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Oblique antstretcher

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Oblique antstretcher

Postby Sokwe » April 15th, 2011, 5:59 pm

I have finally found a c/5 orthogonal support for an oblique trail of ants that allows the completion of an antstretcher when combined with the related c/4 diagonal component. Here is the complete wavestretcher (c/4 diagonal component by Hartmut Holzwart):
x = 103, y = 75, rule = B3/S23
70bo$68b2ob2o$67b3o$64b2o3bo$64bo3bo2$60bo3b3o$59bobo$58bo2bo$60b2o$
57bo2bo4bo$58b3o2bobo$63b3o$58bob4o$57bo$58bo$55bo2bobo$55b2o$51b2o4bo
$50b3obobo$50bo$52b2o$52b2o2$49b3o$51bo$48bo3bo$48bo4bo$48bo29b2o5b2o
5b2o5b2o$48b5o23bo3bo3bo2bo3bo2bo3bo3bo$76bo3bobob3o5b3obobo3bo$76bo5b
2o2b3ob3o2b2o5bo$46b2o21b2o5b2ob3o15b3ob2o$40bobo3bobo20bobo4bo25bo$
31b2o6b2o2b2o2bo21bobo5bo3bo15bo3bo$30b2o10bobo24bo3b2o3bo2bo15bo2bo$
31bobo9bobo5bo7bob4obo6b2o$26bo4b3o9b2o4b4o4bob3obobobo6bo$25b5ob3o2bo
bob2o2b3ob2o3b4o12bo$25bo2b2o6bo4bo2bo2bo3bo2b2o5bobo3bob2o$35bo3bo4bo
3b4obo3bo4b7o$27b2o2b2ob2o2bo10b2ob2o4bo4bo$35bo28bo$21b3o3bo5b2o18bo$
21bo5bo2bob2o17b2o$22bo3b2obo$25b2o3bobo$13b3o10bo$13bo5b3o2b2o$14bo2b
2ob3ob2o$16bo10bo$17bobob2o4bo$19b2obo$17b2o3bobo$16b2o$18bo$15b2o$14b
3o$13b2obo$12b4obo$17b3o$18b2o$10b3ob2o$9bo3b3o$12b3o$8bobobo$7b4o$7bo
$8b2o$9bo2bo$2o$obo3b3o$o3bo4bo$3b2o$3bo5bo!

There were a lot of promising partial results for the lower wing of the c/5 component, so there may be smaller solutions.

There is also the possibility of a c/6 diagonal support for an oblique trail of ants; however, I am not sure if a search for such a pattern would currently be feasible.
-Matthias Merzenich
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Re: Oblique antstretcher

Postby dvgrn » April 15th, 2011, 7:22 pm

Sokwe wrote:I have finally found a c/5 orthogonal support for an oblique trail of ants that allows the completion of an antstretcher when combined with the related c/4 diagonal component.

Wow! Congratulations -- a new kind of growing spaceship for the record books. This has been on the Life wishlist for well over half a decade now. It will be interesting to see how long it takes before smaller variants show up...
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Re: Oblique antstretcher

Postby HartmutHolzwart » April 16th, 2011, 2:06 pm

Great!

How did you find the divsion point? Did you branch off when finding a part supported by a simple spark?
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Re: Oblique antstretcher

Postby Sokwe » April 16th, 2011, 3:57 pm

HartmutHolzwart wrote:How did you find the divsion point? Did you branch off when finding a part supported by a simple spark?

