## Oblique antstretcher

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

### Oblique antstretcher

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/S2370bo\$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\$48bo29b2o5b2o5b2o5b2o\$48b5o23bo3bo3bo2bo3bo2bo3bo3bo\$76bo3bobob3o5b3obobo3bo\$76bo5b2o2b3ob3o2b2o5bo\$46b2o21b2o5b2ob3o15b3ob2o\$40bobo3bobo20bobo4bo25bo\$31b2o6b2o2b2o2bo21bobo5bo3bo15bo3bo\$30b2o10bobo24bo3b2o3bo2bo15bo2bo\$31bobo9bobo5bo7bob4obo6b2o\$26bo4b3o9b2o4b4o4bob3obobobo6bo\$25b5ob3o2bobob2o2b3ob2o3b4o12bo\$25bo2b2o6bo4bo2bo2bo3bo2b2o5bobo3bob2o\$35bo3bo4bo3b4obo3bo4b7o\$27b2o2b2ob2o2bo10b2ob2o4bo4bo\$35bo28bo\$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!`

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
Sokwe
Moderator

Posts: 1386
Joined: July 9th, 2009, 2:44 pm

### Re: Oblique antstretcher

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...

dvgrn
Moderator

Posts: 5221
Joined: May 17th, 2009, 11:00 pm

### Re: Oblique antstretcher

Great!

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

Posts: 408
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Re: Oblique antstretcher

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
Sokwe
Moderator

Posts: 1386
Joined: July 9th, 2009, 2:44 pm

### Re: Oblique antstretcher

Here's a related solution that is shorter, but wider:
`x = 112, y = 50, rule = B3/S2351b2o5b2o5b2o5b2o\$49bo3bo3bo2bo3bo2bo3bo3bo\$49bo3bobob3o5b3obobo3bo\$49bo5b2o2b3ob3o2b2o5bo\$49b2ob3o15b3ob2o\$49bo25bo\$50bo3bo15bo3bo\$46b2o3bo2bo15bo2bo\$40bobo3bobo\$31b2o6b2o2b2o2bo\$30b2o10bobo31bo10bo3b3o5b3o3bo\$31bobo9bobo5bo7bob4obo8bo2bo5b2ob5ob2o3b2ob5ob2o\$26bo4b3o9b2o4b4o4bob3obobobo2b2o3bo2bo3bob2obo5bobobobo5bob2obo\$25b5ob3o2bobob2o2b3ob2o3b4o12bobo2bo4bobo3bobo3b5ob5o3bobo3bo\$25bo2b2o6bo4bo2bo2bo3bo2b2o5bobo3bob2o3bo4bo5b3o5b2o3b2o5b3o\$35bo3bo4bo3b4obo3bo4b7o10bo2bo2bob3o13b3obo2bo\$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
Sokwe
Moderator

