User:Saka/Elastic

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WORK IN PROGRESS

Quickly after I found out about CA and Golly, I found out about rules like Diamoeba or Stains. I have since been interested in rules that generate solid white shapes with interesting edge dynamics and movement.

I decided to put the interesting rules I have found here, because I don't think they are deserving of their own page, since they are not interesting because of any engineering or spaceships or any of the usual stuff, but because of their peculiar and interesting dynamics.

B2e3ai4arw5678/S3-an4ar5i678 (SlugWorld)

Thread: https://conwaylife.com/forums/viewtopic.php?f=11&t=2820 Catagolue: https://catagolue.appspot.com/census/b2e3ai4arw5678s3-an4ar5i678

Dynamics

This rule generates quadrilaterals with which have one bouncy side. To see what I mean, run this pattern.

x=98, y = 87, rule = B2e3ai4arw5678/S3-an4ar5i678 51bobo$49bob3obo$47bob7obo$45bob11obo$43bob15obo$41bob19obo$39bob23obo $37bob27obo$35bob31obo$33bob35obo$33b39o$31b43o$29bob43o$27bob45o$25bo b47o$25b49o$23b51o$23b53o$21b55o$19bob57o$19b59o$17b63o$17b63o$15b67o$ 15b67o$13b71o$13b71o$11b75o$11b75o$9b79o$9b79o$7b83o$7b83o$5b87o$5b87o $3b91o$3b91o$b95o$b95o$98o$98o$2b94o$2b94o$4b90o$4b90o$6b86o$6b86o$8b 82o$8b82o$10b78o$10b78o$12b74o$12b74o$14b70o$14b70o$16b66o$16b66o$18b 62o$18b62o$20b58o$20b58o$22b54o$22b54o$24b50o$24b50o$26b46o$26b46o$28b 42o$28b42o$30b38o$30b38o$32b34o$32b34o$34b3ob26o$34b2o2b26o$40b22o$40b 22o$42b18o$39bo2b18o$40bo3b14o$44b14o$46b10o$46b10o$48b6o$48b6o$50b2o$ 50b2o! [[ STEP 10 STOP 550 ]]

Did you see that? The top edge of that quadrilateral bounced a bit, which I find nice. This bouncing behavior is amplified in other rules...

Spaceships

This rule has many (possibly infinite) c/5d spaceships of different periods. The highest period one to have shown up so far is this period 970 (194c/970d) ship

x=20, y = 44, rule = B2e3ai4arw5678/S3-an4ar5i678 12b2o$12b2o$11b7o$12b4obo$10b8o$11b7o$9b10o$10b9o$10b9o$11b8o$9b11o$ 10b10o$8b10obo$8b11o$8b11o$9b10o$7b12o$8b12o$6b12obo$7b11o$7b10o$8b11o $6b13o$7b13o$5b13obo$5b14o$5b14o$6b13o$4b15o$5b15o$3b15obo$4b14o$2b15o $3b16o$b18o$b19o$b19o$2b16o$12ob3obo$b9obo3bo$10o$b7o$b5obo$3bobo! [[ AUTOSTART TRACK 0.2 -0.2 ZOOM 2.5 ]]

You can see how it works, a single engine with some companions on the side, and a fluctuating tail. Nearly all the c/5d's in this rule work like this. I say nearly all, because there's one c/5d that seems to be unique. It's a p5 c/5d. Yeah, it doesn't sound as exciting as the others, but it seems to be unique.

x=6, y = 6, rule = B2e3ai4arw5678/S3-an4ar5i678 4o$3obo$2obobo$2bob2o$3b3o$3b3o! [[ AUTOSTART TRACK 0.2 -0.2 GPS 5 ZOOM 15 ]]

This rule also harbors a unique c/24o, surprisingly:

x=7, y = 10, rule = B2e3ai4arw5678/S3-an4ar5i678 2bobo$b5o$2b3o$7o$7o$b5o$b5o$2b3o$bo3bo$2bobo! [[ AUTOSTART TRACK 0 -1/24 GPS 24 ZOOM 12 ]]

One more, this rule contains two known c/19d spaceships (Which is also rather surprising), and looking at the similarity between the two known ones, I propose that there is a family of c/19d's, somewhere out there. We just haven't found them yet.