While performing a simple short, wide search, I found a partial result that seemed to split and stay separate for several columns. The fact that I quickly found a simple spark that could support the top branch encouraged me to search for a solution to the bottom branch (I can probably attribute most of my success here to luck).
-Matthias Merzenich
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Re: Oblique antstretcher

Postby Sokwe » April 17th, 2011, 11:56 pm

Here's a related solution that is shorter, but wider:
x = 112, y = 50, rule = B3/S23
51b2o5b2o5b2o5b2o$49bo3bo3bo2bo3bo2bo3bo3bo$49bo3bobob3o5b3obobo3bo$
49bo5b2o2b3ob3o2b2o5bo$49b2ob3o15b3ob2o$49bo25bo$50bo3bo15bo3bo$46b2o
3bo2bo15bo2bo$40bobo3bobo$31b2o6b2o2b2o2bo$30b2o10bobo31bo10bo3b3o5b3o
3bo$31bobo9bobo5bo7bob4obo8bo2bo5b2ob5ob2o3b2ob5ob2o$26bo4b3o9b2o4b4o
4bob3obobobo2b2o3bo2bo3bob2obo5bobobobo5bob2obo$25b5ob3o2bobob2o2b3ob
2o3b4o12bobo2bo4bobo3bobo3b5ob5o3bobo3bo$25bo2b2o6bo4bo2bo2bo3bo2b2o5b
obo3bob2o3bo4bo5b3o5b2o3b2o5b3o$35bo3bo4bo3b4obo3bo4b7o10bo2bo2bob3o
13b3obo2bo$27b2o2b2ob2o2bo10b2ob2o4bo4bo9b2obobo5bo23bo$35bo28bo8bo$
21b3o3bo5b2o18bo$21bo5bo2bob2o17b2o$22bo3b2obo$25b2o3bobo$13b3o10bo$
13bo5b3o2b2o$14bo2b2ob3ob2o$16bo10bo$17bobob2o4bo$19b2obo$17b2o3bobo$
16b2o$18bo$15b2o$14b3o$13b2obo$12b4obo$17b3o$18b2o$10b3ob2o$9bo3b3o$
12b3o$8bobobo$7b4o$7bo$8b2o$9bo2bo$2o$obo3b3o$o3bo4bo$3b2o$3bo5bo!
-Matthias Merzenich
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Re: Oblique antstretcher

Postby calcyman » April 18th, 2011, 5:15 pm

Impressive! This warrants mention on pentadecathlon.com; I shall add it imminently.

Anyway, it enables the construction of a space non-filler. Unlike previous space non-fillers, however, the diagonals grow faster.

