo$87bo50bo7b2o$86b2o55b2o$83b2o57bo2b3o$o19bo61bo2b3o54bobo2bo$b2o15bobo61bobo2bo55b2o$2o17b2o
62b2o$8bo$6bobo$7b2o2$20bobo$21b2o$21bo3$71b3o$16b3o$18bo48b3o$17bo51b
o$20b2o46bo$21b2o$20bo4$45b3o$45bo$46bo3$2b3o$4bo$3bo$6b2o$5bobo$7bo!
#289 in 13G, with a satisfying cleanup:

Code: Select all

x = 145, y = 42, rule = B3/S23
o14bo$b2o13bo$2o12b3o8$36bo$37b2o$36b2o4$131bo$59bo72b2o$57b2o72b2o6b
2o$58b2o78bo2bo$39bo2bobo92bobobo$37bobo2b2o94bo2b2o$38b2o3bo97bo$142b 3o$132bo11bo$130bobo$131b2o2b2o$136b2o$135bo2$132b2o$133b2o$132bo2$10b
3o$12bo$11bo43bo$54b2o$54bobo$70b2o$70bobo$70bo! calcyman Posts: 2096 Joined: June 1st, 2009, 4:32 pm ### Re: 17 in 17: Efficient 17-bit synthesis project All of these new syntheses have helped construct some larger still-lifes as well. The following merge request contains new recipes from old: https://gitlab.com/parclytaxel/Shinjuku ... equests/36 What do you do with ill crystallographers? Take them to the mono-clinic! Sokwe Moderator Posts: 1480 Joined: July 9th, 2009, 2:44 pm ### Re: 17 in 17: Efficient 17-bit synthesis project #152 in 13: Code: Select all x = 160, y = 18, rule = B3/S23 48bobo$6bo42b2o50bo49bo$5bo43bo50bobo39bo7bobo$bo3b3o93bo38bobo8bo$b2o 50b2o47b3o36b2o9b3o$obo50bobo49bo49bo$48b2o4bo49bo49bo$49b2o7bo39bo5b
2o37b3o3b2o3b2o$48bo7b2o41b2o44bo2bo2bo$57b2o39b2o44bo3bo2bo$149b2o$
153b2o$152bobo$57b3o37b3o54bo$59bo39bo$58bo39bo48b3o8b2o$149bo7b2o$
148bo10bo!
This was derived trivially from the synthesis displayed in Catagolue. I simply started with an integral with tub and hook instead of a hook with tail. I suppose that the last step is not included among the automatic construction components.

Edit: #81 in 16:

Code: Select all

x = 267, y = 22, rule = B3/S23
20bo$19bo$13bo5b3o$13bobo$13b2o49bo49bo49bo49bo49bo$63bobo47bobo47bobo 47bobo47bobo$62bobo4bo42bobo47bobo47bobo47bobo$11b2o49bo6bo42bo49bo49b o49bo$4bo6bobo47b2obo4bo41b2obo46b2obo46b2obo46b2obo$5b2o4bo45b2obo2bo bo7b2o32b2obo2bobo44bo2bobo44bo2bobo44bo2bobo$4b2o51b2ob2o2bo7b2o33b2o
b2o2bo45b2o2bo9bo35b2o3bo44b2o3bo$74bo99bobo37bo50b2o$103b2o61bo7b2o
38b2o$104b2o60b2o87b3o$103bo61bobo3b2o84bo$171bobo45b2o35bo3b2o$171bo
37b3o6b2o40bobo$6bo204bo8bo39bo$6b2o202bo4b2o$bo3bobo206bobo$b2o213bo$obo! Edit 2: #77 in 14 based on the same idea as #152 above: Code: Select all x = 113, y = 27, rule = B3/S23 8bo$6b2o$7b2o2$10bo$2bo7bobo$obo7b2o$b2o3$54b2o48b2o$10bo44bo39bo9bo$
9bo44bo38bobo8bo$4bo4b3o43b3o36b2o9b3o$2b2o54bo49bo$3b2o52bo49bo$51bo
5b2o37b3o3b2o3b2o$52b2o44bo2bo2bo$b2o48b2o44bo3bo2bo$2o100b2o$2bo103b
2o$12bo92bobo$11b2o37b3o54bo$11bobo38bo$51bo48b3o8b2o$102bo7b2o$101bo
10bo!
Edit 3: #15 in 11 by improving the previously-solved #22:

Code: Select all

x = 147, y = 67, rule = B3/S23
20bobo$20b2o$21bo8$22bobo$22b2o$23bo13$bo67bo69bo$o68b3o67b3o$3o17bo
44bo6bo69bo$9bo9bo44bobo4bo69bo$9bobo7b3o42bobo5b3o59bo7b3o$9b2o54bo4b obo2bo56bobo5bobo2bo$3b2o65b2o2bobo56b2o5b2o2bobo$3bobo69bo69bo$3bo61b
2o$65bobo$65bo69b3o$137bo$15b3o118bo$15bo$16bo25$31b2o$30b2o$32bo! -Matthias Merzenich Goldtiger997 Posts: 547 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: 17 in 17: Efficient 17-bit synthesis project #235 in 13G: Code: Select all x = 96, y = 36, rule = B3/S23 4bo$5bo44bo$3b3o45bo$40bo8b3o$14bo26bo17bo$15bo23b3o17bobo$13b3o43b2o 2$85bo$14b3o66bobo$16bo67b2o$15bo35b2o34bo$50bobo33bobob2o$50bo36b2obo$51bo2b2o35bo2b2o$52bo2bo36bo2bo$51b2obo36b2obo$51bo2b2o35bo2b2o$53bo
39bo$52b2o38b2o$b2o$obo$2bo6$3o3b3o$2bo5bo21b2o$bo5bo21b2o$31bo$3b2o$
4b2o20bo$3bo21b2o$25bobo!
This is a close-relative of 16.712, which was probably the most difficult xs16 during the 16 in 16 project.

Kazyan
Posts: 867
Joined: February 6th, 2014, 11:02 pm

### Re: 17 in 17: Efficient 17-bit synthesis project

#270 in 13G:

Code: Select all

x = 213, y = 35, rule = B3/S23
obo$b2o$bo2$130bo$125bo3bo35b2o$126b2ob3o32bo2bo$81bo43b2o33bo3bo2bo$81bobo77b2o2b2o$81b2o77b2o$77bo$78b2o129bo$77b2o125bo4bobo$203bobo3b2o
$204bo$87b2o32bo5b2o32bo5b2o32bo5b2o$74b2o5b2o2bo2bo31bobo2bo2bo31bobo 2bo2bo31bobo2bo2bo$73bobo5bo3b2o34bo3b2o34bo3b2o34bo3b2o3b2o$24bo50bo 6b3o37b3o37b3o37b3o5bobo$24bobo57bo39bo39bo39bo5bo$24b2o3$24b2o$23b2o$
25bo6$3b2o$2bobo35b2o$4bo35bobo$40bo!
I suspect that the base 12-bit still life can be done in 7G.
Tanner Jacobi

Sokwe
Moderator
Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: 17 in 17: Efficient 17-bit synthesis project

#174 in 15:

Code: Select all

x = 193, y = 31, rule = B3/S23
52bo$53b2o$52b2o35bo$89bobo$89b2o4$9bo$7b2o$8b2o58bobo69bo8bo$69b2o67b
2o8bo$69bo69b2o7b3o$2bo58b2o$obo49b2o7b2o$b2o3bo44bobo16b2o57bo59bo$5b o47bo15b2o56b3o57b3o$5b3o63bo54bo13bo45bo$127bo10b2o47bo$126b2o11b2o
45b2o$127bob2o56bob2obo$55b2ob2o65bobob2o54bobobob2o$55b2ob2o65b2o8bo 49b2o$135b2o5bo$134bobo4b2o$141bobo43b2o$186b2o$188bo$182b3o$184bo$183bo! This uses an alternate block-to-snake that is less obtrusive than the standard method. The following three block-to-snake converters should probably be added to Catagolue/Shinjuku's automatic synthesis components: Code: Select all x = 151, y = 22, rule = B3/S23 134bobo$135b2o$135bo5$7bo70bo69bo$7bobo68bobo67bobo$bo5b2o63bo5b2o55bo
6bo5b2o$2bo70bo62bo6bo$3o68b3o60b3o4b3o3$6b2o69b2o68b2o$6bobo68bobo67b
obo$6bo70bo69bo3$13b2o50b2o$4b2o7bobo48bobo7b2o68b2o$4b2o7bo52bo7b2o
68b2o!
Extrementhusiast wrote:Ship-to-carrier transition in one less
This gives #21 in 16:

Code: Select all

x = 174, y = 25, rule = B3/S23
68bo$66b2o$55bobo9b2o102bo$55b2o114bobo$56bo114b2o$42bo$43bo20bo$41b3o 20bobo103b2o$64b2o103b2o$171bo$obo114bo49bo$b2o50bo58b2o2bobo43b2o2bob o$bo3b3o44bobo50bobo4bobo2bo44bobo2bo$5bo47b2o51b2o7b2o48b2o$6bo99bo6b
2o48b2o$112bobo46bo2bo$112b2o47b2o$64bo$63b2o39b2o4bo$63bobo3b2o34b2o 2b2o$48b3o18bobo32bo4bobo$50bo18bo44b2o$49bo3b2o58b2o$53bobo59bo$53bo!
Sokwe wrote:#15 in 11 by improving the previously-solved #22
This gives #99 in 16:

Code: Select all

x = 200, y = 46, rule = B3/S23
65bo$63b2o$64b2o7$10bobo$11b2o$obo8bo17bo$b2o27bo$bo26b3o2$37bo$36bo$
36b3o4$194bo3bo$30bo164bobo$28bobo162b3ob3o$29b2o2$102bo44bo48bo$101bo
bo42bobo46bobo$31bo68bobo42bobo46bobo$31bobo66bo44bo11bobo34bo$27bo3b 2o65bob2o41bob2o10b2o33bob2o$28bo68bobo2bo39bobo2bo10bo32bobo2bo$26b3o 68bo3b2o39bo3b2o43bo3bobo$96b2o43b2o47b2o4bo3$99b2o3bo$98bo2bo2bobo41b
o4b2o$99b2o3b2o42b2o3bobo$147bobo3bo3$138b2o$137bobo7b2o$139bo8b2o$
147bo!
-Matthias Merzenich