Posts: 1386
Joined: July 9th, 2009, 2:44 pm

### Re: Oblique antstretcher

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/S23177bobo35bobo\$177bo2bo33bo2bo\$176bo2bo35bo2bo\$173bob2o41b2obo\$172b5o41b5o\$171bo2bo45bo2bo\$173bo47bo\$167b3o3bo47bo3b3o\$167bobo55bobo\$166bobo3bo49bo3bobo\$168bo4bo47bo4bo\$165b3o4b2o47b2o4b3o\$167bo3b2o49b2o3bo\$165b2ob2o55b2ob2o\$168bobo53bobo\$166b3o57b3o\$167b2o57b2o\$162b3o65b3o\$164bo65bo\$158b7o65b7o\$157bo2bobo69bobo2bo\$160b2o71b2o2\$160bo73bo\$157b2o77b2o\$157b2o77b2o\$156b2o2b2o71b2o2b2o\$158b2o75b2o\$155bo2b2obo31b2o5b2o31bob2o2bo\$156b2o2bo24b4obobobo5bobobob4o24bo2b2o\$184b3obobob2obo3bob2obobob3o\$184bo3bobo13bobo3bo\$149bo4b2o21b2o6bob3o5b2ob2o5b3obo6b2o21b2o4bo\$136bo11bo2bo2bobo19bo2bo5b2o21b2o5bo2bo19bobo2bo2bo\$135b2o10bo3bo3bo23bo5b5o15b5o5bo23bo3bo3bo7b2o\$135bobo10bo3bo24b2o9b2o15b2o9b2o24bo3bo9b2o\$150b2o14bo3b2o6b6o27b6o6b2o3bo14b2o9bobo\$130b2o5b3o12b2o4b3o5bob2obob3o2b3o33b3o2b3obob2obo5b3o4b2o11b3o4bo\$129b2o2b2ob5ob2ob2obo7b2obobob2o4bobob2o2b2o37b2o2b2obobo4b2obobob2o7bob2obo2b3ob5o\$131bo2bob3o3b2o3b3o3bobo3bo2bo2b5o4b2obo39bob2o4b5o2bo2bo3bobo3b3o3bo6b2o2bo\$133b3o2bo8bo3b2o3bob2o5b3o3b3o2bo41bo2b3o3b3o5b2obo3b2o3bo4bo\$132bo5bo6b2o10bo2b2o9bo51bo9b2o2bo10b2o2b2ob2o2b2o\$126b2o9bo3bo18bo11b2o47b2o11bo17bo\$126bobo3b2o2bo3bo18b2o73b2o17b2o5bo3b3o\$126bo4b2obo24b2o73b2o18b2obo2bo5bo\$129bo2b3ob2obo118bob2o3bo\$118b2o9b2ob3o120bobo3b2o\$118bobo3bo4bobo129bo10b3o\$118bo3b3ob2o3b2o129b2o2b3o5bo\$121b2o8b2o129b2ob3ob2o2bo\$124b3o4bo128bo10bo\$122bo3b3o131bo4b2obobo\$121bo6bo136bob2o\$121bo2bob2o135bobo3b2o\$120b2obo146b2o\$120bobo146bo\$112b3o4b4o148b2o5b2o\$112bo5bo3b2o147b3o3bobo\$113bo3bo3b3o147b4o4bo\$115b2o3bobo148bo2b2o\$114b2o3b2obo148b2ob3o\$113b3o2bobo154b2ob2o\$106bo4b2o157b2o5b2obo\$105b2o4bo2b2o160bo3bo4b2o\$105bobo5b2o164b2o3bob2o\$107bo3bob2o161bo2bo6bo\$108bobo166bob2obo3bo\$105bobob2o3bo162bo2b3o3bo\$106bob3o168b4o3bo\$101bo8bobo167b3o\$100b4o3bo182b2o\$100bo2b3ob2o176b3o3b2o\$102bo3bobo173b2ob4obo\$103b2ob2o178bo\$105b2o181bo\$98b3o2b3o181bo2bob2o\$98bo2b2obo180bo3b3obo\$99b2ob2o185b3obo\$96b5obo191b2o\$95b2o2bo195b2o\$94b3o196b2o2bo\$88b2o6bo199bo\$88bo2b2o205b2o2b3o\$88bo3bobo203b4o2bo\$85