All periods that are multiples of 26 now have non-trivial population-minimised oscillator implementations in Skopje:
Code: Select all
x = 154, y = 115, rule = B2-a/S12
8b5o26b5o30b5o2$9bobo63bobo$9bobo63bobo$10bo29bobo33bo$41bo$41bo2$11bo
65bo$12b2o8bo2bo52b2o$22bo2bo14bo27bo$20b2obobo13bo14bo13bo2b3o19bo$o
2bo18bo2bo13bo11b2obo13bo2bo16b3o2bo$o2bo18bo2bo24bo3bo13bo2b3o16bo2bo
$obob2o45b2obo13bo19b3o2bo$o2bo50bo38bo$o2bo8b2o$14bo4$15bo69bo$14bobo
67bobo$14bobo67bobo2$13b5o65b5o12$10b5o36b5o30b5o2$11bobo73bobo$11bobo
73bobo$12bo39bobo33bo$53bo$53bo2$13bo75bo$14b2o74b2o$52bo$51bo$51bo2$o
3bo71bo3bo$o3b3o69bo3b3o$ob2o2bo69bob2o2bo$o3b3o69bo3b3o$o3bo71bo3bo2$
34bo3bo$32b3o3bo$32bo2b2obo$32b3o3bo$34bo3bo2$60bo$60bo$59bobo$23b2o$
25bo2$58b5o2$26bo$25bobo$25bobo2$24b5o81bo9b2o$108b2o9bo20$149bo3bo$
147b3o3bo$147bo2b2obo$147b3o3bo$149bo3bo5$138b2o$140bo4$141bo$140bobo$
140bobo2$139b5o!
Can someone find a stable or low-period periodic reflector?
Edit: Phase-shifting loops – here a p204 (with four reflectors loop lengths are always multiples of 12 – this is the smallest period with only one repetition), p37 (hence there must be at least one 26-tick gap per repetition), p63 and p100:
Code: Select all
x = 228, y = 55, rule = B2-a/S12
7b7o53b7o59b7o52b7o2$9bobo57bobo122bobo$9bobo57bobo64bo57bobo$9bobo57b
obo63bobo56bobo$69b3o$136bo3$136b2o$69bo67bo63bo$70bo6bo59bo$o69bo4b3o
107bo14b2o$o2bo181bo2bo$o2bo181bo2bo$obob2o153bo25bobob2o$o2bo7bobo20b
o113bo10bo25bo2bo7bobo$o2bo7bo22bo27bobo18bo37bo26bo6b3obo25bo2bo7bo
11bo$o29b3obo29bo16bobo37bo25b2o10bo25bo20b2o$34bo86bob3o29b3obo$30b3o
bo17bo68bo10b2o25bo$34bo17bo68bob3o6bo26bo$17b3o14bo17bob3o64bo10bo69b
3o$17bo34bo10b2o24bo31bo80bo$52bob3o6bo25bo137bo$52bo10bo24bo138bo$52b
o169bobo2bo$143bo74bo2bo5bo$106bo36bo74bo3bobo2bo$23b3o44bo24bo10bo36b
2o72bo9bo$23bobo43bo25bo6b3obo120bo$23bobo43bo24b2o10bo$23bobo76b3obo
37bo68b2o$106bo106bo$21b7o78bo36bobo67bo$144bo$75bobo16bo$75bo18bobo$
141b7o70bo$215b2o$218bo2$81b3o4bo125b7o$81bo6bo$89bo5$87b3o$87bobo$87b
obo$87bobo2$85b7o!
But with six such reflectors there will be a decrease in minimum population for some periods – the glider here takes 666 (6 mod 12) ticks to return to its starting point:
Code: Select all
x = 74, y = 59, rule = B2-a/S12History
15.7A23.7A2$17.A.A27.A.A2$17.A.A26.A3.A2$48.A10$11.C.C$13.C59.A$70.A
2.A$73.A$A67.A2.A.A$A72.A$A.3A65.A2.A$A4.A67.A$A.3A28.A$A32.A$A30.5A
2$32.A.A3$30.7A21$39.A.A$38.5A$39.A.A$39.A.A$40.A2$37.7A!