x=54, y = 25, rule = B2e3ai4arw5678/S3-an4ar5i678 14bo3bob3o23b3obobo$14b3ob4o22bob8o$12b11obo17bob9o$8b3ob13o18b11o$8b 17o16b12o$6b18o17b13o$6b19o14b15o$4b19o17b14o$5b19o16b12o$5b19o17b12o$ 5b20o14b12o$3b20o16b11obo$4b19o14b13o$2b19o18b5ob3o$3b19o17b5o3bo$3b 19o19bo$3b19o19bo$b19o$2b18o$18o$b13o3bo$b11obo$bob5o3bo$b5obo$5bo! [[ AUTOSTART TRACK 1/19 -1/19 GPS 19 ]]

B3aijn45aiy6acn78/S3inq4aiqr5aiy6acn78

"That's a beautiful rule. Watching it is like watching a battle going on between two types of patterns, the diamonds and the combs. The diamonds seem to have the upper hand most of the time, but every now and then a comb will make a valiant attempt to take over, only to succumb once again to the hungry diamonds."
— wildmyron, https://conwaylife.com/forums/viewtopic.php?f=11&t=803&p=41146#p41072

Original mention: https://conwaylife.com/forums/viewtopic.php?f=11&t=803&p=41146#p41062

Dynamics

The quote above provides a poetic summary of the dynamics of this rule, but here are the two tribes, the diamonds and the combs.

x=30, y = 14, rule = B3aijn45aiy6acn78/S3inq4aiqr5aiy6acn78 6b2o18b2o$6b2o18b2o$4b6o14b6o$4b6o16b2o$2b10o12b6o$2b10o14b2o$14o10b6o $14o12b2o$2b10o12b6o$2b10o14b2o$4b6o14b6o$4b6o16b2o$6b2o18b2o$6b2o! [[ AUTOSTART LOOP 20 GPS 8 ]]

This rule creates growing diamonds which are occasionally assaulted by the emergent comb patterns. Here is a sample:

x=30, y = 29, rule = B3aijn45aiy6acn78/S3inq4aiqr5aiy6acn78 6bobo$8b2o2bobobobobobo$5bob6obobobobo3bo$3b18obob3o$2b23obo$2b25o$ob 26o$28obo$b29o$b29o$2b28o$2b26o$3b25o$6b21o$6b21o$6b20o$7b19o$7b18o$8b 17o$9b15o$12b12o$11b12o$13b10o$11b11o$14b8o$12b8o$15b5o$14b4o$16b2o! [[ ZOOM -3 STEP 10 ]]

It looks a bit like a cloth waving around in the wind.

Spaceships

This rule has one known spaceship found by Goldtiger997 from a soup search. It is of speed 4c/150d (Simplified 2c/75d):

x=7, y = 13, rule = B3aijn45aiy6acn78/S3inq4aiqr5aiy6acn78 2b2o$2b2o$5o$2b3o$6o$4o$6o$2b3o$6o$3b4o$b6o$3b3o$3bo! [[ AUTOSTART TRACK 2/75 -2/75 ZOOM 8.5 ]]

B2e3ai4arw5678/S3-an4ar5i678

Original mention: https://conwaylife.com/forums/viewtopic.php?f=11&t=803&p=41146#p41059

Dynamics

This rule is similar to slugs in that it makes bouncing quadrilaterals, but in this rule they sometimes get very large. However, the larger ones seem to behave differently. Here's a large sample, it somewhat reminds me of folding paper.