Kazyan
Posts: 867
Joined: February 6th, 2014, 11:02 pm

### Re: 17 in 17: Efficient 17-bit synthesis project

#233 in 16G:

Code: Select all

x = 140, y = 29, rule = B3/S23
119bobo$106bo12b2o$107bo12bo3bo$105b3o15bo$123b3o$72bo$70bobo$71b2o$
74bo59bo$74bobo55b2o$74b2o57b2o2$13bo59bo$3bobo6bo59b2o$4b2o6b3o57bobo 62bo$4bo34bobo27bo49b2obo14bobo$39b2o27bobo47bo2b2o14b2o$40bo27b2o48b
2o$13b2o119b3o$12b2o24b2o28b2o48b2o14bo$3o11bo23bo3b2o24bo3b2o44bo3b2o 11bo$2bo36bo2bo26bo2bo46bo2bo$bo38bobo27bobo47bobo$41bo29bo49bo3$16b2o 120b2o$15b2o120b2o$17bo121bo! An idea for #263: Code: Select all x = 13, y = 14, rule = LifeHistory 5.A$5A$.4A2$8.A2.2A$4.2A.A.A2.A$4.2A.A.2A$8.A$9.A.A$10.2A$4.4A$8.A$3.
A6.A$10.A! EDIT: This can almost definitely become a 12G solution for #223: Code: Select all x = 47, y = 19, rule = B3/S23 41bo$41bobo$bo39b2o$o$4o$b2o31bo$33bobo$2b2o26b2o2bobo$bo2bo24bo2b2o2b o4bobo$2b2o25bobo2b2o5b2o$30bobo9bo$3b2o26bo$2b4o38bo$5bo38bobo$4bo39b 2o2$43bo$42b2o$42bobo!
Last edited by Kazyan on July 1st, 2019, 2:51 pm, edited 1 time in total.
Tanner Jacobi

A for awesome
Posts: 1902
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: 17 in 17: Efficient 17-bit synthesis project

Kazyan wrote:An idea for #263:

Code: Select all

x = 13, y = 14, rule = LifeHistory
5.A$5A$.4A2$8.A2.2A$4.2A.A.A2.A$4.2A.A.2A$8.A$9.A.A$10.2A$4.4A$8.A$3. A6.A$10.A!
Modifying the synthesis for xs17_o4s3qp3z01 by sparking a different 3G century might yield a cheap xs19_3lmgdbz1221, which can be turned into #263 in 7G:

Code: Select all

x = 28, y = 24, rule = B3/S23
19bo$18bo$18b3o$bo$2bo20bo$3o19bo$22b3o10$5b2o$5bobo$5bo3$3b3o4b2o14b
2o$5bo4bobo12b2o$4bo5bo16bo!

Code: Select all

x = 12, y = 15, rule = B3/S23
7b2o$6bo2bo$7b3o$o9b2o$b2o4b2obo$2o4bobo2bo$6b2o2b2o2$2bobo$3b2o$3bo5b o$8b2o$3b2o3bobo$4b2o$3bo! Code: Select all x = 14, y = 15, rule = B3/S23 8bo$7bo$7b3o$5bo$3bobo$4b2o2$9b2o$8bo2bo$9b3o$12b2o$bo7b2obo$b2o7bo2b
o$obo5bo3b2o$8b2o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

Sokwe
Moderator
Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: 17 in 17: Efficient 17-bit synthesis project

A for awesome wrote:xs19_3lmgdbz1221, which can be turned into #263 in 7G
5G, actually. The last step can be done with just one glider:

Code: Select all

x = 12, y = 8, rule = B3/S23
7b2o$6bo2bo$3o4b3o$2bo7b2o$bo5b2obo$8bo2bo$6bo3b2o$6b2o! -Matthias Merzenich Kazyan Posts: 867 Joined: February 6th, 2014, 11:02 pm ### Re: 17 in 17: Efficient 17-bit synthesis project With those observations and some help from popseq, #263 in 15G: Code: Select all x = 125, y = 45, rule = B3/S23 obo$b2o$bo11$21bo$20bobo$20bobo$6bo14bo$7b2o$6b2o5$23b2o$22b2o$7bo16bo
$5bobo72b2o38b2o$6b2o6b2o63bo2bo36bo2bo$15b2o63b3o30b3o4b3o$14bo58bo9b
2o30bo7b2o$74b2o4b2obo30bo5b2obo$9b2o62b2o4bobo2bo36bo2bo$10b2o67b2o2b 2o34bo3b2o$9bo109b2o$75bobo$76b2o$76bo5bo$81b2o$76b2o3bobo$4b3o70b2o$6bo69bo$5bo$45bo$44b2o$44bobo! Tanner Jacobi Extrementhusiast Posts: 1797 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: 17 in 17: Efficient 17-bit synthesis project #223 in twelve gliders, but only because of an improvement in the final step: Code: Select all x = 146, y = 37, rule = B3/S23 48bo$49bo$47b3o95bo$143bobo$144b2o$135bo$136bo6bo$85bo48b3o5b2o$86bo 55bobo$84b3o51b2o$4bo132bo2bo$5bo69bo9bo50bobobo$3b3o68bobo8b2o50bobo$
74bobo7bobo52bobo$3o72bo62bobobo$2bo135bo2bo$bo137b2o12$81b3o$81bo$82b
o2$77b2o$77bobo$42b2o33bo23b2o$41bobo56b2o$43bo58bo!  I'm not sure that an eight-glider synthesis for the related 18-bitter exists using the current method and predecessor. I Like My Heisenburps! (and others) Freywa Posts: 589 Joined: June 23rd, 2011, 3:20 am Location: Singapore Contact: ### Re: 17 in 17: Efficient 17-bit synthesis project #80 is reduced to 12 by improving its predecessor: Code: Select all x = 126, y = 36, rule = B3/S23 obo$b2o$bo14$61bo51bo10bo$60bobo49bobo7b2o$11bo47bo2b3o46bo2b3o6b2o$12b2o45bobo3bo45bobo3bo$11b2o9bo37b2o2bobo45b2o2bobo$21bo43bo51bo$21b
3o2$123bo$123bobo$119b2o2b2o$118b2o$12bo107bo$13b2o$12b2o46b2o60b2o$
60b2o59b2o$11bo9bo101bo$10b2o8bobo34b3o$10bobo7bobo36bo$21bo36bo!
Edit: Another such improvement clears #155:

Code: Select all

x = 119, y = 34, rule = B3/S23
88bo11bo$89bo8bobo$87b3o9b2o9$bo$obo$b2o7bo$9bo$9b3o88bo$99bobo$8b2o 90b2o6bo$7bobo97bobo$9bo82b2o12bo2bo$91bobo13b2o$93bo10$116b3o$116bo$
117bo!
Edit 2: Improves #231 to 14:

Code: Select all

x = 64, y = 29, rule = B3/S23
14bo$8bobob2o47bo$9b2o2b2o45bobo$9bo50bo2bo$58b2obobo$21bobo34bo2b2o$
15bo5b2o37bo$16b2o4bo36b2o$15b2o38b3o$20b2o29b3o$21b2o30bo$20bo31bo5$b
2o$obo$2bo8$12b3o$14bo$13bo! Princess of Science, Parcly Taxel Freywa Posts: 589 Joined: June 23rd, 2011, 3:20 am Location: Singapore Contact: ### Re: 17 in 17: Efficient 17-bit synthesis project With the latest syntheses, 150 expensive xs17s remain: Code: Select all #CLL state-numbering golly x = 603, y = 217, rule = B3/S23 218bo198b3o$217b2o197bo3bo$218bo201bo$218bo200bo$218bo199bo$218bo
198bo$217b3o196b5o4$17b3o17bo19b3o17b3o19bo16b5o16b3o16b5o16b3o17b
3o17b3o17bo19b3o17b3o19bo16b5o16b3o16b5o16b3o17b3o17b3o17bo19b3o
17b3o19bo16b5o16b3o16b5o16b3o17b3o$16bo3bo15b2o18bo3bo15bo3bo17b2o 16bo19bo3bo19bo15bo3bo15bo3bo15bo3bo15b2o18bo3bo15bo3bo17b2o16bo 19bo3bo19bo15bo3bo15bo3bo15bo3bo15b2o18bo3bo15bo3bo17b2o16bo19bo3b o19bo15bo3bo15bo3bo$16bo3bo16bo22bo19bo16bobo16bo19bo22bo16bo3bo
15bo3bo15bo3bo16bo22bo19bo16bobo16bo19bo22bo16bo3bo15bo3bo15bo3bo
16bo22bo19bo16bobo16bo19bo22bo16bo3bo15bo3bo$16bobobo16bo21bo18b2o 16bo2bo17b3o16b4o19bo17b3o17b4o15bobobo16bo21bo18b2o16bo2bo17b3o 16b4o19bo17b3o17b4o15bobobo16bo21bo18b2o16bo2bo17b3o16b4o19bo17b3o 17b4o$16bo3bo16bo20bo21bo15b5o19bo15bo3bo17bo17bo3bo19bo15bo3bo16b
o20bo21bo15b5o19bo15bo3bo17bo17bo3bo19bo15bo3bo16bo20bo21bo15b5o
19bo15bo3bo17bo17bo3bo19bo$16bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3b o17bo17bo3bo15bo3bo15bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3bo17bo17b o3bo15bo3bo15bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3bo17bo17bo3bo15bo 3bo$17b3o16b3o17b5o16b3o19bo17b3o17b3o18bo18b3o17b3o17b3o16b3o17b
5o16b3o19bo17b3o17b3o18bo18b3o17b3o17b3o16b3o17b5o16b3o19bo17b3o
17b3o18bo18b3o17b3o9$36b2o38b2o58b2o18b2obo36bo58bo3b2o34b2o2b2o 14b2obob2o35b2o40bo18bo17b2o2b2o35b2o56b2o39bo$b3o32bobob2o34bo60b
o18bob2o35bobo2b2o53b3o2bo34bo3bobo13bob2obo2bo32bo2bo35b2obobo16b
obo15bo2bo2bo34bobo56bobo37bobo2b2o$o3bo33b2obo35bo59bob2o19b2o34b o2bo2bo55b2o37bobobo17bo2b2o31bobo2bo34bob2o2bo14bobobo15bobobo34b obo60bo36bo2bo2bo$o3bo32bo38b2o2bo57bobo16b2o2bo35b3obo55bo38b2o2b
o15b3o37bob3o38b2o14bo2bobo14b2o2bo35bo2b3o55b2o38bob2o$obobo32bo 40b3o55bobo17bob2o40bo56bo39bo18bo40bo38b2o18b2obo16bo39b2o2bo54bo 39b2o$o3bo30b2o39b2o57bobobo16bo42bo58b2o36bo61bo37bo20bo17bo41bo
57bob3o36bo$o3bo30bo39bo2bo56bo2bo16b2o41bo60bo36b2o57b3o39bo17bob o17b2o38bo60bobo36bo$b3o32bo39bobo57b2o60b2o58bo96bo40b2o17b2o58b
2o63bo34b2o$35b2o40bo180b2o279b2o12$36b2ob2o37b2o38b2o41b2o33bo98b
2o2b2o14b2obo38b2o18b2o21b2o55b2o76b2o21bo17bo24b2o$bo34bob2o39bo 39bo2b2o33b2o2bo33bobo4b2o91bo3bobo13bob2o37bo2bo15bo2bo16b2o2bobo 54bo2bo75bobo18b3o16bobo20bobobo$2o39bo34b3o40bobobo32bo2bobo34bo
2bo2bo94bobobo17b2o34bobobo15b2obob2o13bobo2bo54bo2bobo77bo16bo19b
o2bob2o15bob2o$bo35b2ob2o34bo2b3o35bobo2bo34bob2o36b2obobo93b2o2bo 15b2obo2bo33bo2b2o16bobobo16b2o55b2obo2bo74b2o18bo19bob2obo15bo3bo$bo35bo40bo2bo34bob2o36b2o41bobo95bo18bobo2b2o34b2o18bo18b2o59bob
2o74bo19b2o18b2o21bob2o$bo33bobo38bobo37bo40bo41bo95bo21bo40bo19bo 18bo59bo77bo19bo4bo15bo18b3o$bo33b2o38bobo37b2o38bo42b2o95b2o58b3o
21bo16bo59b2o78b2o2b2o14bo2bobo13bo19bo$3o73bo78b2o198bo22b2o16b2o 140bo2bo15bo2bo14b2o$538b2o18b2o12$38b2o40b2o59b2o14bo77b2o3b2o13b 2o2b2o14b2o18b2o2b2o56b2o18b2ob2o18b2o16b2o78b2o19bo15b2o23b2o$b3o
33bobo41bo54b2o2bobo13bobo2b2o72bo2bo2bo13bo2bo2bo13bo2bobo14bo3bo
56bo2bo15bo2bobo14b2o2bobo15bo2bo76bo2bo17bobo14bobo18b2o2bo$o3bo 31bo39bo2bo57bo2bo15bo2bo2bo74b2obo15bobob2o14b2ob2o16bobobo53bobo 2bo14b2obo2bo13bo3bo16bo2bobo76bo2bo15bobobo16bo16bo2bobo$4bo32b2o
37b5o56bob2o16bob2o77bob2o15bobo17bo18b2o2b2o54bo4bo15bob2o16bob2o
14bo4bo75bob2obo15bobobo14b2o18bob2o$3bo35bo96b2o18b2o79bo21bo17bo 19bo59b4o16bo18b2o18b4o75bobo2bo14b2o3bo14bo19b2o$2bo32b4o39bo58bo
19bo78bo21bo19b2o15bo62bo17b2o19bo19bo77bo2bo16bo19bo20bo$bo33bo 40b3o56bo19bo80b2o20b2o19bo15b2o59bo38bo19bo80b2o18bo19b2o17bo$5o
31bo38bo59b2o18b2o121bo77b2o37b2o18b2o100bo20bob2o13b2o$37bo37b2o 201b2o236b2o20b2obo$36b2o11$17bo21b2o95b2o19bo17b2ob2o55b2o18b2o3b o14b2o2bo120bo157bo41bo$b3o12bobo2b2o14bo2bo95bo19bobo17bobo56bo2b
ob2o13bo3bobo13bo2bobo114b2o2bobo153bobobo39bobo$o3bo12bobo2bo13bo b2o97bo18bo2bob2o13bo2b3o55b2obo15bo2bo2bo13b2obo115bo3bobo153b2ob obo38bo2bo$4bo14b2o16bo2b3o95bo18bob2obo14b2o2bo56bo2bo15bob3o15bo
119bob2o157bobo36b2obobo$2b2o14bo19bo3bo93bobo17b2o20bo58bo2b2o16b o18bo118b2o157b2o2bo37bo2b2o$4bo11b3o16b3o97bobob2o16bo18bo59bo22b
o15b2o120bo157bo42bo$o3bo10bo19bo99bobo2bo14bo20b2o58b2o20b2o15bo 119bo161bo37b3o$b3o11b2o119bobo16b2o119bo118b2o159b2o37bo$137bo 137b2o12$60bo16b2o57b2o22b2o73b2o2b2o14b2o3b2o33b2obob2o13b2o21b2o
78b2o15b2o2b2o78bo38bo$3bo54b3o17bo57bo19b2o3bo73bo2bo2bo13bo2bo2b o33bob3obo13bobo18b3obo77bo16bo3bo78bobo34bobobo$2b2o53bo18bo2b2o
57bo17bo2bo77b2obo15bob3o56b3o15bo5bo74b2o2bo15bo3bo76bobo35b2obob
o$bobo52bo2b2o15b2obo2bo54b2o18bob2o77bob2o15bo41b2o15bo3bo15bo5bo 72bo2b3o14b2o2b2o76bobobo36bobo$o2bo53b2obo17bo2b2o53bo19b2o2bo76b
o20bo37bobobo15b3obo16bo3b2o73b2o18bobo76b2o3b2o33b2o2bo$5o53bo16b obo57bo2b3o14bo2bo77bo18b3o38b2o21bo18bobo77bo17bobo76bo39bo$3bo
52bobo16b2o59b2obo16b2o78b2o17bo62bo20b2o74bobo19bo78bo39bo$3bo51b obo83bo176b2o95b2o100bo37b2o$56bo83b2o374b2o12$16b2o40bo77b2o21bo 36bo38b2o3b2o33b2o18bo3b2o37bob2o55bo137b2o21bo42bo$5o11bo3b2o35bo
bobo74bo21bobo34bobo2b2o33bo2bo2bo33bo19b3o2bo35b3obo55bobo136bo
19bobobo39b3o$o17bo2bo35bob2obo75bo19bo2bo34bobo2bo35b2obo36bob2o 17b2o35bo5bo54bo2bo137bo17b2obo39bo$o16b2obo35b2o4bo74b2o17b2o2b2o
36b2o39bo36b3o2bo15bo2b3o33bo5bo52b2ob2o136b2o20bobo38bo$b3o14bob 2o35bo4b2o72bo19bo40bo39b2o41bo15bobo3bo34bob3o55bo137bo19b2o2b2o 37b2o$4bo10b3o37bo79bo2b3o16bo40b2o37bo40b2o17bo40b2o57bo137bo4b2o
13bo41bo$o3bo10bo39b2o79b2o2bo17bo40bo38bo39bo116b2o139b2o2bo16bo 39bo$b3o134bo17bobo38bo39b2o40bo115bo142bobo15b2o37b2o$138b2o15bob o39b2o79b2o116bo141b2o55bo$156bo238b2o199bo$597bo$596b2o9$16b2o22b 2o36b2o16b2o98bo38bo2bo16b2o2bo15b2o3b2o35bo20bo16b2ob2o38b2o39bo 17bo38bo38b2o3b2o16bo40b2o$b3o12bobo17b2o3bo35bobo17bo97bobo2b2o
33b6o14bo2bobo14bo4bo35bobob2o14b3o2b2o13bobo2bo36bo39bobo15bobo
37b3o36bo2bo2bo13bobobo39bobo$o3bo14bo16bo2bo36bo19bo99bobo2bo39bo 14bobo2bo15bo3bo33bo2b2obo13bo5bo13bo4b2o34b2o2bo34b2o2bo15bobobo 39bo37b2obo14b2obo43bo$o19bo17b3o35bob4o14b2o100b2o37b4o16bob2o15b
5o35b2o18bo5bo13b2o37bo2b3o34bob2o16bobo2bo35b2o2bo37bob2o16bobo
39b2o$4o13b4o56bo3bo15bo99bo40bo19bo60b2o16bo3b2o15bo37bo40bo18bob 3o34bo2b2o35b3o17b2o2b2o38bo$o3bo12bo18b3o39bo17bo3b2o96b2o36bo19b
obo19bo41bo17bobo14bobo39b2o38bo19bo38b2o37bo19bo43bo$o3bo13bo16bo 2bo36b3o18bobo2bo97bo36b2o18b2o19bobo38bo20b2o14b2o41bo36b2o21bo 38bo58bo40b2o$b3o12bobo17b2o37bo19b2ob2o98bo79bo39b2o77bo37bo21b2o
36bo59b2o40bo$15bobo180b2o197b2o37bo58b2o101bo$16bo418b2o158b3o$595bo10$16b2o2b2o18b2o14b2o20bo17b2o22b2o54b2o2b2o53bo59b2o44bo34b
o62bo20b2o17bo16b2o37b2o$5o11bobo2bo14b2o3bo15bo19bobo17bo19b2o2bo 53bo2bo2bo53b3o2b2o53bo40b2o2bobo32bobo60bobo15bo2bobo16bobo15bo 38bo2bob2o$4bo13b2o16bo2bo17bob2o15bo2bo16bo21bobo55bob3o57bo2bo
54bo38bo2bo2bo33bo2bo2b2o52bo2bobo14bobo2bo17bo2bo15bo39b2obo$3bo 13bo20b3o15b2o2bo15bob2obo14b2o20bob2o55bo59b2obo56bo38bo2b2o35b2o bo2bo52b3obo15bo2b2o16b2o2b2o14b2o40bo2bo$3bo13bo40bo18bo2b2o15bo
18b2o60bo59bob2o54b2o39b2o38bob2o57bo17b2o17bo19bo39b3o2b2o$2bo12b 2o19b3o17b2o20bo17bo18bo59b3o58bo58bo2b2o38bo36bo59b2o20bo17bo19bo b3o35bo$2bo12bo19bo2bo16bo19b3o18bobob2o14bobo56bo60b2o57bobo2bo
36bo37b2o58bo19bo20b2o18bobobo$2bo14bo17b2o19bobo16bo19b2ob2obo15b 2o177bo2bo37b2o97bo18b2o20bo22bo$16b2o39b2o238b2o136b2o39bo23b2o$476b2o11$16b2o2b2o35b2obo17b2o96b2o2b2o53bo3b2o14b2o18b2o40b2o22b
2o16b2o38bo38b2o39bo16b2o18b2o17b2o2b2o$b3o12bobo2bo34bo2b2o16bo2b o94bo2bo2bo53b3o2bo14bo2b2o15bo3b2o35bobo17bo3bobo12b2o3bo36b3o38b o39bobo15bo18bo2bobo14bo2bo2bo$o3bo13b2o37bo18bobo2bo94bob2o58b2o
16bobo2bo15bo2bo34bo19bobo2bo14bo2bo37bo3b2o33bo3b3o36bo2bo15bo18b
ob2obo15b2obo$o3bo12bo38b2ob2o15bo2b2o96bo59bo19bo2b2o14b2obo36b2o 18bo2b2o16b3o35bob2o2bo33b4o2bo34b2o2b2o14b2o19bo3bo16bob2o$b3o13b
o40bobo16b2o99b2o57bo20b2o18bo39bo18b2o57bo2b2o37bo36bo19bo19bobo
3b2o12b3o$o3bo10b2o38bobo20bo100bo55b2o22bo16b2o40bo19bo16b3o40bo 38bo37bo19bo4b2o13b2o18bo$o3bo10bo39b2o18b3o100bo56bo22bo17bo40b2o
bo16bo17bo2bo38b2o37bo39b2o18b2o2bo$b3o12bo58bo102b2o57bo20b2o17bo 41bobo15b2o18b2o77b2o39bo20bobo$15b2o219b2o38b2o41bobo153bo22b2o$320bo154b2o11$16b2o38b2o39b2ob2o34b2obo15b2o19bo4b2o32b2obo16bo3b
2o14b2o60bo21b2o18b2o55b2o18b2o58b2o17b2o40b2o$b3o12bobob2o34bo2b 2o37bobo35bob2o16bo18bobo4bo32bob4o14b3o2bo14bo2b2o56bobo17bo2bo 15b2o3bo54bo2bo18bo58bo18bo2bobo34bo2bo$o3bo13b2obo35bobo2bo34bo3b
o54bob2o16bo3bo40bo16b2o16bobobo54bo2b3o14bobobo15bo2bo57bob3o14bo
61bo18bob2obo33b3o$o3bo12bo38b2o3b2o35b2obo35b5o15bobo17b5o37bo2bo 14bo19bo3bo54b2o3bo14bo2b2o16b3o55b2o4bo13b2o59b2o19bo3bo36b3o$b4o
12bo40bo37bobobo35bobo2bo18b2o56bob2o15bo20b3o57bob2o15b2o77bo3b2o
15bo57bo19bobo3b2o32b2o3bo$4bo10b2o38bobo37bobo38bo25bo16bo38bo16b 2o19bobo56bobo20bo16b3o57bo21bo58bobo16b2o38bo$o3bo10bo39b2o39bo
38b2o25b3o13bobo36b2o16bo20b2o57b2o18b3o17bo2bo56b2o21b2o55b2ob3o
55bo$b3o13bo147bo13bo56bo98bo20b2o82bo60bo53b2o$16b2o146b2o69b2o
201b2o60b2o$438bo$439bo$438b2o! There are still two "walls" of expensive SLs blocking a Moore-connected path between left and right. Princess of Science, Parcly Taxel Goldtiger997 Posts: 547 Joined: June 21st, 2016, 8:00 am Location: 11.329903°N 142.199305°E ### Re: 17 in 17: Efficient 17-bit synthesis project #237 in 12G, using a component from Extrementhusiast's collection: Code: Select all x = 78, y = 22, rule = B3/S23 58bo$59bo$11bo45b3o4bo$9b2o54bo11bo$10b2o51b3o9b2o$76b2o$57bo$obo53bob
o$b2o52bo2bo4bo$bo54b2o5bobo$20b2o41b2o5b2o$21bo49bo$20bo49bo$20b2o37b
3o8b2o$22bo49bo$22bo49bo$20b2o48b2o$20bo49bo$21bo49bo$20b2o31b2o15b2o$52bobo$54bo!
Unfortunately a similar technique cannot be employed for the carrier version, because "carrier cis domino snake" costs 9G, so the total would be 17G. The following method will work if someone finds a sufficiently cheap version of this converter that does work when rewound:

Code: Select all

x = 13, y = 15, rule = B3/S23
9bobo$bobo5b2o$2b2o6bo$2bo$6b2o$6bo$7b3o$9bo$10b2o$5b2o5bo$bo2b2o6bo$b 2o3bo3b2o$obo7bo$12bo$11b2o!

dvgrn
Moderator
Posts: 5889
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: 17 in 17: Efficient 17-bit synthesis project

Goldtiger997 wrote:#237 in 12G, using a component from Extrementhusiast's collection...
That's pretty tricky (and lucky), getting the suppressing loaf at no extra cost.

Components like this have gotten me thinking that it might be time to extend the lookup table for synthesise-patt.py. Maybe four-glider collisions would be too ambitious, but what about single gliders, and/or maybe pairs of gliders, colliding in the vicinity of one or two small still lifes? That might produce a fair number of active patterns that 3G collisions can't reach, that would be good to have in synthesise-patt search results.

Along with that, it might be worth reworking the fingerprints of searchable patterns, to use hash value sequences instead of plain population sequences for recognition purposes. When I'm searching for specific sparks that die quickly, sometimes the current match method gives an awful lot of false positives... On the other hand, population mod 64 allows relatively reasonable-sized data files. File size is going to be a bigger problem anyway if constellation+glider collisions get added.

Kazyan
Posts: 867
Joined: February 6th, 2014, 11:02 pm

### Re: 17 in 17: Efficient 17-bit synthesis project

#276 in 12G, based on a step from the synthesis for xs17_mk2dioz56:

Code: Select all

x = 44, y = 51, rule = B3/S23
41bo$41bobo$30bobo8b2o$30b2o$31bo2$7bo28bobo$5bobo28b2o$6b2o29bo2$41bo
bo$2bo30bo7b2o$obo29bo9bo$b2o29b3o3$41bo$39b2o$o14bobo22b2o$b2o13b2o$
2o14bo23$33bo$32b2o$32bobo3$4b2o$3bobo$5bo!
Thus, #274 in 14G:

Code: Select all

x = 13, y = 10, rule = B3/S23
3bo$obobo$2obo$3bobo4bo$2o2b2o4bobo$o9b2o$bo$2o5b3o$7bo$8bo! Tanner Jacobi Freywa Posts: 589 Joined: June 23rd, 2011, 3:20 am Location: Singapore Contact: ### Re: 17 in 17: Efficient 17-bit synthesis project I think it might be – well, it is – high time to add syntheses for the remaining strict 18-bit still lifes that still have no synthesis on Shinjuku. There are less than 300 of them, and many of them have plenty of soups – so much that I can't add them all. You won't have to announce syntheses of these objects here. Princess of Science, Parcly Taxel dvgrn Moderator Posts: 5889 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Contact: ### Re: 17 in 17: Efficient 17-bit synthesis project Kazyan wrote:#276 in 12G, based on a step from the synthesis for xs17_mk2dioz56... Thus, #274 in 14G... #274 is one of the possible Moore-connected doorways through one of the north-south walls that Freywa mentioned a while back. #115 is now a gap in the other wall. Here's xs17_31km853zw56 in 13 gliders (submitted to Catagolue just now): Code: Select all x = 250, y = 75, rule = B3/S23 91bo$89bobo$90b2o7$49bo$48bo$48b3o$40bo$38bobo$39b2o3$149b2o$113bo35b 2o$4bo102bobo2bo122bo$5bo89b3o10b2o2b3o45bo72bobo$3b3o102bo28b3o12bo7b
obo71b2o$151bobo6b2o76b2o$152bo85b2o$242b2o$242bobo$46bo49bo148bo$46bo
49bo41bo104b2obob2o$46bo49bo41bo105bob2obo$b2o135bo103bo$obo239b2o$2bo
12$158b2o$158bobo$158bo5$164b3o$164bo$165bo14$191b3o$191bo$192bo4$202b
o$201b2o$201bobo!
Next up: east-west paths using von Neumann steps rather than Moore steps, maybe? Or just a completely blank row or column -- #109 (xs17_312jaik8zw23) would knock out a column, but it only has one soup.


text:
# multiplication operator on $L^{2}$

Let $(X,\mathcal{A},\mu)$ be a measure space and $f\colon X\to\mathbb{K}$ a measurable function. Then $M_{f}\colon\phi\mapsto f\phi$ is the multiplication operator with $f$ defined on the subspace $Dom(M_{f})=\{\phi\in L^{2}_{\mathbb{K}}(X,\mathcal{A},\mu)\colon f\phi\in L^{2% }_{\mathbb{K}}(X,\mathcal{A},\mu)\}$. It plays an important role in quantum mechanics where the multiplication with the coordinates on $\mathbb{R}^{n}$ is the position operator.

Title multiplication operator on $L^{2}$ MultiplicationOperatorOnL2 2013-03-22 15:42:28 2013-03-22 15:42:28 scineram (4030) scineram (4030) 8 scineram (4030) Definition msc 47B38 operator multiplication operator

format: plain


text:
# How do you find the vertical, horizontal or slant asymptotes for (x² - 3x - 7)/(x+3) ?