Edit 2: The above phase-shifting loops have been implemented in Skopje; here's the output for p963, the smallest period for which all periods equal to or longer than it can be represented in this form:
Code: Select all
x = 339, y = 339, rule = B2-a/S12
12b7o2$15bo2$13bo3bo2$14bobo$o$o4bo$o12bobo$ob2o3bo5bo$o$o4bo$o2$19b3o
$19bo5$26b2o$25bo5$32b2o2$32bo4$38b2o$38bo$38bo4$45bo$44bo$44bo5$50bob
o$50bo5$56b3o$56bo3$53bo2$52b2o9b2o$62bo4$60bo$58b2o9b2o2$69bo3$66bo$
64b3o8b2o$75bo$75bo3$72bo$70bobo9bo$81bo$81bo3$78bo$78bo$77bo9bobo$87b
o3$84bo$84bo$83b2o8b3o$93bo3$90bo2$89b2o9b2o$99bo4$97bo$95b2o9b2o2$
106bo3$103bo$101b3o8b2o$112bo$112bo3$109bo$107bobo9bo$118bo$118bo3$
115bo$115bo$114bo9bobo$124bo3$121bo$121bo$120b2o4$127bo2$126b2o5$134bo
$132b2o5$140bo$138b3o5$146bo$144bobo5$152bo$152bo$151bo4$158bo$158bo$
157b2o4$164bo2$163b2o9b2o2$174bo4$180b2o$180bo$180bo4$187bo$186bo$186b
o5$192bobo$192bo5$198b3o$198bo5$205b2o$204bo5$211b2o2$211bo4$217b2o$
217bo$217bo3$214bo$212bobo9bo$223bo$223bo3$220bo$220bo$219bo9bobo$229b
o3$226bo$226bo$225b2o8b3o$235bo3$232bo2$231b2o9b2o$241bo4$239bo$237b2o
9b2o2$248bo3$245bo$243b3o8b2o$254bo$254bo3$251bo$249bobo9bo$260bo$260b
o3$257bo$257bo$256bo9bobo$266bo3$263bo$263bo$262b2o8b3o$272bo3$269bo2$
268b2o9b2o$278bo4$276bo$274b2o9b2o2$285bo3$282bo$280b3o5$288bo$286bobo
5$294bo$294bo$293bo4$300bo$300bo$299b2o4$306bo2$305b2o5$313bo$311b2o5$
319bo$317b3o2$338bo$333bo4bo$338bo$325bo5bo3b2obo$323bobo12bo$333bo4bo
$338bo$322bobo2$321bo3bo2$323bo2$320b7o!
The maximum number of gliders (25×12 = 300) is attained at (e.g.) p977:
Code: Select all
x = 995, y = 995, rule = B2-a/S12
12b7o2$15bo2$13bo3bo2$14bobo$o$o4bo$o12bobo$ob2o3bo5bo$o$o4bo$o2$
19b3o$19bo5$26b2o$19bo5bo$17b3o4$32b2o$25bo$23bobo6bo4$38b2o$31bo
6bo$31bo6bo$30bo3$45bo$37bo6bo$37bo6bo$36b2o4$43bo6bobo$50bo$42b2o
4$56b3o$50bo5bo$48b2o4$63b2o$56bo5bo$54b3o4$69b2o$62bo$60bobo6bo4$
75b2o$68bo6bo$68bo6bo$67bo3$82bo$74bo6bo$74bo6bo$73b2o4$80bo6bobo$
87bo$79b2o4$93b3o$87bo5bo$85b2o4$100b2o$93bo5bo$91b3o4$106b2o$99bo
$97bobo6bo4$112b2o$105bo6bo$105bo6bo$104bo3$119bo$111bo6bo$111bo6b
o$110b2o4$117bo6bobo$124bo$116b2o4$130b3o$124bo5bo$122b2o4$137b2o$
130bo5bo$128b3o4$143b2o$136bo$134bobo6bo4$149b2o$142bo6bo$142bo6bo
$141bo3$156bo$148bo6bo$148bo6bo$147b2o4$154bo6bobo$161bo$153b2o5$
161bo$159b2o5$167bo$165b3o9bo$176bo$176bo5$182bobo$182bo5$188b3o$
182bo5bo$180b2o4$195b2o$188bo5bo$186b3o4$201b2o$194bo$192bobo6bo4$
207b2o$200bo6bo$200bo6bo$199bo3$214bo$206bo6bo$206bo6bo$205b2o4$
212bo6bobo$219bo$211b2o4$225b3o$219bo5bo$217b2o4$232b2o$225bo5bo$
223b3o4$238b2o$231bo$229bobo6bo4$244b2o$237bo6bo$237bo6bo$236bo3$
251bo$243bo6bo$243bo6bo$242b2o4$249bo6bobo$256bo$248b2o4$262b3o$
256bo5bo$254b2o4$269b2o$262bo5bo$260b3o4$275b2o$268bo$266bobo6bo4$
281b2o$274bo6bo$274bo6bo$273bo3$288bo$280bo6bo$280bo6bo$279b2o4$
286bo6bobo$293bo$285b2o4$299b3o$293bo5bo$291b2o4$306b2o$299bo5bo$
297b3o4$312b2o$305bo$303bobo6bo4$318b2o$311bo6bo$311bo6bo$310bo3$
