Miscellaneous topics in Conway's Game of Life -- unfinished projects of all kinds and conditions

26 July 2020

Spaceship Construction For Fun and Profit

Glider synthesis technology for Conway's Life spaceships -- i.e., the techniques needed to construct spaceships by crashing gliders into each other -- continues to improve. This is due in large part to the impressive efforts of a new generation of Lifenthusiasts. The current list of glider-constructible spaceships includes loafer, dart, crab, x66, weekender, puffership, B29, Pushalong 1, copperhead, fireship, spider, 25P3H1V0.1, 25P3H1V0.2, 27P4H1V1, 30P5H2V0, 30P4H2V0.4, 31P8H4V0, 46P4H1V0, 56P6H1V0, 58P5H1V1, 60P5H2V0, and 70P2H1V0.1.

The full list of spaceships with known glider recipes can be found on the LifeWiki Glider Synthesis page. Considering that only one spaceship in the above list (60P5H2V0) had a known synthesis at the beginning of 2013, this is a lot of progress!

Here's a showcase animation created by Saka a few months ago to document the construction of 58P5H1V1, a 58-bit c/5 spaceship:

Code: Select all
x = 536, y = 536, rule = B3/S23
504bobo$504b2o$505bo2$503bo$501b2o$502b2o5bobo$17bo491b2o$18bo491bo$
16b3o$492bo20bobo$491bo21b2o8bobo$491b3o20bo8b2o$20bo503bo$5bobo13b2o$
6b2o12b2o$6bo2$4bo510bo$2bobo509bo$3b2o10bobo496b3o8bo$9bo6b2o505b2o$
10b2o4bo507b2o$9b2o$529bo$527b2o$493bobo32b2o$481bobo9b2o$481b2o11bo$
482bo52bo$533b2o$56bo430bobo44b2o$54bobo430b2o40bobo$55b2o431bo40b2o$
530bo$62bo$63bo$61b3o$487bo$486bo$486b3o20bo$463bobo41b2o$463b2o43b2o
13bo$464bo58bobo$523b2o$67bo$68bo435bo$66b3o426bo6b2o$470bo24bobo5b2o$
31bo438bobo22b2o$32b2o436b2o$31b2o$508bo$506b2o$74bo432b2o$75bo$73b3o$
461bo$461bobo$461b2o4$81bo404bo$82bo402bo$80b3o402b3o$452bo$452bobo$
436bo15b2o$434b2o$426bobo6b2o57bo$426b2o64b2o$427bo49bo15b2o$73bo402bo
$74bo401b3o$72b3o351bo$425bo$425b3o2$61bo$59bobo$60b2o406bo$467bo$65bo
bo399b3o$66b2o3bo$66bo5bo6bo$70b3o7b2o$79b2o9$408bo$407bo$400bobo4b3o$
114bo285b2o63bobo$115bo285bo63b2o$113b3o350bo6$465bo$458bo4b2o$458bobo
3b2o$458b2o5$394bobo$123bo270b2o$124b2o269bo$123b2o$136bo$137bo$135b3o
$398bo$397bo$397b3o$134bobo$135b2o300bo$135bo301bobo$437b2o$134bo$135b
o$133b3o$385bo$384bo52bo$384b3o48b2o$436b2o$380bo30bo$373bo4b2o31bobo$
371b2o6b2o30b2o$141bo230b2o46bo$139bobo276b2o$140b2o277b2o$372bo$129bo
bo240bobo$130b2o240b2o$130bo4$363bo37bo$140bo222bobo35bobo$141b2o27bo
192b2o36b2o$140b2o29b2o$170b2o6$382bo$382bobo$382b2o11$196bo$197b2o$
196b2o4$364bo$348bo15bobo$348bobo13b2o$348b2o10$195bo$196b2o134bobo25b
o$195b2o135b2o26bobo$333bo26b2o2$196bo$194bobo$195b2o$178bo21bobo151bo
bo2bo$176bobo22b2o151b2o3bobo$177b2o22bo141bo11bo3b2o$341b2o$342b2o10$
205bo$203bobo$204b2o2$212bo$213b2o$212b2o103$214bo$197b2o15b2o$198b2o
7b3o3bobo$197bo11bo136b3o$208bo137bo$320b2o25bo$319b2o$321bo3$320b3o$
320bo14b2o$182bo138bo12b2o$182b2o152bo$181bobo27bo$211b2o$210bobo130bo
$337b3o2b2o$337bo4bobo$338bo15$346b2o10bo$185b3o158bobo8b2o$187bo158bo