Nov 3, 2016

The vertical asymptote is $x = 3$
and the slant asymptote is $y = x - 6$

#### Explanation:

As we cannot divide by zero, so $x \ne - 3$
$\therefore x = - 3$ is a vertical asymptote

As the degree of the numerator is greater than the degree of the denominator, we would expect a slant asymptote. W e have to do a long division.
$\textcolor{w h i t e}{a a a a}$${x}^{2} - 3 x - 7$$\textcolor{w h i t e}{a a a a}$∣$x + 3$
$\textcolor{w h i t e}{a a a a}$${x}^{2} + 3 x$$\textcolor{w h i t e}{a a a a a a a a}$∣$x - 6$
$\textcolor{w h i t e}{a a a a a}$$0 - 6 x - 7$
$\textcolor{w h i t e}{a a a a a a a}$$- 6 x - 18$
$\textcolor{w h i t e}{a a a a a a a a a}$$0 + 11$

Finally we have, $\frac{{x}^{2} - 3 x - 7}{x - 3} = x - 6 + \frac{11}{x + 3}$
The slant asymptote is $y = x - 6$

graph{(y-((x^2-3x-7)/(x+3)))(y-x+6)=0 [-58.5, 58.5, -29.27, 29.28]}


text:
MathSciNet bibliographic data MR2684182 (2011g:46069) 46E40 (28B05 46G10) Meziani, L. On the dual space \$C\sp *\sb 0(S,X)\$$C\sp *\sb 0(S,X)$. Acta Math. Univ. Comenian. (N.S.) 78 (2009), no. 1, 153–160. Journal

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
## FreeBSD Part 2

So I tried FreeBSD in VirtualBox. Step 2 was to try and install it on my Thinkpad. Unfortunately, I am having boot issues. Perhaps it was too many operating systems. I deleted everything but Windows 10 and then reinstalled Fedora 29. I may try again on my Intel NUC that I am currently using PopOS with. In the mean time, the Raspberry Pi 3 is getting a go at it. The wifi does not work, so it is tethered to my router so I can install X11. I used the image from the FreeBSD website. When I get everything installed, we’ll see how the experience is.

## Playing with FreeBSD 12

So my use case is run FreeBSD in VirtualBox in Windows. The first experiment ended up in failure, but not because I was using Windows, rather because I can’t get the X server to behave. So I will need to attempt this again. I will say that my goal is to do 3D graphics and game development.

However, I did discover some neat things I can use this OS for. For instance, I am rediscovering WindowMaker. I thought it was cool that the PlayStation 2 Linux Kit used it as the default window manager. I used it often in the 1990’s. It still looks good. But, it doesn’t work out of the box for any kind of real work.

There are several packages I am trying: redshift, compton, and xdg-user-dirs, xscreensaver. Anyways, here is my current pkg install command list.

pkg install bash tmux htop vim emacs w3m wget curl nano
pkg install xorg slim windowmaker enlightenment wmakerconf
pkg install redshift compton xdg-user-dirs xscreensaver xeyes
pkg install firefox gimp
pkg install ...

I will note that I find it ironic that it takes 1 gigabyte to do the first line which are supposed to be command line utilities! By using emacs-nox and vim-console, it goes down to 279 MiB instead. These are the dockapps I installed for WindowMaker.

pkg install wmcpuload wmclock wmnetload wmsystemtray wmtop wmmemload
pkg install inconsolata-ttf

The Xdefaults file needs to be updated so that xterm doesn’t look too small. I use the following settings:

*xterm*foreground: #cfcfcf
*xterm*background: #000000
*xterm*font: xft:Inconsolata:size=16

## C++ Vector and Matrix Library

I am working on an open source Vector and Matrix Library for C++ and TypeScript. I am calling it FluxionsGTE and FluxionsWebGTE, respectively.

// TypeScript
class Vector3 {
constructor(public x: number = 0, public y: number = 0, public z: number = 0) { }
}
// C++
template <class T>
class TVector3
{
public:
T x, y, z;

TVector3(T x = T(0), T y = T(0), T z = T(0)) { }
};

using Vector3f = TVector3<float>;

## Conversion between specular exponent, specular roughness, and specular glossiness

Ever need to convert between specular exponent, roughness, and glossiness? for the Blinn-Phong BRDF, these three values represent the same concept. Specular Exponent is the actual value used to compute the BRDF. Let’s call that variable $e$. The roughness $m$ and glossiness $g$ values are numbers between 0 and 1 and they are additive inverses of each other. In other words

$$g = 1 – m \, ,$$

$$m = 1 – g \, .$$

The exponent is given by

$$e = \frac{2}{m^2} – 2$$

or

$$e = \frac{2}{{(1 – g)}^2} – 2 \, .$$

The BRDF $f_r(\omega_i, \omega_g)$ is

$$f_r(\omega_i, \omega_o) = \pi \frac{F(\omega_i \cdot \omega_h) D(\omega_i) G_2(\omega_i \cdot \omega_g, \omega_o \cdot \omega_g)}{4 (\omega_i \cdot \omega_g) (\omega_o \cdot \omega_g)}$$

where Blinn-Phong $D(\omega_i)$ is given by

$$D_{\mathrm{Blinn-Phong}}(\omega_i, \omega_h, e) = \frac{e+2}{2\pi} (\omega_i \cdot \omega_h)^e$$

and the resulting specular illumination is given by
$$\mathbf{L}_o = f_r(\omega_i, \omega_o) \mathbf{L}_i (\omega_i) \mathbf{V}_i (\omega_i) (\omega_g \cdot \omega_i) \, .$$

## Commodore VIC 20 NTSC and PAL colour/color palettes

I’m posting this mostly so I can look at the colors any time I want.

NTSC

PAL

## 1hgj 102: Eats Shoots & Leaves (to the left)

The theme to this past #OneHourGameJam was to make a game based to the object of the left. My main goal was to make a game where a player can fire a projectile towards an enemy that is pursuing the player. Halfway through as I was making a sprite for a spaceship, the idea of a panda seemed appealing. So I made the game with a panda who can only fire in the left direction.

https://www.mfactorgames.com/games/1hgj_102

## The Lost Button (One Hour Game Jam 101)

A man has ten buttons. When one button gets lost, he starts his quest to find it. To play, simply click the button. To hear the music, turn up the volume.

To play The Last Button, please go to the following link. To see other games from One Hour Game Jam 101, go to www.onehourgamejam.com.

## One Hour Game Jam #101

Last blog post, I mentioned One Hour Game Jam which happens every Saturday. So this week, I’m going to jump in and make my first entry since LD29 a few years ago. I’ll probably dust off the old LD29 Manifold code and get ready for the compo.

I have already been practicing making music in 10 minutes or less. Several times this week, the composing bug hit me and I’m confident of putting something together in 15 minutes. But either workflow has something to do with it or being distracted by sound design is.

I have recently taken a sampling approach to this problem. Ableton Live has been the tool of choice lately and recording clips and then sequencing them is very time effective. It is very important to decide what core set of sounds will be needed so that the note entry takes up most of the time. Using an APC40mkii is then very easy to record the sequence of clips using its scene launch capability.

For this weekend, the computer will be set up just for that. The hardware synthesizers will be configured and ready to go and all the tracks will be set to record their respective sounds. The mastering track will be set so exporting the master audio is streamlined.

It’ll be exciting to see what this weekends compo will bring out musically. Can’t wait… In the meantime, warming up to the 21 day challenge, lets dust off the game engine.


text:
### Playing around with errors in Python - KeyboardInterrupt

It's really hard to write code that doesn't throw errors, no matter what language one programs in. I've gotten used to writing modular code that helps maintain a constant train of thought and reduce the chance of errors occurring but still, from time to time, only after running the code do i go "Ohh, No!". I've been reading up on advanced concepts in python for about a week now and one thing I came across was the Python Standard Library reference of the Built-in Exceptions. I've come across most of these errors, a few more commonly than the rest. I thought that it'd be an interesting exercise to write code that intentionally raises the errors listed in that reference.

To start with, let's look at something that's not exactly an Error but is an interesting thing to play around with, KeyboardInterrupt. If a code is producing error messages or if it's not responsive or if you just wish to halt it, most of us press CTRL+C, which corresponds to KeyboardInterrupt. The interesting thing is that, the same way we can catch an exception using the try-except statements thereby preventing the program from halting, we can catch a KeyboardInterrupt and prevent it from halting out program. And just to rub it in, we can print annoying messages mocking the powerless user.

import time
from random import choice

ANNOYING_MSGS=["\n I'm sorry sir but I can't let you do that.",
"\n You don't have power over me!!!",
"\n I stop when I want to stop!!!"]

def main(i):
print("running "+str(i)+" th loop")
time.sleep(1)

for i in range(10):
try:
main(i)
except KeyboardInterrupt:
print(choice(ANNOYING_MSGS))

The Choice function from the random library is used to return one of the three annoying messages, which is then printed to the terminal when the user presses CTRL+C. That was one way of achieving what I set out to and I'm sure there are many more ways to prevent a Python process from stopping when a user tries to CTRL+C it. Well, that's all for now folks.

### Animation using GNUPlot

Animation using GNUPlotI've been trying to create an animation depicting a quasar spectrum moving across the 5 SDSS pass bands with respect to redshift. It is important to visualise what emission lines are moving in and out of bands to be able to understand the color-redshift plots and the changes in it.
I've tried doing this using the animate function in matplotlib, python but i wasn't able to make it work - meaning i worked on it for a couple of days and then i gave up, not having found solutions for my problems on the internet.
And then i came across this site, where the gunn-peterson trough and the lyman alpha forest have been depicted - in a beautiful manner. And this got me interested in using js and d3 to do the animations and make it dynamic - using sliders etc.
In the meanwhile, i thought i'd look up and see if there was a way to create animations in gnuplot and whoopdedoo, what do i find but nirvana!

In the image, you see 5 static curves and one dynam…

### on MOOCs.

For those of you who don't know, MOOC stands for Massively Open Online Course.

The internet is an awesome thing. It's making education free for all. Well, mostly free. But it's surprising at the width and depth of courses being offered online. And it looks like they are also having an impact on students, especially those from universities that are not top ranked. Students in all parts of the world can now get a first class education experience, thanks to courses offered by Stanford, MIT, Caltech, etc.

I'm talking about MOOCs because one of my new year resolutions is to take online courses, atleast 2 per semester (6 months). And I've chosen the following two courses on edX - Analyzing Big Data with Microsoft R Server and Data Science Essentials for now. I looked at courses on Coursera but I couldn't find any which was worthy and free. There are a lot more MOOC providers out there but let's start here. And I feel like the two courses are relevant to where I …

### On programmers.

I just watched this brilliant keynote today. It's a commentary on Programmers and the software development industry/ecosystem as a whole.

I am not going to give you a tl;dr version of the talk because it is a talk that I believe everyone should watch, that everyone should learn from. Instead, I am going to give my own parallel-ish views on programmers and programming.
As pointed out in the talk, there are mythical creatures in the software development industry who are revered as gods. Guido Van Rossum, the creator of Python, was given the title Benevolent Dictator For Life (BDFL). People flock around the creators of popular languages or libraries. They are god-like to most programmers and are treated like gods. By which, I mean to say, we assume they don't have flaws. That they are infallible. That they are perfect.
And alongside this belief in the infallibility of these Gods, we believe that they were born programmers. That programming is something that people are born wit…


text:
#### Abstract

In this post, we derive the bias-variance decomposition of mean square error for regression.