325bo$317bo6bo$317bo6bo$316b2o4$323bo2$322b2o5$330bo$328b2o9b2o$
339bo$339bo4$346bo$345bo$345bo5$344bo6bobo$351bo$343b2o4$357b3o$
351bo5bo$349b2o4$364b2o$357bo5bo$355b3o4$370b2o$363bo$361bobo6bo4$
376b2o$369bo6bo$369bo6bo$368bo3$383bo$375bo6bo$375bo6bo$374b2o4$
381bo6bobo$388bo$380b2o4$394b3o$388bo5bo$386b2o4$401b2o$394bo5bo$
392b3o4$407b2o$400bo$398bobo6bo4$413b2o$406bo6bo$406bo6bo$405bo3$
420bo$412bo6bo$412bo6bo$411b2o4$418bo6bobo$425bo$417b2o4$431b3o$
425bo5bo$423b2o4$438b2o$431bo5bo$429b3o4$444b2o$437bo$435bobo6bo4$
450b2o$443bo6bo$443bo6bo$442bo3$457bo$449bo6bo$449bo6bo$448b2o4$
455bo6bobo$462bo$454b2o4$468b3o$462bo5bo$460b2o4$475b2o$468bo5bo$
466b3o4$481b2o$474bo$472bobo6bo4$487b2o$480bo6bo$480bo6bo$479bo4$
486bo$486bo$485b2o4$492bo2$491b2o9b2o2$502bo4$508b2o$508bo$508bo4$
515bo$507bo6bo$507bo6bo$506b2o4$513bo6bobo$520bo$512b2o4$526b3o$
520bo5bo$518b2o4$533b2o$526bo5bo$524b3o4$539b2o$532bo$530bobo6bo4$
545b2o$538bo6bo$538bo6bo$537bo3$552bo$544bo6bo$544bo6bo$543b2o4$
550bo6bobo$557bo$549b2o4$563b3o$557bo5bo$555b2o4$570b2o$563bo5bo$
561b3o4$576b2o$569bo$567bobo6bo4$582b2o$575bo6bo$575bo6bo$574bo3$
589bo$581bo6bo$581bo6bo$580b2o4$587bo6bobo$594bo$586b2o4$600b3o$
594bo5bo$592b2o4$607b2o$600bo5bo$598b3o4$613b2o$606bo$604bobo6bo4$
619b2o$612bo6bo$612bo6bo$611bo3$626bo$618bo6bo$618bo6bo$617b2o4$
624bo6bobo$631bo$623b2o4$637b3o$631bo5bo$629b2o4$644b2o$637bo5bo$
635b3o4$650b2o$643bo$641bobo6bo5$649bo$649bo$648bo4$655bo$655bo$
654b2o9b2o$664bo5$671b2o2$671bo4$677b2o$670bo6bo$670bo6bo$669bo3$
684bo$676bo6bo$676bo6bo$675b2o4$682bo6bobo$689bo$681b2o4$695b3o$
689bo5bo$687b2o4$702b2o$695bo5bo$693b3o4$708b2o$701bo$699bobo6bo4$
714b2o$707bo6bo$707bo6bo$706bo3$721bo$713bo6bo$713bo6bo$712b2o4$
719bo6bobo$726bo$718b2o4$732b3o$726bo5bo$724b2o4$739b2o$732bo5bo$
730b3o4$745b2o$738bo$736bobo6bo4$751b2o$744bo6bo$744bo6bo$743bo3$
758bo$750bo6bo$750bo6bo$749b2o4$756bo6bobo$763bo$755b2o4$769b3o$
763bo5bo$761b2o4$776b2o$769bo5bo$767b3o4$782b2o$775bo$773bobo6bo4$
788b2o$781bo6bo$781bo6bo$780bo3$795bo$787bo6bo$787bo6bo$786b2o4$
793bo6bobo$800bo$792b2o4$806b3o$800bo5bo$798b2o4$813b2o$806bo5bo$
804b3o5$812bo$810bobo5$818bo$818bo$817bo9b3o$827bo5$834b2o$833bo5$
840b2o$833bo$831bobo6bo4$846b2o$839bo6bo$839bo6bo$838bo3$853bo$
845bo6bo$845bo6bo$844b2o4$851bo6bobo$858bo$850b2o4$864b3o$858bo5bo
$856b2o4$871b2o$864bo5bo$862b3o4$877b2o$870bo$868bobo6bo4$883b2o$
876bo6bo$876bo6bo$875bo3$890bo$882bo6bo$882bo6bo$881b2o4$888bo6bob
o$895bo$887b2o4$901b3o$895bo5bo$893b2o4$908b2o$901bo5bo$899b3o4$
914b2o$907bo$905bobo6bo4$920b2o$913bo6bo$913bo6bo$912bo3$927bo$
919bo6bo$919bo6bo$918b2o4$925bo6bobo$932bo$924b2o4$938b3o$932bo5bo
$930b2o4$945b2o$938bo5bo$936b3o4$951b2o$944bo$942bobo6bo4$957b2o$
950bo6bo$950bo6bo$949bo3$964bo$956bo6bo$956bo6bo$955b2o4$962bo6bob
o$969bo$961b2o4$975b3o$969bo5bo$967b2o5$975bo$973b3o2$994bo$989bo
4bo$994bo$981bo5bo3b2obo$979bobo12bo$989bo4bo$994bo$978bobo2$977bo
3bo2$979bo2$976b7o!