10bobo$186bo$181b2o$180bobo195bo$182bo7b2o185b2o$189bobo185bobo$191bo
2$178b3o203b3o$180bo172b3o23bo4bo$179bo173bo24b2o5bo$354bo23bobo12$
134b2o$135b2o$134bo2$140bo$140b2o$139bobo3$136b2o$137b2o$98b2o31bo4bo$
97bobo31b2o$99bo30bobo239b2o$371b2o$373bo2$414b2o$409b2o3bobo$404b2o2b
2o4bo$404bobo3bo$404bo8$418bo$417b2o$417bobo8$434b2o$434bobo$434bo14$
141b3o$143bo$142bo$78b3o$80bo$79bo2$75bo$75b2o$65b2o7bobo$64bobo$66bo
3$69bo$69b2o$68bobo$470b2o$449bo20bobo$95b2o351b2o20bo$94bobo351bobo$
96bo2$90b2o$91b2o386b2o$90bo369b2o17bobo$460bobo16bo$449b2o9bo$449bobo
$83b2o364bo$84b2o$83bo404b2o$451b2o35bobo$88b3o359b2o36bo$90bo361bo$
89bo$498b2o$498bobo$454b3o41bo$454bo$455bo3$502b3o$502bo$503bo2$28b2o$
27bobo$29bo7$15b2o$bo12bobo$b2o13bo$obo8bo$11b2o$10bobo4$2b2o$3b2o480b
o$2bo481b2o$484bobo2$8b2o40b3o$9b2o41bo$8bo42bo5$12b3o506bo$14bo505b2o
$13bo4b2o500bobo$17bobo$19bo506b2o$514b2o10bobo$41b3o469b2o11bo$43bo
471bo$21b2o19bo$20bobo$22bo15b2o$39b2o472bo$28bo9bo473b2o$28b2o482bobo
$27bobo$520b2o$519b2o$521bo$515b3o$515bo$40b2o474bo$41b2o$40bo!
[[
WIDTH 720
AUTOSTART
GPS 20
PAUSE 2 "58P5H1V1 Synthesis"
PAUSE 2 "By Kazyan (Tanner Jacobi)\nand Goldtiger997"
PAUSE 2 "The synthesis was posted \non the forums on April 3, 2020."
T 60 "At the time this animation was made,\nit cost 161 gliders."
T 139 "It has since been reduced to 100 gliders."
GPS 30 T 202 "Let's zoom in."
ZOOM 12 GPS 60
T 203 PAUSE 3 "First glider collision."
T 216 PAUSE 3 "Beehive at beehive made."
PAUSE 2 "This will become the 'centerpiece'\nof the consttruction."
T 455 "A complex seed constellation is gradually\nbuilt up around the beehive at beehive."
T 456 PAUSE 3 "OK, that last part was cool.\nIt will happen again on the other side."
X -12
PAUSE 2 "11 cells are added all at once."
T 485 "\n"
GPS 30 "Magic..."
T 550 X 0
COLOR POLY Red
POLYT 550 650 50
POLYLINE 266 252 269 255 264 260 261 257 266 252 12
POLYLINE 280 266 283 269 278 274 275 271 280 266 12
T 599 X 10 Y -10 "More of the superstructure is\nincrementally constructed."
T 600 PAUSE 3 "See those 2 long barges? \n They're going to get extended 4 times."
T 872 "\n"
T 873 PAUSE 3 "...And now they're boats, I guess. \n (Barges are a type of boat, right?)"
PAUSE 1 X 0 Y 0
T 936 PAUSE 3 "Here comes the really fun part!" ZOOM 5.5
PAUSE 2 "Hope you don't mind some SFX..."
PAUSE 0.5 LAYERS 10 DEPTH 2 THEME Fire
PAUSE 0.5 ZOOM 1 ANGLE 45 T 945
PAUSE 1 T 960 ZOOM 7.7 ANGLE 0 THEME Poison LAYERS 1
T 1000 "And the ship is done!"
T 1094 "Wait, don't forget cleanup!" THEME Blues X -6 Y 3
T 1100 PAUSE 3 X 25 Y -25 "The construction is complete!" ZOOM 15
LOOP 1500
]]
#C By: Saka

As the pop-up captions mention, the synthesis has already been improved significantly to less than two-thirds of its original cost. Below is a recipe using just 100 gliders. Type J / Shift+J or use the onscreen < and > buttons to move between the incremental construction stages.