### Regression Decomposition

In regression analysis, it’s common to decompose the observed value as following:

where the true regression $f_x$ is regarded as a constant given $x$. The error (or the data noise) $\epsilon_{x}$ is independent of $f_x$ with the assumption that $\epsilon_{x}$ follows a Gaussian distribution of mean 0 and variance $\sigma^2$. Noticed that (0) is only a description of the data. When we replace $f_x$ with its estimation $\hat{f}_x$, (0) turns into a more practical form:

Where the estimation of the true regression $\hat{f}_x$ is regarded as a non-constant given $x$, and the residual $r_x$ describes the gap between $y_x$ and $\hat{f}_x$. Based on (0) and (1), we can make the following observations:

### Bias-variance decomposition

Using (2) and (3), we can show that why minimizing mean squared error for regression problem is useful. For the derivation, we need a few more identities related to expectation and variance. Given any two independent random variable x, y, and a constant c, we have:

Begin with the definition of mean squared error; we can rewrite it in the form of expected value:

By expanding $(y_x - \hat{f}_x)^2$, we get

Noted that $2 \mathrm{E} \big[ \epsilon_{x} \hat{f}_x \big] = 2 \mathrm{E} \big[ \epsilon_{x} \big] \mathrm{E} \big[ \hat{f}_x \big] = 0$ because $\epsilon_{x}$ is independent of $\hat{f}_x$ and $\mathrm{E} \big[ \epsilon_{x} \big] = 0$ %

And we reach our final form (7) which is the sum of data noise variance $\sigma^2$, prediction variance $\mathrm{Var} \big[ \hat{f}_x \big]$ and the squared prediction bias $(f_x - \mathrm{E} \big[ \hat{f}_x \big])^2$. Such result is the bias-variance decomposition.

#### Why variance matter in regression?

Lowing the prediction bias certainly gives the model higher accuracy on the training dataset; however, to obtain similar performance outside of training dataset, we want to prevent the model from overfitting the training dataset. Given that the true regression has zero variance, a robust model should have prediction variance as small as possible, and this is consistent with the objective of the mean squared error.


text:
# Tag Info

2

Well that depends. As always, you should be very careful with such reasoning as Due to the fact that gravity is related to the square of the distance should not the gravitational sum of every particle exceed the force when calculated by the center of mass. because this is a problematic statement. In general your (Newtonian) gravitational potential is ...

0

The principle in general is called superposition in physics or linearity in mathematics. It is very useful when you want to study a system for that system to be approximately linear. What linearity is, in a more general context. Here "linear" is the property of a function (or an operator, or whatever) to distribute over addition. So for example if you have ...

1

"I find lots of solutions on the internet that say you can replace the cavity with a negative density, why?" Because they use a trick to calculate the potential easier. They assume that the empty hole is neutral, but composed of a positive charge density equal to that of the sphere plus a negative charge density of the same amount. In this way you can ...

0

I think we should start with the local form of Gauss's law $\nabla.\vec{E}=\rho$ Now $$\int \nabla.\vec{E}\,dv=\int \rho\,dv$$ Using Gauss's divergence theorem we have $$\int\vec{E}.\vec{ds}=q$$ I assume $\epsilon_{0}$ to be 1 but you can always put that back into this. I think this way of looking at it does not assume any coordinate dependence.. Ofcourse ...

1

When the point charge is not at the center of the sphere, the electric field lines will not intersect the sphere at right angles. Consequently, there is an initial component of electric field along the surface of a conductor. We know this results in a force on the charge carriers inside the conductor, and these charge carriers will re-arrange until the ...

0

If $c$ is unknown, then you don't know it and you'll have to leave it (either directly or in another form, like $\rho$ or $Q$) as a variable in your expressions. So indeed you can either replace $c$ with $\rho/r^2$ or $Q / (4\pi R^5/3)$, but you cannot eliminate it completely unless they ask for some problem with a very fortuitous cancellation.

Top 50 recent answers are included


text:
# FirstRib initrd easy changes rollback

### Rolling back to a previous boot session state

The following can be used with either a non-pseudo-full-install (i.e. a FirstRib typical normal frugal install) or with a FirstRib pseudo-full-install.

Because standard FirstRib initrd allows up to 100 layers in its overlay filesystem (by default, but easily increased to say 1000 by one NNN codeline modification) it becomes simplicity itself to implement rollback to a previous boot session state. Here is how:

Once you have updated and added whatever you wish to have installed at a certain date and time, you can then simply put a two digit number in front of the upper_changes savefolder name, which will make it load at that layer position read-only on next reboot.

Actually it is possible to do the same with savefiles (instead of savefolders) in FirstRib though you'd then need to make a new upper_changes savefile for future changes. You'd also need to convert the original .ucimg to either a normal directory or a squashed filesystem prior to making it a NNrollback. Can't use uncompressed directories on vfat or ntfs partitions of course, since symlinks and permissions only work properly on Linux format, so use sfs rollbacks on such partitions.

#### For example (with upper_changes savefolder), rename upper_changes to 50upper_changes

I just chose numeric 50 to allow plenty of room for future rollback upper_changes since they would come immediately after each other in the layering structure up to 99upper_changes, which is the top layer number allowed by default.

At this stage, if you wish to save space on your persistence media device you optionally can convert the 50upper_changes directory into a squashfs (known in FirstRib by extension sfs) via command:

mksquashfs 50upper_changes/ 50changes.sfs

Note in the above that only the double-digit numeric is important to FirstRib, the rest of the name can be anything you like, so even 50 as a directory name alone or 50.sfs would work.

That optional conversion is fine, if you want it, because FirstRib initrd has that innovative feature that it doesn't care whether addon layers are uncompressed directories, squashed filesystem (sfs) files, or a mixture of both. It is your choice…

Then on reboot a brand new empty upper_changes savefolder will be created automatically by FirstRib initrd (if using savefiles instead, you need to make an empty Linux-formatted one yourself for FirstRib to use as the top read-write save persistence layer, calling it <any_name.ucimg>).

Later, should you wish to make a new date/time rollback, just repeat the above steps, but using higher rollback double-digit (NN) filename. For example, 51upper_changes or, if you wish 51<any_name>, and again you can optionally make an sfs file out of that. The double-digit NN numbers don't need to be consecutive, as long as they get progressively higher as you make more rollbacks.

Of course you would be advised to normally avoid ever putting any other layer inbetween changes rollback layers since the merged result may mess up matters between rollbacks… though it is possible to do so with care. Not messing up package manager databases is the main issue you want to avoid; because of that importance to maintain package manager database consistency you should only ever remove top-most rollback layer (or simply disable it by making first two characters non-numeric; I myself usually disable simply by adding a ‘D’ to the front of the filename). Removing some in-between rollback NNfilesystem would almost certainly corrupt the package manager database, so be warned…

Note that FirstRib initrd does not itself provide any utility to merge such rollback NNfilesystems together - that's a user utility someone would write (actually one such was written in the past by rufwoof of PLDF). Merging the rollback files into one is basically a remaster, though, I think an actual live-whilst-running remaster utility, for a being used FirstRib-based system, has also been written by someone (fredx181 of PLDF?). I will not be covering such utilities here though, nor probably producing any myself since these are user-utilities and I concentrate on the build system components only, which doesn't mean I won't ever write versions of such myself.

My audience here, by the way - well, I don't know… but this blog was written and produced for my children.

Tiny Linux Blog: https://www.tinylinux.info/

##### wiak
###### sometimes Linux system/apps developer

My earlier research interests included TCP/IP performance/optimisation over noise-prone, long-delay, VSAT links; and cloud-based, autobuild, virtual machines network construction methodologies for distance learning data-comms students’ research and laboratory work.


text:
# How do you find the first and second derivative of sin^2(lnx)?

May 9, 2016

Use of chain rule twice and at the second derivative use of quotent rule.

First derivative

$2 \sin \left(\ln x\right) \cdot \cos \left(\ln x\right) \cdot \frac{1}{x}$

Second derivative

$\frac{2 \cos \left(2 \ln x\right) - \sin \left(2 \ln x\right)}{x} ^ 2$

#### Explanation:

First derivative

$\left({\sin}^{2} \left(\ln x\right)\right) '$

$2 \sin \left(\ln x\right) \cdot \left(\sin \left(\ln x\right)\right) '$

$2 \sin \left(\ln x\right) \cdot \cos \left(\ln x\right) \left(\ln x\right) '$

$2 \sin \left(\ln x\right) \cdot \cos \left(\ln x\right) \cdot \frac{1}{x}$

Although this is acceptable, to make the second derivative easier, one can use the trigonometric identity:

2sinθcosθ=sin(2θ)

Therefore:

$\left({\sin}^{2} \left(\ln x\right)\right) ' = \sin \frac{2 \ln x}{x}$

Second derivative

$\left(\sin \frac{2 \ln x}{x}\right) '$

$\frac{\sin \left(2 \ln x\right) ' x - \sin \left(2 \ln x\right) \left(x\right) '}{x} ^ 2$

$\frac{\cos \left(2 \ln x\right) \left(2 \ln x\right) ' x - \sin \left(2 \ln x\right) \cdot 1}{x} ^ 2$

$\frac{\cos \left(2 \ln x\right) \cdot 2 \cdot \frac{1}{x} \cdot x - \sin \left(2 \ln x\right)}{x} ^ 2$

$\frac{2 \cos \left(2 \ln x\right) - \sin \left(2 \ln x\right)}{x} ^ 2$


text:
ACTA issues

## Orthogonal decompositions induced by generalized contractions

Laurian Suciu

Acta Sci. Math. (Szeged) 70:3-4(2004), 751-765
5843/2009

 Abstract. It is well-known (see [1], [9]) that the invariant vectors for a contraction $T$ on a Hilbert space ${\cal H}$ and for its adjoint $T^*$ coincide. As an immediate consequence one obtains the orthogonal decomposition $${\cal H}= \overline{{\cal R}(I_{\cal H}-T)} \oplus{\cal N}(I_{\cal H}-T),$$ where ${\cal N}(S)$ and ${\cal R}(S)$ denote the kernel, respectively the range, of an operator $S$ on ${\cal H}$. In this paper we obtain such a decomposition for a class of generalized contractions, more specifically for $A$-contractions, i.e. the operators $T \in{\cal B(H)}$ which satisfy $T^*AT \le A$, where $A$ is a positive operator on ${\cal H}$. We also derive several applications involving some decompositions for quasinormal operators and for oblique projections. AMS Subject Classification (1991): 47A20, 47B20 Received January 5, 2004, and in revised form April 5, 2004. (Registered under 5843/2009.)


text:
## Kritische Schichtanalyse der Unterstützungsstruktur von CMS Phase-2 Pixelsensoren

The following bachelor thesis discusses a thermal analysis of the support and readout structure of Phase-2 pixel detectors from the Inner Tracker of the CMS detector. The structure is analyzed with a finite element analysis in ANSYS. The model is simulated with different heat loads in the heat-generating parts and the temperature distribution is discussed. Besides, there a critical layer analysis on the different layers of the model is performed. Criteria for the criticality of a material layer are derived and applied to the model. The results show that the current detector design is sufficient to achieve temperatures below $-20\,^\circ\mathrm{C}$.


text:
## Drawbacks of Online Voting

3

BBC has an article which asks if it is time for countries to adopt online voting. While, there may be many advantages of this, what are the principle drawbacks of online voting? It is possible that hacking may counter the advantages of online voting.