b2o3bo2bo208bobobo\$84b2o4bo208bobobob3o\$85bobo219bo\$82b3o220bo\$82bo2bo222b3o\$82bobo225bo\$83bobo220b2o\$83bo225bo\$82b2obo222b2o\$82b2o223bo\$80bo227bo2bo\$79bobo229b2o\$78b2o230b4o\$78bobo232bo\$75b3o2bo232bob2o\$71bo3bo236b3obo\$70b2o4b2o235b2obo3b2o\$70bobo2b3o237bo5b2o\$76b2o235b3o3bobo\$72bobo239bobobob2o\$64bo6b2o2bo239b2obobo\$63b6o2b3o242b2o2bo3bo2b2o\$63bo7b2o3bo240b3o3bo4b2o\$64bo253bob2o2bob2o\$72bo246b2o2bobo\$66b4o2bo250b2o\$67b3o252b4o\$62b3ob4o256bob2o\$56b3o2bo2b3obo253bo6bo4b2o\$56bo4b2o263b2o2bo2bobo\$57bo4bo3b2o256bob3ob2o3bo\$60b2obobo262bob3o\$59b3o270bo\$47b2o9b3o272bo\$47bobo7b2o271bo3bo8b3o\$47bo8b3obo270bo3bo9bo\$50bo3bob5obo267b3o2b3o6bo\$49bobob2o7bo270bobob3o2bo\$49bo3bobo275b6o3bob2o\$48bo2b2o280b2o2bo5bo\$48b2o2bo285bo2bob2o\$43b2o3b2obo289bo\$43bobo3bob3o284bob2obo3b3o\$43bo294bobo2bo5bo\$48b2o3bo285b2o7bo\$38b2o6bob2o294b3o6bo\$37b2o6b3o297bo7b2o\$38bo2bob3o4b2o289b4o2bo4bobo\$38b2obo300b2ob4obo\$38b2o5bo299b2obo2bobo\$35bo8bobo298b3o3b3o\$34b5o2bo309bo4b2o\$34bo2b2o2bo2bobo299bobo3b2o3b2o\$36b3o4b2o301bo2bo2b3obo\$41bobo306b5o\$40b3o303bo6b2o\$38b2o308bo4bo\$349bo\$38bo2bo310b2o\$38bo2bo310b2o\$34bo4b2o\$33bobo2b2o310bo2bo\$32bo6bo310bo2bo\$36bo314b2o4bo\$33b2obo3bo311b2o2bobo\$35bobo2bo311bo6bo\$37bobo315bo\$32b2o317bo3bob2o\$28bo3bobo4bo311bo2bobo\$26bo2bo3bo4bobo311bobo\$20bo3b3o2bo8bo2bo316b2o\$19bo4b2ob2o8bo2bo311bo4bobo3bo\$19bo7b2o8b4o2b2o306bobo4bo3bo2bo\$19b3obo2bo2bo7bo3b4o305bo2bo8bo2b3o3bo\$19bobo4bobo9bo2bo309bo2bo8b2ob2o4bo\$17bob2o18bo307b2o2b4o8b2o7bo\$17bobo18bo308b4o3bo7bo2bo2bob3o\$17b3o18bo311bo2bo9bobo4bobo\$11bobo25b2o311bo18b2obo\$9bobobobo20b2ob2o312bo18bobo\$7b2o2b2o2b2o22b2o312bo18b3o\$7bob2o2b4o20bobo311b2o25bobo\$7b2o4bo23b3o311b2ob2o20bobobobo\$14bo21bo314b2o22b2o2b2o2b2o\$5bo6bo23b3ob2o310bobo20b4o2b2obo\$4bo4bob2o27bobo309b3o23bo4b2o\$3b2ob2o2b2o25b2obobo312bo21bo\$4b2o31b3o310b2ob3o23bo6bo\$3b2o32bobo309bobo27b2obo4bo\$2b3o28bo6bo308bobob2o25b2o2b2ob2o\$2o30bo2bo2b2o312b3o31b2o\$32bo2b4o313bobo32b2o\$obo30b2ob2o313bo6bo28b3o\$bo34b2o314b2o2bo2bo30b2o\$36bo316b4o2bo\$36bo317b2ob2o30bobo\$36bo317b2o34bo\$30b2o323bo\$29b2ob3o320bo\$29b2o2b2o320bo\$29bo2bobo325b2o\$29b4ob2o321b3ob2o\$32bob2o321b2o2b2o\