x=530, y = 441, rule = B2e3ai4arw5678/S3-an4ar5i678 303bo$303bobo$301b5obo3bo$299bob7ob3obo$297bob15obo3bo$295bob19ob3obo$ 295b27obo3bo$293b31ob3ob3o$291bob39o$289bob42o$287bob46o$287b48o$285b 50o$283bob49o$281bob53o$279bob54o$279b56o$277b57o$275bob59o$273bob60o$ 273b62o$271b63o$269bob65o$269b66o$267b68o$265bob67o$265b71o$263b72o$ 261bob72o$259bob73o$257bob77o$255bob78o$253bob80o$251bob81o$249bob85o$ 247bob86o$245bob88o$243bob89o$241bob93o$239bob94o$237bob96o$235bob97o$ 233bob101o$231bob102o$229bob104o$227bob105o$225bob109o$223bob110o$221b ob112o$219bob113o$219b117o$217b118o$217b120o$215b121o$215b123o$213b 124o$213b126o$211b127o$209bob129o$207bob130o$207b134o$205b136o$203bob 138o$203b139o$201b143o$201b143o$199b147o$199b147o$197b151o$197b150o$ 195b154o$195b154o$193b158o$193b158o$191b162o$191b161o$189b165o$189b 165o$187b169o$187b169o$185b173o$185b172o$183b176o$183b176o$181b180o$ 181b180o$179b184o$179b183o$177b187o$177b187o$175b191o$175b191o$173b 195o$173b194o$171b198o$171b198o$169b202o$169b202o$167b206o$167b205o$ 165b209o$165b209o$163b213o$163b213o$161b217o$161b216o$159b220o$159b 220o$157b224o$157b224o$153b230o$153b229o$151b233o$151b233o$149b237o$ 149b237o$147b241o$147b240o$143b246o$143b246o$141b250o$141b250o$137b 256o$137b255o$135b259o$135b259o$133b263o$133b263o$131b267o$131b266o$ 129b270o$129b270o$127b274o$127b274o$125b278o$125b277o$123b281o$123b 281o$121b285o$121b285o$119b289o$119b288o$117b292o$117b292o$115b296o$ 115b296o$113b300o$113b299o$111b303o$111b303o$109b307o$109b307o$105b 313o$105b312o$101b318o$101b318o$97b324o$97b324o$93b330o$93b329o$89b 335o$89b335o$85b341o$85b341o$81b347o$81b346o$79b350o$79b350o$77b354o$ 77b354o$75b358o$75b357o$73b361o$73b361o$71b365o$71b365o$67b371o$67b 370o$65b374o$65b374o$61b380o$61b380o$57b386o$57b385o$53b391o$53b391o$ 49b397o$49b397o$45b403o$45b402o$43b406o$43b406o$41b410o$41b410o$39b 414o$39b413o$37b417o$37b417o$35b421o$35b421o$31b427o$29bob426o$23bo3bo b430o$21bob3ob432o$15bo3bob440o$15b3ob442o$13b450o$11bob449o$11b453o$ 5bo3b455o$5b3ob457o$3b463o$3b465o$b466o$469o$469o$2b469o$2b469o$4b469o $4b468o$6b468o$6b468o$8b468o$8b468o$10b468o$10b467o$12b467o$12b467o$ 14b467o$14b467o$16b467o$16b466o$18b466o$18b465o$20b465o$20b465o$22b 465o$22b464o$24b464o$24b463o$26b463o$26b463o$28b463o$28b463o$30b463o$ 30b462o$32b462o$32b462o$34b462o$34b461o$36b461o$36b461o$38b461o$38b 460o$40b460o$40b459o$42b459o$42b458o$44b458o$44b457o$46b457o$46b456o$ 48b456o$48b455o$50b455o$50b455o$52b455o$52b454o$54b454o$54b453o$56b 453o$56b453o$58b453o$58b452o$60b452o$60b451o$62b451o$62b450o$64b450o$ 64b449o$66b449o$66b448o$68b448o$68b448o$70b448o$70b447o$72b447o$72b 446o$74b446o$74b445o$76b445o$76b445o$78b445o$78b444o$80b444o$80b444o$ 82b444o$82b443o$84b443o$84b442o$86b442o$86b441o$88b441o$88b440o$90b 440o$90b438o$92b437o$92b435o$94b434o$94b432o$96b431o$96b429o$98b428o$ 98b426o$100b425o$100b423o$102b422o$102b420o$104b419o$104b417o$106b416o $106b414o$108b413o$108b411o$110b410o$110b408o$112b402ob4o$112b396ob3o 3b2o$114b395o2b2o$114b393o$116b386o$116b384o$118b383o$118b381o$120b 374o$120b372o$122b371o$122b362ob6o$124b360o2b2o$124b358o$126b356o$126b 354o$128b352o$128b350o$130b348o$130b346o$132b344o$132b342o$134b340o$ 134b338o$136b336o$136b334o$138b332o$138b318o$140b316o$140b312o$142b 308o$142b304o$144b298o$144b298o$146b294o$146b295o$148b291o$148b289o$ 150b285o$150b283o$152b281o$152b277o$154b275o$154b273o$156b269o$156b 269o$158b264o$158b259o$160b257o$160b255o$162b253o$162b251o$164b246o$ 164b244o$166b243o$166b241o$168b236o$168b234o$170b233o$170b231o$172b 227o$172b227o$174b221o$174b221o$176b215o$176b215o$178b209o$178b209o$ 180b203o$180b203o$182b197o$182b197o$184b191o$184b191o$186b185o$186b 185o$188b179o$188b179o$190b173o$190b173o$192b167o$192b167o$194b161o$ 194b161o$196b155o$196b155o$198b149o$198b149o$200b143o$200b143o$202b 137o$202b137o$204b5ob125o$204b4o2bob123o$212bob117o$214bob115o$216bob 109o$218bob107o$220bob101o$222bob99o$224bob93o$226bob91o$228bob85o$ 230bob83o$232bob75o$234b75o$236b69o$236bob67o$238bob63o$240bob61o$242b 37ob17o$244b17ob3ob13o3b3ob11o$244bob13obo3bo3b5o11bo3b3o$246b3ob3ob3o bo11b3o17bo$248bo3bo3bo! [[ STEP 10 ]]