Question was closed 2018-02-01T13:00:32.520

3"It is possible that hacking may counter the advantages of online voting." Yes! Try hacking an offline vote on a large scale. Requires much, much more effort. Some things best remain under as many human eyes as possible. – Trilarion – 2018-02-01T10:10:27.167

1@Trilarion It depends if you are comparing to paper-based offline voting, or to US-style "electronic voting machines". The latter have many of the problems of online voting. – Federico Poloni – 2018-02-01T10:29:01.090

@FedericoPoloni With offline vote I really meant a pen and paper vote with manual counting afterwards, completely free of any electronic devices. The traditional way which works quite well if you ask me. I would have to read the linked article in order to know why anyone would want to switch. – Trilarion – 2018-02-01T10:31:07.907

10

One of the main problems is that in most countries voting is anonymous. It's hard to find a way that people can vote online, without authentication (because anyone can only vote 1 time) and assure that the vote is not bound to an identity.

Hacking is also a major drawback, as regular voting is highly decentralised in most countries. That makes it hard to manipulate on a large scale (especially from outsiders. i.e. not the government itself). If there is confirmed fraud on an online system (for example, more votes than citizens). All votes are invalid and should be redone. In regular voting only the affected district should be redone.

Also, it's nearly impossible to check if someone isn't forced to vote for someone. In most countries, you're forced to vote alone in some kind of box where you have privacy. Nobody can force you to vote for a candidate or check what you have done in the box. There could be someone with a gun on your head when you vote on your computer at home.

Regarding anonymous votes, I think (technically) it's not too hard to limit every person to one vote, but don't log the relationship between the voter and the vote itself. Check if the voter already voted? If not, his vote with only the information of who he voted for will be sent to the server. – Zure – 2018-02-01T11:59:43.700

2There is no problem to technically realise this indeed. The problem is that we as citizens cannot be sure it's programmed this way. In regular voting, it's clear that your identity is protected, you put your voting paper in a box with all other papers. – Mathias Maes – 2018-02-01T12:10:29.283

It is realizable by posting the code publicly and enforcing that it's the actual code used. For example private & verifiable voting has been implemented in Ethereum http://fc17.ifca.ai/preproceedings/paper_80.pdf . The caveat is that it scales really badly at O(n^2) and requires 100% participation. But more advances might be made...

– csiz – 2018-02-01T14:31:54.037

5

The main two problems are security-related.

### Auditability

Auditability (that is, the ability to recount votes when results get challenged) is the most important problem by far for elections that matter.

With physical ballots, you can always recount the results; and, in theory at least, the ballots get stored for years. With electronic votes, any amount of tampering could theoretically happen to the votes. Or, as happened recently in the US, the votes could get deleted.

You can use techs like blockchain to reduce the risk of tampering with individual bulletins, but even that offers little protection if bulletins get tampered with wholesale - e.g. on the fly as they are cast, or by overwriting all votes before the counting.

In practice the only real protection is printing the electronic ballot and having the voter vet and physically cast it. You can then use the electronic votes to compute the results. And if the result gets challenged, you can always resort to counting the physical ballots manually.

### Anonymity

Anonymity has multiple underlying problems that relate to preventing people from voting more than once. The latter is easy enough in theory: maintain a list of people who already voted, and prevent them from voting twice.

In practice it's less simple. At the physical level, timestamps can get in the way of perfect anonymity if the user-related tokens themselves aren't anonymous as well - but then you also need to figure out how to securely and anonymously deliver the token.

Also, you might want to allow voters to be able to change their votes just in case. Because they might want to correct a mistake, for instance. Or, like in Estonia, because you might want a voter to be able to verify that what they've voted is what's registered in the system.

In theory you could use a cryptographically secure one-way hashing algorithm to guarantee anonymity here, but that still leaves the door open to tampering - e.g. by hacking voting devices so it confirms you've voted on X while actually casting a vote on Y.

Note that, in practice, physical votes aren't a panacea either. Horror stories include:

• Ballot stuffing, e.g. when a ballot box is left behind during a (fake) fire emergency.
• Ballot theft, e.g. by intercepting votes sent by snail mail, by making a ballot box disappear, etc.
• Irregular votes, e.g. when someone votes for you using a fake ID (or indeed no ID at all, in countries where there's no such a thing), or when dead voters are mysteriously casting votes.

It's arguably difficult to scale any of this when physical ballots are involved, but the point here is that physical ballots aren't a silver bullet. Electronic voting, for all its problems, is not without merits in this sense.

As one who worked a bit in the field, I expect that what will triumph in the end is a combination of the two as hinted further up: electronic votes backed with physical ballots. It gives you the best of both worlds: quick counts and auditability. (It might simply take the shape of a sophisticated enough ballot counting machine.)

The last mentioned drawback of paper ballots affects digital ballots in exactly the same way since the problem lies in the method of authentication. In practice both digital and remote authentication carry additional challenges compared to manual and local authentication. – David Foerster – 2018-02-01T12:58:14.657

@DavidFoerster: Precisely. What I was trying to convey is that offline voting and electronic voting suffer from mostly the same problems. The only real difference between the two is the potential ease or difficulty of scaling an attack. – Denis de Bernardy – 2018-02-01T13:23:58.970

2

Transparency is one of the biggest arguments against online voting.

The more complicated the process by which votes are represented, the more expert knowledge you need to be able to trace the "route" necessary to transform the voters will into something countable and then into the actual result.

When you vote on paper you can "just" count - the "route" taken is physical, i.e. you can monitor the paper trail, it does not take much expert knowledge.

Whereas if you let people vote online, that puts more responsibility in terms of data security into the hands of the voter (which might be perceived as positive), but knowledge about how votes will be counted or how you would go about verifying that the voting process was not corrupted, requires more than just basic computer knowledge.

(1) While I can see an argument for the average non-IT layman agreeing with what you said, I'm hardpressed to agree with the assertion that humans are less prone to error than machines, in regards to counting votes. (2) how you would go about verifying that the voting process was not corrupted, requires more than just basic computer knowledge Knowing how a manual count is done (and knowing whether it was done correctly) also requires more than the basic skill of filling in a ballot. I don't quite understand what you're trying to point out. – Flater – 2018-02-01T10:41:07.533

@Flater 1) Less error prone was not my point, from where did you get that? 2) Understanding how the counting works for online voting and understanding it FULLY involves not only knowledge of cryptography, but also all other protocols involved in traffic and you still cannot vouch for the hardware the software runs on. If you want to fully understand how your mark on a paper gets to be counted in the results, just follow the paper. You do not need to know several pretty technical protocols and the medium (pen and paper) can be understood by pretty much everyone that went to elementary school. – DrCopyPaste – 2018-02-01T10:59:53.583

You're grossly oversimplifying. The manual counting process is not found on the ballot. Following the paper gets you nowhere. Someone counts the papers in their box, reports that number to their local head of office, who then contacts a regional head, etc... The counting process is a system, not a piece of paper. Even if they write the totals on paper every step of the way, that is not a guarantee that the system was applied correctly. Secondly, cryptography has nothing to do with the counting system. Cryptography is related to the security. Completely different. – Flater – 2018-02-01T11:05:05.487

How does it get me nowhere? I can sit infront of the ballot while voting is legal (e.g. 8am to 8pm) I can sit there and verify that only people who were allowed to vote handed in their vote. How would I ensure that with as low a technical expertise as possible if the vote was not physical? – DrCopyPaste – 2018-02-01T11:09:42.813

I pointed to verifying that the voting process was not corrupted, not only the counting, and security is part of the voting process. (Which obiously has to somehow be related to the counting process, if it weren't what would be the point? I of course assume we still want to vote anonymously) – DrCopyPaste – 2018-02-01T11:12:15.130

2

Drawbacks :

• User identity protection.
• Hacks to tamper the data.
• force voting

solution to drawbacks :

use bitcoin's base technology blockchain to secure the user identity. Most importantly it will be tamper proof. Main challenge here will be design the right architecture and flow. for force voting allow the voting duration for say 10 days and within that duration allow user to change their vote.

1How does that answer the question? "what are the principle drawbacks of online voting?" – DrCopyPaste – 2018-02-01T10:22:48.510

right. updated it . – Abhijit Gujar – 2018-02-01T10:27:00.030

1how would a public ledger solve the problem of user identity protection, i.e. anonymity? – Federico – 2018-02-01T12:03:54.157

2

One aspect easily overseen is that secret voting not only means "no one can observe my vote against my will", but also "no one can observe my vote even if I want to". Mail voting aside, this is an extremely important concept of traditional votes, as it makes it nearly impossibly to buy or blackmail votes. If someone gives me \$100 for my vote, how could I prove I voted for him? I am not allowed to share my vote with someone. In online voting, it's more like mail voting, which can only be tolerated for that reason if it's only a fraction of the votes.


text:
# Solubility equilibrium [closed]

This is a worked example about solubility equilbrium I am new to this subject and I am really confused first of all I know that Q is the product of concentration of Ag and Cl in the solution and ksp is the product of molar solubility of Ag and Cl then why the difference of these two is not amount of precipitation second: if we are not given ksp value of AgCl and we are given only the last part ( part b) how can we find the ksp value?
P.s: after change the amount of cl become zero and amount of Ag become 99*10^-6 so it means that after mixing two solution precipitate is formed and amount of dissolved Ag ions become 99*10^-6 and all of Cl ion is precipitated am I right?
(Sorry if my questions doesn't make sense for you it is because I am new to subject and I don't have any teacher I really tried hard on this example and I saw lots of videos about this subject but I didn't understand it)

## closed as off-topic by Mithoron, Jon Custer, airhuff, Tyberius, Todd MinehardtMar 2 '18 at 22:47

This question appears to be off-topic. The users who voted to close gave this specific reason:

If this question can be reworded to fit the rules in the help center, please edit the question.