x = 392, y = 392, rule = B3/S23
177bobo35bobo$177bo2bo33bo2bo$176bo2bo35bo2bo$173bob2o41b2obo$172b5o
41b5o$171bo2bo45bo2bo$173bo47bo$167b3o3bo47bo3b3o$167bobo55bobo$166bob
o3bo49bo3bobo$168bo4bo47bo4bo$165b3o4b2o47b2o4b3o$167bo3b2o49b2o3bo$
165b2ob2o55b2ob2o$168bobo53bobo$166b3o57b3o$167b2o57b2o$162b3o65b3o$
164bo65bo$158b7o65b7o$157bo2bobo69bobo2bo$160b2o71b2o2$160bo73bo$157b
2o77b2o$157b2o77b2o$156b2o2b2o71b2o2b2o$158b2o75b2o$155bo2b2obo31b2o5b
2o31bob2o2bo$156b2o2bo24b4obobobo5bobobob4o24bo2b2o$184b3obobob2obo3bo
b2obobob3o$184bo3bobo13bobo3bo$149bo4b2o21b2o6bob3o5b2ob2o5b3obo6b2o
21b2o4bo$136bo11bo2bo2bobo19bo2bo5b2o21b2o5bo2bo19bobo2bo2bo$135b2o10b
o3bo3bo23bo5b5o15b5o5bo23bo3bo3bo7b2o$135bobo10bo3bo24b2o9b2o15b2o9b2o
24bo3bo9b2o$150b2o14bo3b2o6b6o27b6o6b2o3bo14b2o9bobo$130b2o5b3o12b2o4b
3o5bob2obob3o2b3o33b3o2b3obob2obo5b3o4b2o11b3o4bo$129b2o2b2ob5ob2ob2ob
o7b2obobob2o4bobob2o2b2o37b2o2b2obobo4b2obobob2o7bob2obo2b3ob5o$131bo
2bob3o3b2o3b3o3bobo3bo2bo2b5o4b2obo39bob2o4b5o2bo2bo3bobo3b3o3bo6b2o2b
o$133b3o2bo8bo3b2o3bob2o5b3o3b3o2bo41bo2b3o3b3o5b2obo3b2o3bo4bo$132bo
5bo6b2o10bo2b2o9bo51bo9b2o2bo10b2o2b2ob2o2b2o$126b2o9bo3bo18bo11b2o47b
2o11bo17bo$126bobo3b2o2bo3bo18b2o73b2o17b2o5bo3b3o$126bo4b2obo24b2o73b
2o18b2obo2bo5bo$129bo2b3ob2obo118bob2o3bo$118b2o9b2ob3o120bobo3b2o$
118bobo3bo4bobo129bo10b3o$118bo3b3ob2o3b2o129b2o2b3o5bo$121b2o8b2o129b
2ob3ob2o2bo$124b3o4bo128bo10bo$122bo3b3o131bo4b2obobo$121bo6bo136bob2o
$121bo2bob2o135bobo3b2o$120b2obo146b2o$120bobo146bo$112b3o4b4o148b2o5b
2o$112bo5bo3b2o147b3o3bobo$113bo3bo3b3o147b4o4bo$115b2o3bobo148bo2b2o$
114b2o3b2obo148b2ob3o$113b3o2bobo154b2ob2o$106bo4b2o157b2o5b2obo$105b
2o4bo2b2o160bo3bo4b2o$105bobo5b2o164b2o3bob2o$107bo3bob2o161bo2bo6bo$
108bobo166bob2obo3bo$105bobob2o3bo162bo2b3o3bo$106bob3o168b4o3bo$101bo
8bobo167b3o$100b4o3bo182b2o$100bo2b3ob2o176b3o3b2o$102bo3bobo173b2ob4o
bo$103b2ob2o178bo$105b2o181bo$98b3o2b3o181bo2bob2o$98bo2b2obo180bo3b3o
bo$99b2ob2o185b3obo$96b5obo191b2o$95b2o2bo195b2o$94b3o196b2o2bo$88b2o
6bo199bo$88bo2b2o205b2o2b3o$88bo3bobo203b4o2bo$85b2o3bo2bo208bobobo$
84b2o4bo208bobobob3o$85bobo219bo$82b3o220bo$82bo2bo222b3o$82bobo225bo$