Code: Select all
x = 425, y = 162, rule = B3/S23
241bo159bo$240bo159bo$240b3o157b3o3$172bo234bo$173bo12bo218b2o$171b3o
12bobo213bo3b2o$186b2o212b2o$401b2o$130bo280bo$131bo278bo$71bo13b2o42b
3o104bo44bo53bo54bo19b3o$71b2o12bobo147bobo42bobo51bobo52bobo$70bobo
12bo148bobo37b2o3bobo46b2o3bobo47b2o3bobo$6bo120b2o10bo38b2o54bo39bo4b
o16bo31bo4bo49bo4bo$7bo118bobo11bo36bobo51b2obo40b3obo15bo33b3obo21bo
28b3obo$5b3o117bobo10b3o35bobo51bo2bo44bo16b3o34bo22bobo29bo$125b2o49b
2o53b2o44bo53bo23b2o29bo$79b2o48b2o49b2o53b2o39bo3b2o48bo3b2o49bo3b2o$
78bo2bo46bo2bo47bo2bo51bo2bo37bo3bo2bo39bo6bo3bo2bo47bo3bo2bo13bo$79b
2obo7b2o37b2obo47b2obo51b2obo36b2o3b2obo39b2o4b2o3b2obo6bo39b2o3b2obo
6bo4b2o$81bobo6bobo38bobo48bobo29b3o20bobo42bobo37b2o12bobo4bobo45bobo
4bobo3bobo$81bobo6bo40bobo48bobo31bo20bobo42bobo51bobo5bo46bobo5bo$82b
o49bo50bo3b2o26bo22bo3b2o39bo3b2o48bo3b3o48bo3b3o$186bobo52bobo42bobo
51bo54bo$185bobo52bobo42bobo51bobo52bobo$185b2o29bo23b2o43b2o52bobo49b
obo2bo$216b2o122bo50b2o3bobo$215bobo179b2o$7b2o129b2o83b2o71b2o114b3o$
bo4bobo130b2o81bobo71bobo113bo$b2o5bo129bo85bo71bo116bo$obo234bo$236b
2o87b3o$22b3o195bo15bobo88bo$22bo23bo173b2o104bo$23bo22b2o171bobo98b2o
$45bobo273b2o$320bo2$328b2o$329b2o3b2o$328bo4bobo$335bo11$114b2o$115b
2o$114bo26$356bo$357b2o$356b2o$364bo$362bobo$363b2o$356bo$357b2o49bo$
356b2o48b2o$400bobo4b2o$64bobo333b2o$65b2o334bo$65bo58bo235bo$125bo
235bo$77bo45b3o233b3o29bo$75b2o314bobo$76b2o128bo141bo27bobo12b2o22bob
o$134bobo70b2o137bobo28b2o27bo8b2o$135b2o69b2o139b2o28bo26b2o10bo$135b
o75bobo191b2o$212b2o$212bo$415bo$413b2o$414b2o$208bo$209b2o$208b2o$
218bobo$17bobo132bo66b2o15bo68bo74bo$18b2o36bo94bobo65bo10bo4bobo61bo
4bobo67bo4bobo$18bo37b2o79b2o11bobo76bobo2bobo58b2obobo2bobo64b2obobo
2bobo28bo$55bobo78bobo12bo77bo2bo2bo53bo6bobo2bo2bo66bobo2bo2bo28bo$
138bo75b2o14b2o58bo5bo2b2o70bo2b2o32b3o$16bo50bo27bobo54bo60bobo20bo
51b3o6b2o6bo51bo14b2o6bo$10b2o3bobo43b2o3bobo5b2o19b2o49b2o3bobo5b2o
54bo14b2o3bobo5b2o54b2o3bobo5b2o43b2o15b2o3bobo5b2o$10bo4bo2bo42bo4bo
2bo3bo2bo19bo49bo4bo2bo3bo2bo68bo4bo2bo3bo2bo53bo4bo2bo3bo2bo41bobo15b