Q is known as the ionic product which is defined as product of concentration of ions of the electrolyte, each raised to the power of their coefficients in the balanced chemical equation in solution at any concentration. $\pu{K_{sp}}$ is the same but it is applicable only for a saturated solution.

To find the solubility for the salt with the given $\pu{K_{sp}}$ value, For $\ce{AgCl}$, we have the equilbrium, $$\ce{ AgCl(s) <=> Ag+(aq) + Cl-(aq)}$$ If initally we have $‘a ‘$ moles of AgCl, at equilbrium we will have $’a-s ‘$ and we have $\ce{[Ag+]=[Cl-]=s}$. Hence we get the relation as, $$\pu{K_{sp}} = s^2$$ This is the maximum concentration of the ions present in solution at equilbrium.(because $\pu{K_{sp}}$ = Q). When Q just crosses $\pu{K_{sp}}$, salt is precipitated out.

Since they are products of ionic concentration, we can’t directly subract Q and $\pu{K_{sp}}$ to find the amount of salt precipitated.

I’m just working backwards to get $\ce{K_{sp}}$.

Let mass of $\ce{AgCl}$ precipitated be $’m ‘$ g.
No. of moles precipitated $n = \frac{m}{M}$. Let the volume be $’V’$ litres,
$\ce{[AgCl]}$ precipitated $x = \frac{n}{V}$

$$\ce{Ag+ + Cl- -> AgCl}$$

We know initial concentrations of the ions. Let $\ce{[Ag+]}$ and $\ce{[Cl-]}$ be $’p‘$ and $’q‘$ respectively.
Then solubility product is,
$$\ce{K_{sp}} = (p-x)(q-x)$$

Hope that makes sense.

• And all the $\ce{Cl-}$ is precipitated, what you said is correct. – MollyCooL Mar 2 '18 at 9:31
• you mean when Q=Ksp s=amount of precipitated ions? And also can you please do the calculation to find ksp value from part b? Because when I did the calculation for ksp It didn't come up to be 1.6*10^-10 which is the actual ksp value for AgCl – Elize Mar 2 '18 at 11:09
• When Q=$\pu{K_{sp}}$, at this point addition of more salt results in precipitation. Solubility is the maximum moles of salt that can be dissolved per Litre of solution at a given temperature. I ll make my answer more clear. Please list out what we are given exactly and I shall try to find $\pu{K_{sp}}$. Thanks – MollyCooL Mar 2 '18 at 11:37
• Suppose that we are given the mass of precipitated Agcl and the volume of solution and we know the initial mole number of Ag and Cl – Elize Mar 2 '18 at 11:46
• so only in case that Q>ksp preciption occur then if Q=ksp we don't have any precipitation and hence No equilbrium right? – Elize Mar 2 '18 at 12:15


text:
STRESS CONCENTRATION FACTORS FOR A RECTANGULAR HOLE IN INFINITE PLATE

Theoretical stress concentration factors (Kt) of rectangular hole with round corners in infinite plate can be calculated by this calculator for tension loads. Maximum stress at the edge of the hole is also calculated.

There exist some validity conditions for the equations which are used in the calculations. If input parameters don't satisfy validity conditions of equations, a warning message is given by the calculator.

Rectangular Hole with Round Corners in Infinite Plate:

 INPUT PARAMETERS Parameter Value Rectangle height [2a] mm cm m inch ft Rectangle width [2b] Corner radius [r] Axial stress [σ1] MPa psi ksi

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - AXIAL STRESS Parameter Value TENSION STRESS Stress concentration factor [Kt] * --- --- Maximum tension stress [σmax] --- MPa psi ksi

Note 1: * Geometry rises σnom by a factor of Kt . (Kt = σmaxnom)

Definitions:

Stress Concentration Factor: Dimensional changes and discontinuities of a member in a loaded structure causes variations of stress and high stresses concentrate near these dimensional changes. This situation of high stresses near dimensional changes and discontinuities of a member (holes, sharp corners, cracks etc.) is called stress concentration. The ratio of peak stress near stress riser to average stress over the member is called stress concentration factor.

Kt: Theoretical stress concentration factor in elastic range = (σmaxnom)

List of Equations:

 Tension $$0.2\le r/b\le 1.0$$ and $$0.3\le b/a\le 1.0$$ $${ C }_{ 1 }=14.815-15.774\sqrt { r/b } +8.149r/b$$ $${ C }_{ 2 }=-11.201-9.750\sqrt { r/b } +9.600r/b$$ $${ C }_{ 3 }=0.202+38.662\sqrt { r/b } -27.374r/b$$ $${ C }_{ 4 }=3.232-23.002\sqrt { r/b } +15.482r/b$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { b }{ a } +{ C }_{ 3 }{ (\frac { b }{ a } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { b }{ a } ) }^{ 3 }$$ $${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ 1 }$$


text:
Understanding capacitance in oscilloscope probe tip

I am trying to understand the capacitance and resistance in oscilloscope probe tip.

In the above attached image, that 9Mohm resistance is used for that 1x and 10x setting that divides the input voltage by 10 times or not, right?

But which capacitance are we referring to when we say that the probe has some capacitance?

Are we referring to the capacitor marked 1 or marked 2?

And second question, how does this capacitance impact while measuring high speed signals?

3 Answers

The capacitance in parallel with the 9 megohm resistor is the primary factor in determining the probe capacitance presented to the circuit being probed since, by design, most of the signal voltage (90%) appears across it. At low frequencies, the attenuation of the probe is due to the resistors. At high frequencies, however, the reactance of the capacitors becomes dominant. Then the attenuation of the probe depends on the ratio of the capacitors. For this reason, an adjustable capacitor (usually designated as the compensating capacitor) is included within the probe. By adjusting it, the total capacitance of the oscilloscope input capacitor and the compensating capacitor can be made equal to 9 times the probe capacitance. Thus these capacitors would form a 10:1 voltage divider. In this way, the overall probe and oscilloscope input behave as a 10:1 divider over the full bandwidth of the probe. Another way of looking at it is that the idea is to make the time constant of the 9 megohm resistor and probe capacitance be equal to the time constant of the oscilloscope input (including the compensation capacitor). If that is true, the attenuation of the total circuit will be independent of frequency.

C1 is in series with the input capacitance Cin in parallel with the compensation capacitance C2.

So $$\C_{probe}= \frac{1}{\frac{1}{C_1}+\frac{1}{C_2+C_{IN}}}\$$

That capacitance is effectively in parallel with 10M when the probe compensation is properly adjusted.

Typically on a garden-variety 10:1 probe, C1 is 10pF, and C2+Cin is about 90pF (when properly adjusted). It's properly adjusted when 1/C1 = 1/(C2+Cin) which makes the divider ratio frequency independent.

C2 includes the cable capacitance as well as the trimcap.

So the probe tip looks like 10M in parallel with 9pF to ground. Since there's a bit of stray capacitance on the input, in addition to C1 there will be a bit more than 9pF capacitance to ground.

The circuit used in real probes is a bit more complex usually, but the above is the basic idea.

When you're measuring a signal, the probe tip loads the circuit, particularly at high frequencies. If the probe tip looks like 10pF, when measuring a 200MHz sine wave, the impedance of the probe is about 80 ohms, which is rather low. Sharp edges such as logic transitions will be rounded a bit as a result, but 10pF is maybe 20% of the test load capacitance of typical 3.3V logic so it's not necessarily a huge effect, and datasheet tr/tf limits will usually still apply.

A typical 10Mohm probe is 9.5 pF which is mostly due to C1 in series with a much larger C of coax and trimcap combined. This results in an input impedance (s11) that drops below 10MOhms with rising frequency due to C1 above 1kHz while the R1C1=T1 =R2C2=T2 to obtain the 10:1 ratio.

Thus the coax and C2 compensation with scope input C combined is about 9x the C1 value.

The scope probes use special high impedance coax to reduce the pF/m in the 100 Ohm region and thus reduce the probe tip compensation C2 and thus C1 input capacitance.

High speed signals must be low impedance to be captured properly by passive probe with no tip and GND clip but the bandwidth is equalized (flattened) by the C2 calibration of the square edge test signal pulse by matching T1=T2.

Don’t forget the 0.5nH /mm added by the ground clip which must be removed to get the maximum bandwidth of the probe. This reacts with the coax capacitance to produce the classic ringing observed by new users of logic high speed signals when longish >1cm ground clips are used and thus causes a resonance above 20MHz. This can also be eliminated by enabling the 20MHz Scope BW option to suppress the inductive ground ringing.

Modern Tektronix passive probes are 40:1 with 250k scope input R to achieve wider flat bandwidth and C1 values of 3.5 pF.

The typical 5V CMOS 74HCxx impedance is in the region of 50 to 66 Ohms with a wider tolerance when loaded by a 9.5 pF probe has an RC time constant defined by the exponential 64% of the step voltage. But in terms of the standard 10~90% rise time, the BW(-3dB)=0.35/Tr.

Tau=RC = 66Ω*9.5pF =627 ps implies a -3dB bandwidth slightly greater than 74HC CMOS so the effects are minimal but still exist on reducing slew rate with C1 load.


text:
# Solve the Following Equations. 3 (N − 5) = 21 - Mathematics

Sum

Solve the following equations.

3 (n − 5) = 21

#### Solution

3 (n − 5) = 21

Dividing both sides by 3,

n - 5 = 21/3 = 7

n = 7 + 5 = 12 (Transposing −5 to R.H.S.)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 7 Maths
Chapter 4 Simple Equations
Exercise 4.3 | Q 2.2 | Page 89