83bobo220b2o$83bo225bo$82b2obo222b2o$82b2o223bo$80bo227bo2bo$79bobo
229b2o$78b2o230b4o$78bobo232bo$75b3o2bo232bob2o$71bo3bo236b3obo$70b2o
4b2o235b2obo3b2o$70bobo2b3o237bo5b2o$76b2o235b3o3bobo$72bobo239bobobob
2o$64bo6b2o2bo239b2obobo$63b6o2b3o242b2o2bo3bo2b2o$63bo7b2o3bo240b3o3b
o4b2o$64bo253bob2o2bob2o$72bo246b2o2bobo$66b4o2bo250b2o$67b3o252b4o$
62b3ob4o256bob2o$56b3o2bo2b3obo253bo6bo4b2o$56bo4b2o263b2o2bo2bobo$57b
o4bo3b2o256bob3ob2o3bo$60b2obobo262bob3o$59b3o270bo$47b2o9b3o272bo$47b
obo7b2o271bo3bo8b3o$47bo8b3obo270bo3bo9bo$50bo3bob5obo267b3o2b3o6bo$
49bobob2o7bo270bobob3o2bo$49bo3bobo275b6o3bob2o$48bo2b2o280b2o2bo5bo$
48b2o2bo285bo2bob2o$43b2o3b2obo289bo$43bobo3bob3o284bob2obo3b3o$43bo
294bobo2bo5bo$48b2o3bo285b2o7bo$38b2o6bob2o294b3o6bo$37b2o6b3o297bo7b
2o$38bo2bob3o4b2o289b4o2bo4bobo$38b2obo300b2ob4obo$38b2o5bo299b2obo2bo
bo$35bo8bobo298b3o3b3o$34b5o2bo309bo4b2o$34bo2b2o2bo2bobo299bobo3b2o3b
2o$36b3o4b2o301bo2bo2b3obo$41bobo306b5o$40b3o303bo6b2o$38b2o308bo4bo$
349bo$38bo2bo310b2o$38bo2bo310b2o$34bo4b2o$33bobo2b2o310bo2bo$32bo6bo
310bo2bo$36bo314b2o4bo$33b2obo3bo311b2o2bobo$35bobo2bo311bo6bo$37bobo
315bo$32b2o317bo3bob2o$28bo3bobo4bo311bo2bobo$26bo2bo3bo4bobo311bobo$
20bo3b3o2bo8bo2bo316b2o$19bo4b2ob2o8bo2bo311bo4bobo3bo$19bo7b2o8b4o2b
2o306bobo4bo3bo2bo$19b3obo2bo2bo7bo3b4o305bo2bo8bo2b3o3bo$19bobo4bobo
9bo2bo309bo2bo8b2ob2o4bo$17bob2o18bo307b2o2b4o8b2o7bo$17bobo18bo308b4o
3bo7bo2bo2bob3o$17b3o18bo311bo2bo9bobo4bobo$11bobo25b2o311bo18b2obo$9b
obobobo20b2ob2o312bo18bobo$7b2o2b2o2b2o22b2o312bo18b3o$7bob2o2b4o20bob
o311b2o25bobo$7b2o4bo23b3o311b2ob2o20bobobobo$14bo21bo314b2o22b2o2b2o
2b2o$5bo6bo23b3ob2o310bobo20b4o2b2obo$4bo4bob2o27bobo309b3o23bo4b2o$3b
2ob2o2b2o25b2obobo312bo21bo$4b2o31b3o310b2ob3o23bo6bo$3b2o32bobo309bob
o27b2obo4bo$2b3o28bo6bo308bobob2o25b2o2b2ob2o$2o30bo2bo2b2o312b3o31b2o
$32bo2b4o313bobo32b2o$obo30b2ob2o313bo6bo28b3o$bo34b2o314b2o2bo2bo30b
2o$36bo316b4o2bo$36bo317b2ob2o30bobo$36bo317b2o34bo$30b2o323bo$29b2ob
3o320bo$29b2o2b2o320bo$29bo2bobo325b2o$29b4ob2o321b3ob2o$32bob2o321b2o
2b2o$29b3o325bobo2bo$356b2ob4o$29b2o325b2obo$28bobo329b3o$28b2o$30bobo
328b2o$32bo328bobo$362b2o$32bo326bobo$30bobo326bo$28b2o$28bobo328bo$