$29b3o325bobo2bo\$356b2ob4o\$29b2o325b2obo\$28bobo329b3o\$28b2o\$30bobo328b2o\$32bo328bobo\$362b2o\$32bo326bobo\$30bobo326bo\$28b2o\$28bobo328bo\$29b2o328bobo\$362b2o\$29b3o329bobo\$32bob2o325b2o\$29b4ob2o\$29bo2bobo325b3o\$29b2o2b2o321b2obo\$29b2ob3o321b2ob4o\$30b2o325bobo2bo\$36bo320b2o2b2o\$36bo320b3ob2o\$36bo323b2o\$bo34b2o317bo\$obo30b2ob2o317bo\$32bo2b4o316bo\$2o30bo2bo2b2o314b2o34bo\$2b3o28bo6bo313b2ob2o30bobo\$3b2o32bobo313b4o2bo\$4b2o31b3o312b2o2bo2bo30b2o\$3b2ob2o2b2o25b2obobo308bo6bo28b3o\$4bo4bob2o27bobo309bobo32b2o\$5bo6bo23b3ob2o310b3o31b2o\$14bo21bo312bobob2o25b2o2b2ob2o\$7b2o4bo23b3o309bobo27b2obo4bo\$7bob2o2b4o20bobo310b2ob3o23bo6bo\$7b2o2b2o2b2o22b2o314bo21bo\$9bobobobo20b2ob2o311b3o23bo4b2o\$11bobo25b2o311bobo20b4o2b2obo\$17b3o18bo312b2o22b2o2b2o2b2o\$17bobo18bo312b2ob2o20bobobobo\$17bob2o18bo311b2o25bobo\$19bobo4bobo9bo2bo311bo18b3o\$19b3obo2bo2bo7bo3b4o308bo18bobo\$19bo7b2o8b4o2b2o307bo18b2obo\$19bo4b2ob2o8bo2bo309bo2bo9bobo4bobo\$20bo3b3o2bo8bo2bo305b4o3bo7bo2bo2bob3o\$26bo2bo3bo4bobo306b2o2b4o8b2o7bo\$28bo3bobo4bo311bo2bo8b2ob2o4bo\$32b2o316bo2bo8bo2b3o3bo\$37bobo311bobo4bo3bo2bo\$35bobo2bo311bo4bobo3bo\$33b2obo3bo317b2o\$36bo315bobo\$32bo6bo311bo2bobo\$33bobo2b2o311bo3bob2o\$34bo4b2o314bo\$38bo2bo310bo6bo\$38bo2bo310b2o2bobo\$351b2o4bo\$38b2o310bo2bo\$38b2o310bo2bo\$42bo\$38bo4bo308b2o\$37b2o6bo303b3o\$37b5o306bobo\$35bob3o2bo2bo301b2o4b3o\$33b2o3b2o3bobo299bobo2bo2b2o2bo\$34b2o4bo309bo2b5o\$38b3o3b3o298bobo8bo\$38bobo2bob2o299bo5b2o\$41bob4ob2o300bob2o\$37bobo4bo2b4o289b2o4b3obo2bo\$37b2o7bo297b3o6b2o\$38bo6b3o294b2obo6b2o\$43bo7b2o285bo3b2o\$42bo5bo2bobo294bo\$42b3o3bob2obo284b3obo3bobo\$50bo289bob2o3b2o\$47b2obo2bo285bo2b2o\$48bo5bo2b2o280b2o2bo\$48b2obo3b6o275bobo3bo\$49bo2b3obobo270bo7b2obobo\$47bo6b3o2b3o267bob5obo3bo\$46bo9bo3bo270bob3o8bo\$46b3o8bo3bo271b2o7bobo\$58bo272b3o9b2o\$59bo270b3o\$59b3obo262bobob2o\$56bo3b2ob3obo256b2o3bo4bo\$56bobo2bo2b2o263b2o4bo\$56b2o4bo6bo253bob3o2bo2b3o\$62b2obo256b4ob3o\$66b4o252b3o\$67b2o250bo2b4o\$66bobo2b2o246bo\$64b2obo2b2obo253bo\$62b2o4bo3b3o240bo3b2o7bo\$63b2o2bo3bo2b2o242b3o2b6o\$71bobob2o239bo2b2o6bo\$70b2obobobo239bobo\$70bobo3b3o235b2o\$69b2o5bo237b3o2bobo\$70b2o3bob2o235b2o4b2o\$75bob3o236bo3