This rule doesn't really have much more to offer, unfortunately.

B2-ak3-cij4rw5-r678/S2ci3kqy4irw5-c678

Original mention: https://conwaylife.com/forums/viewtopic.php?f=11&t=3120&start=525#p94257 Catagolue: https://catagolue.appspot.com/census/b2-ak3-cij4rw5-r678s2ci3kqy4irw5-c678/

Dynamics

This one is like a battle between the Death of a Square and the growth of a square, but Death wins. At the first few generations, a solid white rectangle with some perturbations at the edges is generated, and those perturbations slowly erode the rectangle, but the rectangle fights back and tries to grow. This moves the rectangle around. Here's a small sample:

x=60, y = 60, rule = B2-ak3-cij4rw5-r678/S2ci3kqy4irw5-c678 2o3b3obo2bo4b3ob2o4bo2b2o2bo2b2o3b3obob3o5bobo$2o2b6o2b2o3b2o2bob3o3bo b6o2b2ob2o3b2o2bo2bo2bobo$8bobo6b2o3b2ob2obo2b2o2bo2bobo4b2o6bo3bobo$ 6o2b2o3bobob5o3b2o2bob2ob3obob5obo4bobo2bobo$4o4bob2obob2o3b2ob2o3b2o 2b4obo2bob5o2bob4o$b3o2b3ob3o3bob2obobo3bobo2bob2o2bo2bob4obo4bob2obo$ b2o7bo2bobo6bo2b5o2b5obobo2b2ob4ob2o2bo2bo$5bobob3obobobo6b2o2b2o2b2o 4b4o2b2obo3bobo4bo$o2b4o2bob3obo5b2o3b2obo3bo2bo2bob3o5b5obo3bo$2bob2o bobo4b2obo2bo4bob2obo6b3ob2o3bo8bobobo$3bo3bo2b6ob3ob2o4b3obo2bo2b5ob 9o2b2o3bo$o2bo3b3o4b3ob8ob3obob4ob2ob2ob5o2b2ob3o2bo$b2o3bo3b2obobob2o 2b2o2bo2bo4b2obo2bobo2b2ob2ob2o5b3o$ob2obob3ob2o2b2o2b3obob2o2b2o3b4ob 3ob3obobo2b3o3b2o$2bo2b4o2b3obo3b2o4b2o2bo7b2obo2bobo5bo2b3obo$2ob2ob 2ob2o5bob3ob5o2bo4b2obobo5bobobo3b3o3bo$2o2bo2bo4bo5b3o4bob2obo2bo2bo 3b2obob2obo3bob4obo$2b2obo2bo2bo2bo3b4o5b3o2bob2ob2o3b3ob3ob2ob4o$b3ob 3obo7b4obob2o2b2obo5b2obo5bobobob2o2bobo$2o4bo5bo5bob3obo5bo5bo5b2o2b 5obob4obo$2bo2b2o3bobo2b3o2b2o4b4o2b3o3b3o3bo3b2obo6b2o$2bo2b2o5b2obob 3ob3o2bobo2b2obo2b2ob3o4bobobob4o$obo3bobob3o4bob2o2bo4b2ob2obo3b2o2b 3obo3bobob2obobo$o7bo2bob3obo3b3o3b2o2b2obo3b2o2b2obob2obo2bo2b2obo$3b 