29b2o328bobo$362b2o$29b3o329bobo$32bob2o325b2o$29b4ob2o$29bo2bobo325b
3o$29b2o2b2o321b2obo$29b2ob3o321b2ob4o$30b2o325bobo2bo$36bo320b2o2b2o$
36bo320b3ob2o$36bo323b2o$bo34b2o317bo$obo30b2ob2o317bo$32bo2b4o316bo$
2o30bo2bo2b2o314b2o34bo$2b3o28bo6bo313b2ob2o30bobo$3b2o32bobo313b4o2bo
$4b2o31b3o312b2o2bo2bo30b2o$3b2ob2o2b2o25b2obobo308bo6bo28b3o$4bo4bob
2o27bobo309bobo32b2o$5bo6bo23b3ob2o310b3o31b2o$14bo21bo312bobob2o25b2o
2b2ob2o$7b2o4bo23b3o309bobo27b2obo4bo$7bob2o2b4o20bobo310b2ob3o23bo6bo
$7b2o2b2o2b2o22b2o314bo21bo$9bobobobo20b2ob2o311b3o23bo4b2o$11bobo25b
2o311bobo20b4o2b2obo$17b3o18bo312b2o22b2o2b2o2b2o$17bobo18bo312b2ob2o
20bobobobo$17bob2o18bo311b2o25bobo$19bobo4bobo9bo2bo311bo18b3o$19b3obo
2bo2bo7bo3b4o308bo18bobo$19bo7b2o8b4o2b2o307bo18b2obo$19bo4b2ob2o8bo2b
o309bo2bo9bobo4bobo$20bo3b3o2bo8bo2bo305b4o3bo7bo2bo2bob3o$26bo2bo3bo
4bobo306b2o2b4o8b2o7bo$28bo3bobo4bo311bo2bo8b2ob2o4bo$32b2o316bo2bo8bo
2b3o3bo$37bobo311bobo4bo3bo2bo$35bobo2bo311bo4bobo3bo$33b2obo3bo317b2o
$36bo315bobo$32bo6bo311bo2bobo$33bobo2b2o311bo3bob2o$34bo4b2o314bo$38b
o2bo310bo6bo$38bo2bo310b2o2bobo$351b2o4bo$38b2o310bo2bo$38b2o310bo2bo$
42bo$38bo4bo308b2o$37b2o6bo303b3o$37b5o306bobo$35bob3o2bo2bo301b2o4b3o
$33b2o3b2o3bobo299bobo2bo2b2o2bo$34b2o4bo309bo2b5o$38b3o3b3o298bobo8bo
$38bobo2bob2o299bo5b2o$41bob4ob2o300bob2o$37bobo4bo2b4o289b2o4b3obo2bo
$37b2o7bo297b3o6b2o$38bo6b3o294b2obo6b2o$43bo7b2o285bo3b2o$42bo5bo2bob
o294bo$42b3o3bob2obo284b3obo3bobo$50bo289bob2o3b2o$47b2obo2bo285bo2b2o
$48bo5bo2b2o280b2o2bo$48b2obo3b6o275bobo3bo$49bo2b3obobo270bo7b2obobo$
47bo6b3o2b3o267bob5obo3bo$46bo9bo3bo270bob3o8bo$46b3o8bo3bo271b2o7bobo
$58bo272b3o9b2o$59bo270b3o$59b3obo262bobob2o$56bo3b2ob3obo256b2o3bo4bo
$56bobo2bo2b2o263b2o4bo$56b2o4bo6bo253bob3o2bo2b3o$62b2obo256b4ob3o$
66b4o252b3o$67b2o250bo2b4o$66bobo2b2o246bo$64b2obo2b2obo253bo$62b2o4bo
3b3o240bo3b2o7bo$63b2o2bo3bo2b2o242b3o2b6o$71bobob2o239bo2b2o6bo$70b2o
bobobo239bobo$70bobo3b3o235b2o$69b2o5bo237b3o2bobo$70b2o3bob2o235b2o4b
2o$75bob3o236bo3bo$75b2obo232bo2b3o$78bo232bobo$78b4o230b2o$79b2o229bo
bo$80bo2bo227bo$84bo223b2o$82b2o222bob2o$82bo225bo$84b2o220bobo$81bo
225bobo$81b3o222bo2bo$86bo220b3o$84bo219bobo$84b3obobobo208bo4b2o$85bo