bo\$75b2obo232bo2b3o\$78bo232bobo\$78b4o230b2o\$79b2o229bobo\$80bo2bo227bo\$84bo223b2o\$82b2o222bob2o\$82bo225bo\$84b2o220bobo\$81bo225bobo\$81b3o222bo2bo\$86bo220b3o\$84bo219bobo\$84b3obobobo208bo4b2o\$85bobobo208bo2bo3b2o\$87bo2b4o203bobo3bo\$87b3o2b2o205b2o2bo\$95bo199bo6b2o\$94bo2b2o196b3o\$95b2o195bo2b2o\$96b2o191bob5o\$98bob3o185b2ob2o\$98bob3o3bo180bob2o2bo\$98b2obo2bo181b3o2b3o\$103bo181b2o\$105bo178b2ob2o\$101bob4ob2o173bobo3bo\$99b2o3b3o176b2ob3o2bo\$100b2o182bo3b4o\$109b3o167bobo8bo\$105bo3b4o168b3obo\$105bo3b3o2bo162bo3b2obobo\$105bo3bob2obo166bobo\$105bo6bo2bo161b2obo3bo\$104b2obo3b2o164b2o5bobo\$105b2o4bo3bo160b2o2bo4b2o\$111bob2o5b2o157b2o4bo\$112b2ob2o154bobo2b3o\$115b3ob2o148bob2o3b2o\$116b2o2bo148bobo3b2o\$112bo4b4o147b3o3bo3bo\$112bobo3b3o147b2o3bo5bo\$112b2o5b2o148b4o4b3o\$122bo146bobo\$120b2o146bob2o\$121b2o3bobo135b2obo2bo\$123b2obo136bo6bo\$121bobob2o4bo131b3o3bo\$120bo10bo128bo4b3o\$118bo2b2ob3ob2o129b2o8b2o\$117bo5b3o2b2o129b2o3b2ob3o3bo\$117b3o10bo129bobo4bo3bobo\$129b2o3bobo120b3ob2o9b2o\$126bo3b2obo118bob2ob3o2bo\$125bo5bo2bob2o18b2o73b2o24bob2o4bo\$125b3o3bo5b2o17b2o73b2o18bo3bo2b2o3bobo\$139bo17bo11b2o47b2o11bo18bo3bo9b2o\$131b2o2b2ob2o2b2o10bo2b2o9bo51bo9b2o2bo10b2o6bo5bo\$139bo4bo3b2o3bob2o5b3o3b3o2bo41bo2b3o3b3o5b2obo3b2o3bo8bo2b3o\$129bo2b2o6bo3b3o3bobo3bo2bo2b5o4b2obo39bob2o4b5o2bo2bo3bobo3b3o3b2o3b3obo2bo\$129b5ob3o2bob2obo7b2obobob2o4bobob2o2b2o37b2o2b2obobo4b2obobob2o7bob2ob2ob5ob2o2b2o\$130bo4b3o11b2o4b3o5bob2obob3o2b3o33b3o2b3obob2obo5b3o4b2o12b3o5b2o\$135bobo9b2o14bo3b2o6b6o27b6o6b2o3bo14b2o\$134b2o9bo3bo24b2o9b2o15b2o9b2o24bo3bo10bobo\$135b2o7bo3bo3bo23bo5b5o15b5o5bo23bo3bo3bo10b2o\$145bo2bo2bobo19bo2bo5b2o21b2o5bo2bo19bobo2bo2bo11bo\$146bo4b2o21b2o6bob3o5b2ob2o5b3obo6b2o21b2o4bo\$181bo3bobo13bobo3bo\$181b3obobob2obo3bob2obobob3o\$153b2o2bo24b4obobobo5bobobob4o24bo2b2o\$152bo2b2obo31b2o5b2o31bob2o2bo\$155b2o75b2o\$153b2o2b2o71b2o2b2o\$154b2o77b2o\$154b2o77b2o\$157bo73bo2\$157b2o71b2o\$154bo2bobo69bobo2bo\$155b7o65b7o\$161bo65bo\$159b3o65b3o\$164b2o57b2o\$163b3o57b3o\$165bobo53bobo\$162b2ob2o55b2ob2o\$164bo3b2o49b2o3bo\$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!

calcyman

Posts: 1902
Joined: June 1st, 2009, 4:32 pm