4ob4obobo6bobo2b2ob2o5b3o2b2o2bob4o4b4o$o3bob4o2bob2obob4obobo3b2ob2o 2b11o5b5o$4bo2bob6obo2bobo4bo3bobobob2obob3o2bo11bo$3b2o3bob3obob5ob3o bobo2b3o3bo3bo6bo4bo3bobo$obo3bo3bobo2b2o3bobo3b4ob2obob3o2bo3bob3ob4o b2o$obo2b3ob4ob3o2b2o2bo5b2o3bo6b2obo2b5o3b2ob2o$ob2obo2b2o5bo2bo3bo2b 2ob3o2b2o4b5o8b2obo$b2ob3o2b4o2bob3o4bob7ob2ob2obob4o2bob3obo2b3o$3bo 5b2o5bob2o3b3ob2obob3o2bob3o2bobob4obobobobo$5b3obobob2o3bob2obo2b2o2b obob2o2bo4b3o3bo2bo2bobo$14bo3bob4o3b2ob2o2b6ob2obo2bo3b2obobo2bo$o3b 2o2bo5b3ob2obo3bo2bo3b4o3b2obobob4ob3obo2bo$3b5ob2ob10obobo2b4o4bo4b2o 2bobo2b7o$3obob3ob2o2b2o4b3o6b3ob3obo2b3o4b2o6b4o$o3b2ob2ob4obobo4b3ob 2obobob2obo3b3o6b3obo2bob2o$o3bo3bo5b2o3bobobo3bo3b2o2bo4b3o2b2ob2o4bo bobo$2o2b2o2bo2bobo4bobob2o2b7o2bo5bo3b4o4b2ob2o$obo3b2o4bo2bobo2b2o2b 2ob2ob4o2bo3bobobobo5bo3bobo$b3o3bob3obo5bob2obo2b2obo3bobobo7b5obo2b 3o$o2bo3b4o4b3obo4b5ob2obobob3o2b2o3b2o4bo3b2o$3bobobobob2obobobo2bo2b 5o2bob2obo3bo2bobobob5o2b2obo$3b2obob4o4b2obob2o7bo3b3o2b3ob2obob2obob 2o2b3o$o2bo10bob5ob2o3b3ob4ob3o3b4o3b5obob2o$2b2obo2b2o2b3obo3bo4bob3o b2o3b3obob2o2b4o4bo3b2o$b2o6bo2b4o5bob4o2bob2obo2b2ob2o2bobo5b3o2b2o$ 4bo2b4obo4b8ob4o2bob4o2bob3o8bo2b2obo$2o2b2o2bo2bobo2bo2bob2ob2obob3o 4bo2bobo2bobobo3b2o2b2o$2o2bo2bo2bobo4bob4ob2obo2b4o2bob2ob2obo5b2ob6o $obo3bo2bo2bo3bo2b4ob2ob4o2bo4bo2bo2bo5bob7o$bobo8b6ob3obo4bobo2bo8b2o bobo3b6o$b2o6bo3bob2obo2bo2bobo4bo2b2ob3o2b4ob3ob2ob3o$3o2b2o4bob2o2bo bob2obobobobobo8bo2bo2bo3bobo2bo$o2bobo3b3o2bobobo5bobo2b2o2bo2b5ob10o 2bob3o$bobobob2o3bobob3obobo2b2obobo2b2obob3o2b5o2bo4b4o$2bo2bo5bo4bo 2bo3b3o2bob2ob3o2bobob3obobob2ob3obobo$o3bo4bo3bob2ob3o4bo3b4obob2ob2o bobo2b3o5bob2o! [[ STEP 5 ]]

It is best experienced at larger soup sizes, so fire up Golly, set the scale to 2:1, and make a large soup.

B2-ak3-cij4jknrw5-r678/S2ci3kqy4ijrwz5-c678