bobo208bo2bo3b2o$87bo2b4o203bobo3bo$87b3o2b2o205b2o2bo$95bo199bo6b2o$
94bo2b2o196b3o$95b2o195bo2b2o$96b2o191bob5o$98bob3o185b2ob2o$98bob3o3b
o180bob2o2bo$98b2obo2bo181b3o2b3o$103bo181b2o$105bo178b2ob2o$101bob4ob
2o173bobo3bo$99b2o3b3o176b2ob3o2bo$100b2o182bo3b4o$109b3o167bobo8bo$
105bo3b4o168b3obo$105bo3b3o2bo162bo3b2obobo$105bo3bob2obo166bobo$105bo
6bo2bo161b2obo3bo$104b2obo3b2o164b2o5bobo$105b2o4bo3bo160b2o2bo4b2o$
111bob2o5b2o157b2o4bo$112b2ob2o154bobo2b3o$115b3ob2o148bob2o3b2o$116b
2o2bo148bobo3b2o$112bo4b4o147b3o3bo3bo$112bobo3b3o147b2o3bo5bo$112b2o
5b2o148b4o4b3o$122bo146bobo$120b2o146bob2o$121b2o3bobo135b2obo2bo$123b
2obo136bo6bo$121bobob2o4bo131b3o3bo$120bo10bo128bo4b3o$118bo2b2ob3ob2o
129b2o8b2o$117bo5b3o2b2o129b2o3b2ob3o3bo$117b3o10bo129bobo4bo3bobo$
129b2o3bobo120b3ob2o9b2o$126bo3b2obo118bob2ob3o2bo$125bo5bo2bob2o18b2o
73b2o24bob2o4bo$125b3o3bo5b2o17b2o73b2o18bo3bo2b2o3bobo$139bo17bo11b2o
47b2o11bo18bo3bo9b2o$131b2o2b2ob2o2b2o10bo2b2o9bo51bo9b2o2bo10b2o6bo5b
o$139bo4bo3b2o3bob2o5b3o3b3o2bo41bo2b3o3b3o5b2obo3b2o3bo8bo2b3o$129bo
2b2o6bo3b3o3bobo3bo2bo2b5o4b2obo39bob2o4b5o2bo2bo3bobo3b3o3b2o3b3obo2b
o$129b5ob3o2bob2obo7b2obobob2o4bobob2o2b2o37b2o2b2obobo4b2obobob2o7bob
2ob2ob5ob2o2b2o$130bo4b3o11b2o4b3o5bob2obob3o2b3o33b3o2b3obob2obo5b3o
4b2o12b3o5b2o$135bobo9b2o14bo3b2o6b6o27b6o6b2o3bo14b2o$134b2o9bo3bo24b
2o9b2o15b2o9b2o24bo3bo10bobo$135b2o7bo3bo3bo23bo5b5o15b5o5bo23bo3bo3bo
10b2o$145bo2bo2bobo19bo2bo5b2o21b2o5bo2bo19bobo2bo2bo11bo$146bo4b2o21b
2o6bob3o5b2ob2o5b3obo6b2o21b2o4bo$181bo3bobo13bobo3bo$181b3obobob2obo
3bob2obobob3o$153b2o2bo24b4obobobo5bobobob4o24bo2b2o$152bo2b2obo31b2o
5b2o31bob2o2bo$155b2o75b2o$153b2o2b2o71b2o2b2o$154b2o77b2o$154b2o77b2o
$157bo73bo2$157b2o71b2o$154bo2bobo69bobo2bo$155b7o65b7o$161bo65bo$159b
3o65b3o$164b2o57b2o$163b3o57b3o$165bobo53bobo$162b2ob2o55b2ob2o$164bo
3b2o49b2o3bo$162b3o4b2o47b2o4b3o$165bo4bo47bo4bo$163bobo3bo49bo3bobo$
164bobo55bobo$164b3o3bo47bo3b3o$170bo47bo$168bo2bo45bo2bo$169b5o41b5o$
170bob2o41b2obo$173bo2bo35bo2bo$174bo2bo33bo2bo$174bobo35bobo!
What do you do with ill crystallographers? Take them to the mono-clinic!
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