o4bo2bo3bo2bo$11b3obo3bo42b3obo3bo3bobo70b3obo3bo3bobo69b3obo3bo3bobo
54b3obo3bo3bobo60b3obo3bo3bobo$14bo5bo44bo5bo3bo58b2o14bo5bo3bo73bo5bo
3bo58bo5bo3bo58bo5bo5bo3bo$13bo7bo42bo7bo62b2o12bo7bo75bo7bo60bo7bo59b
3o4bo7bo$12bo3b2o4bo40bo3b2o4bo60bo13bo3b2o4bo73bo3b2o4bo58bo3b2o4bo
57bo6bo3b2o4bo$11bo3bo2bo4bo8b2o28bo3bo2bo4bo72bo3bo2bo4bo71bo3bo2bo4b
o56bo3bo2bo4bo56b2o4bo3bo2bo4bo25bobo$11b2o3b2obo4bo6b2o29b2o3b2obo4bo
71b2o3b2obo4bo70b2o3b2obo4bo55b2o3b2obo4bo61b2o3b2obo4bo24b2o$18bobo4b
o7bo35bobo4bo77bobo4bo4bo71bobo4bo4bo56bobo4bo4bo62bobo4bo4bo19bo$18bo
bo5bo42bobo5bo76bobo5bo2bobo50b2o18bobo5bo2bobo55bobo5bo2bobo61bobo5bo
2bobo$19bo3b3o44bo3b3o23b2o53bo3b3o2bobo50bobo19bo3b3o2bobo57bo3b3o2bo
bo63bo3b3o2bobo$22bo50bo25b2o57bo6bo53bo22bo6bo61bo6bo67bo6bo13b2o$21b
obo48bobo26bo55bobo81bobo42b2o22bobo35b3o34bobo18b2o$18bobo2bo45bobo2b
o79bobo2bo78bobo2bo4bo38b2o18bobo2bo4bo32bo31bobo2bo4bo15bo$18b2o3bobo
43b2o3bobo77b2o3bobo76b2o3bobobobo36bo20b2o3bobobobo30bo32b2o3bobobobo
$24b2o49b2o83b2o82b2obo2bo62b2obo2bo32b2o34b2obo2bo$212b3o33b2o65bob2o
34b2o35bob2o$214bo100bo36bo32b2o3bo$213bo102b3o66bo5b3o$79b2o237bo64bo
bo7bo$80b2o301b2o$79bo268b3o$350bo$163b3o183bo3bo$165bo149b2o36b2o$
157bo6bo13b2o71b2o62bobo34bobo4bo59b3o$157b2o18b2o55b3o13b2o49bo13bo
43b2o58bo$156bobo20bo56bo15bo48b2o55bobo24b2o33bo$235bo64bobo82bobo22b
3o$385bo24bo$245b3o163bo$228b2o17bo169bo5bo$227bobo16bo13b2o154b2o4b2o
$229bo29b2o155bobo3bobo$261bo96b3o$254bo105bo3b2o7bo$182b2o69b2o104bo
5b2o6b2o$182bobo68bobo7bo100bo7bobo$182bo79b2o$262bobo102b2o7b2o$366bo
bo6bobo$368bo8bo28b3o$406bo$407bo!
#C [[ THEME Fire LOOP 150 ]]
#C [[ POI X -196 Y -60 Z 11 ]]
#C [[ POI X -130 Y -60 Z 11 ]]
#C [[ POI X -80 Y -60 Z 11 ]]
#C [[ POI X -29 Y -60 Z 11 ]]
#C [[ POI X 26 Y -60 Z 11 ]]
#C [[ POI X 71 Y -60 Z 11 ]]
#C [[ POI X 125 Y -60 Z 11 ]]
#C [[ POI X 180 Y -60 Z 11 ]]
#C [[ POI X -193 Y 44 Z 11 ]]
#C [[ POI X -142 Y 44 Z 11 ]]
#C [[ POI X -57 Y 44 Z 11 ]]
#C [[ POI X 27 Y 44 Z 8 ]]
#C [[ POI X 96 Y 44 Z 8 ]]
#C [[ POI X 171 Y 44 Z 7 ]]

For anyone interested in the more convoluted side of Life technology, these glider constructions make it possible to create circuitry that converts one type of spaceship into another. The current status of this effort is also documented in a LifeWiki article.

02 July 2020

Newer Better Faster Smaller Stable Signal Circuits

In 2020 so far there's been a major surge in interest in stable circuitry. For example, on January 26 Entity Valkyrie constructed a period-11040 spider gun, and on May 22 a 58P5H1V1 gun -- the first-ever guns to fire c/5 orthogonal spaceships and c/5 diagonal spaceships, respectively. In both cases, as is almost inevitable for new glider synthesis, cheaper recipes have since been found, making it possible to construct significantly smaller guns.

More recently, Entity Valkyrie also found the key cleanup mechanism for an incomplete color-changing glider lane shifter found by Martin Grant. The result was the Bandersnatch, so named because of its association with Snarks and Boojums in Lewis Carroll's poem The Hunting of the Snark (appropriately subtitled "an agony in eight fits".)

Code: Select all
#N Bandersnatch #O Entity Valkyrie and Martin Grant, 5 June 2020
#C Spartan 0-degree color-changing glider shifter
x = 50, y = 46, rule = B3/S23
o$b2o$2o16$45bo$44bobo$44bobo$43b2ob3o$31b2o16bo$31b2o10b2ob3o$43b2ob
o7$46b2o$37bo8b2o$36bobo$36bo2bo$37b2o$20b2o$19bobo$19bo24b2o$18b2o24b
2o5$35b2o$35b2o!
#C [[ THUMBNAIL THUMBSIZE 3 AUTOSTART WIDTH 640 HEIGHT 540 X 7 Y 10 THUMBSIZE 2 ZOOM 16 GPS 40 LOOP 200 ]]
The Bandersnatch is a significant discovery, and has already helped to solve quite a few glider adjustment problems. For example, it enabled Goldtiger997 to build a highway robber with 863-tick recovery time. (The current record is a larger staged-recovery design with 742-tick recovery time.) The Bandersnatch consists of just seven well-separated still lifes, which is Spartan by the modern definition, so it is bound to become very useful in self-constructing circuitry as well.

In April, Louis-Fran├žois Handfield constructed a much more compact universal regulator than the previous best known mechanism.

The following month Handfield also adapted Martin Grant's new HL161H conduit to make a useful color-changing edge shooter, HSW47T214. Its output lane is transparent, so it can serve as a merge circuit in a fairly compact glider adjustment toolkit.

On June 8, a collaborative effort produced a fully universal *WSS-to-glider converter that recovers in only 588 ticks. It accepts LWSSes, MWSSes, and HWSSes equally well, and works even if the input spaceship is moved by an odd number of cells along the input lane. Previous spaceship signal converters usually only worked if the spaceship was moved in two-cell increments, since the phase of these spaceships is different in odd and even positions.

Code: Select all
#C universal *WSS-to-glider converter, repeat time 588 ticks
x = 679, y = 92, rule = B3/S23
591bo$591b3o$594bo$593b2o8b2o$603bo$601bobo18bo11b2o$601b2o18bobo10b2o
$587b2o32bobo$587b2o26b2o2b3ob2o$615bo2bo$613bobo3b3ob2o$613b2o6bob2o$
587b2o$587b2o5$611b2o13b2o$611b2o13b2o16b2o4bob2o$641b2o2bo4b2obo$640b
o2b2o3b2o$641bo5bo3b2o$642b3o2bob2obo$644bo3bobobob2obo$629b2o20b2obob
2o$630bo$627b3o$627bo$634b2o$616b2o17bo$617bo17bobo$616bo19b2o16b2o$
616b2o36b2o$607b2o$2b2o334bo268bobo$o4bo330bo3bo249bo2bo14bo$6bo334bo
252bo3b2o54b2o$o5bo329bo4bo248bo3bo2bo2bo53b2o$b6o330b5o249b4o3b2o19b
2o$619b2o$603b2o$603bobo$604bo$654bo$653bobo$654bo$629b2o$630bo$627b3o
$591b2o34bo16b2o$586b2o2bo2bo17b2o30bobo$583bo2bo4bobo17bobo29bo$582bo
bobo5bo20bo28b2o25bo$583bo2bob2o23b2o52b3o$586bo2bo76bo$587bo4bo73b2o$
588b5o2$590bo83b2o$589bobo2b2o29bo49bo$590b2o3bo27b3o49bob2o$592b3o27b
o44b2o4b3o2bo$592bo29b2o43b2o3bo3b2o$672b4o$642bo15b2o15bo$640b3o10b2o
2bobo12b3o$639bo14bo2bo13bo$626b2o11b2o11bo2b3o14b5o$626b2o24b3o21bo$
655bo18bo$654b2o18b2o$669bo$667b3o$666bo$595b2o68bo2b2o$595b2o69b2o2bo
$601b2o48b2o16b2o$601b2o48b2o3$599b2o$599b2o5b2o$606b2o31b2o3bo$639bo
3bobo$640bo3bobob2o$641bo4bob2o$627b2o10bob5o$627b2o9bobo4bob2obob2o$
639bo2b2obo2bob2obo$640b2obob2o12b2o$659b2o!
#C [[ X 285 Y 0 Z 5 AUTOSTART PAUSE 2 STEP 5 LOOP 2000 ]]

As the MWSS collision shows, the mechanism even works if the next spaceship arrives before the second half of the bait constellation (the boat) has been reconstructed.

Toward the end of June the stable-circuitry construction binge continued with a number of new stable eaters and spaceship-to-X converters, including a much smaller HWSS Heisenburp -- but these will probably fit much better in a future post.