Thread for basic questions

For general discussion about Conway's Game of Life.
HartmutHolzwart
Posts: 840
Joined: June 27th, 2009, 10:58 am
Location: Germany

Re: Thread for basic questions

Post by HartmutHolzwart » January 3rd, 2021, 6:03 am

BTW., I never noticed the wonderful graph function of life viewer! Really great!

Is there a way to feed this into Wolfram alpha or other tools that analyze the pop plot automatically?

MathAndCode
Posts: 5141
Joined: August 31st, 2020, 5:58 pm

Re: Thread for basic questions

Post by MathAndCode » January 3rd, 2021, 11:55 pm

The crystal sequence includes a traffic light, so it only works if the glider stream has even period. What are the crystal analog(s) for when a glider stream of odd period is fired at some junk?
I am tentatively considering myself back.

Hunting
Posts: 4395
Joined: September 11th, 2017, 2:54 am

Re: Thread for basic questions

Post by Hunting » January 4th, 2021, 1:26 am

GUYTU6J wrote:
January 2nd, 2021, 12:11 pm
Bumping up one of my earlier questions...
77topaz wrote:
February 5th, 2020, 2:27 am
GUYTU6J wrote:
February 5th, 2020, 1:37 am
What's the growth rate?
...

Code: Select all

x = 7, y = 9, rule = B2n3aikq4ceiz6c/S2-i3-a4i
2b3o$2bobo$2bo2b2o$3bo2bo$4b3o$3bo$2bo$obo$3o!
#C [[ GRAPH ]]
...For the second, the growth rate is asymptotically quadratic.
The quadratic element is actually due to the outermost MMS breeder. By putting the central region into a torus, it gets rid of that factor:

Code: Select all

x = 1506, y = 1511, rule = B2n3aikq4ceiz6c/S2-i3-a4i:T1506,1511
706bo$705bobo$706b2o2$744bo$743bobo$743b2o9$706bo$379bo325bobo$378bobo
325b2o$377bo3bo$376bo5bo361bo$375bo7bo359bobo$376bo5bo360b2o$377bo3bo$
378bobo$379bo6$706bo$705bobo$706b2o2$744bo$743bobo$743b2o9$706bo$394bo
310bobo$393bobo310b2o$392bo3bo$391bo5bo346bo$390bo7bo344bobo$391bo5bo
345b2o$392bo3bo$393bobo$394bo6$706bo$705bobo$706b2o2$744bo$743bobo$
743b2o9$706bo$409bo295bobo$408bobo295b2o$407bo3bo$406bo5bo331bo$405bo
7bo329bobo$406bo5bo330b2o$407bo3bo$408bobo$409bo6$706bo$705bobo$706b2o
2$744bo$743bobo$743b2o9$706bo$424bo280bobo$423bobo280b2o$422bo3bo$421b
o5bo316bo$420bo7bo314bobo$421bo5bo315b2o$422bo3bo$423bobo$424bo6$706bo
$705bobo$706b2o2$744bo$743bobo$743b2o9$706bo$439bo265bobo$438bobo265b
2o$437bo3bo$436bo5bo301bo$435bo7bo299bobo$436bo5bo300b2o$437bo3bo$438b
obo$439bo6$706bo$705bobo$706b2o2$744bo$743bobo$743b2o9$706bo$454bo250b
obo$453bobo250b2o$452bo3bo$451bo5bo286bo$450bo7bo284bobo$451bo5bo285b
2o$452bo3bo$453bobo$454bo6$706bo$705bobo$706b2o2$744bo$743bobo$743b2o
9$706bo$469bo235bobo$468bobo235b2o$467bo3bo$466bo5bo271bo$465bo7bo269b
obo$466bo5bo270b2o$467bo3bo$468bobo$469bo6$706bo$705bobo$706b2o2$744bo
$743bobo$743b2o9$706bo$484bo220bobo$483bobo220b2o$482bo3bo$481bo5bo
256bo$480bo7bo254bobo$481bo5bo255b2o$482bo3bo$483bobo$484bo6$706bo$
705bobo$706b2o2$744bo$743bobo$743b2o9$706bo$499bo205bobo$498bobo205b2o
$497bo3bo$496bo5bo241bo$495bo7bo239bobo$496bo5bo240b2o$497bo3bo$498bob
o$499bo6$706bo$705bobo$706b2o2$744bo$743bobo$743b2o9$706bo$514bo190bob
o$513bobo190b2o$512bo3bo$511bo5bo226bo$510bo7bo224bobo$511bo5bo225b2o$
512bo3bo$513bobo$514bo6$706bo$705bobo$706b2o2$744bo$743bobo$743b2o9$
706bo$529bo175bobo$528bobo175b2o$527bo3bo$526bo5bo211bo$525bo7bo209bob
o$526bo5bo210b2o$527bo3bo$528bobo$529bo6$706bo$705bobo$706b2o2$744bo$
743bobo$743b2o9$706bo768bo$544bo160bobo766bobo$543bobo160b2o765bo3bo$
542bo3bo925bo5bo$541bo5bo196bo726bo7bo$540bo7bo194bobo726bo5bo$541bo5b
o195b2o728bo3bo$542bo3bo927bobo$543bobo929bo$544bo6$706bo738bo$705bobo
736bobo$706b2o735bo3bo$1442bo5bo$744bo696bo7bo$743bobo696bo5bo$743b2o
698bo3bo$1444bobo$1445bo7$706bo708bo$559bo145bobo706bobo$558bobo145b2o
705bo3bo$557bo3bo850bo5bo$556bo5bo181bo666bo7bo$555bo7bo179bobo666bo5b
o$556bo5bo180b2o668bo3bo$557bo3bo852bobo$558bobo854bo$559bo6$706bo678b
o$705bobo676bobo$706b2o675bo3bo$1382bo5bo$744bo636bo7bo$743bobo636bo5b
o$743b2o638bo3bo$1384bobo$1385bo7$706bo648bo$574bo130bobo646bobo$573bo
bo130b2o645bo3bo$572bo3bo775bo5bo$571bo5bo166bo606bo7bo$570bo7bo164bob
o606bo5bo$571bo5bo165b2o608bo3bo$572bo3bo777bobo$573bobo779bo$574bo6$
706bo618bo$705bobo616bobo$706b2o615bo3bo$1322bo5bo$744bo576bo7bo$743bo
bo576bo5bo$743b2o578bo3bo$1324bobo$1325bo7$706bo588bo$589bo115bobo586b
obo$588bobo115b2o585bo3bo$587bo3bo700bo5bo$586bo5bo151bo546bo7bo$585bo
7bo149bobo546bo5bo$586bo5bo150b2o548bo3bo$587bo3bo702bobo$588bobo704bo
$589bo6$706bo558bo$705bobo556bobo$706b2o555bo3bo$1262bo5bo$744bo516bo
7bo$743bobo516bo5bo$743b2o518bo3bo$1264bobo$1265bo7$706bo528bo$604bo
100bobo526bobo$603bobo100b2o525bo3bo$602bo3bo625bo5bo$601bo5bo136bo
486bo7bo$600bo7bo134bobo486bo5bo$601bo5bo135b2o488bo3bo$602bo3bo627bob
o$603bobo629bo$604bo6$706bo498bo$705bobo496bobo$706b2o495bo3bo$1202bo
5bo$744bo456bo7bo$743bobo456bo5bo$743b2o458bo3bo$1204bobo$1205bo7$706b
o468bo$619bo85bobo466bobo$618bobo85b2o465bo3bo$617bo3bo550bo5bo$616bo
5bo121bo426bo7bo$615bo7bo119bobo426bo5bo$616bo5bo120b2o428bo3bo$617bo
3bo552bobo$618bobo554bo$619bo6$706bo438bo$705bobo436bobo$706b2o435bo3b
o$1142bo5bo$744bo396bo7bo$743bobo396bo5bo$743b2o398bo3bo$1144bobo$
1145bo7$706bo408bo$634bo70bobo406bobo$633bobo70b2o405bo3bo$632bo3bo
475bo5bo$631bo5bo106bo366bo7bo$630bo7bo104bobo366bo5bo$631bo5bo105b2o
368bo3bo$632bo3bo477bobo$633bobo479bo$634bo6$706bo378bo$705bobo376bobo
$706b2o375bo3bo$1082bo5bo$744bo336bo7bo$743bobo336bo5bo$743b2o338bo3bo
$1084bobo$1085bo7$706bo348bo$649bo55bobo346bobo$648bobo55b2o345bo3bo$
647bo3bo400bo5bo$646bo5bo91bo306bo7bo$645bo7bo89bobo306bo5bo$646bo5bo
90b2o308bo3bo$647bo3bo402bobo$648bobo404bo$649bo6$706bo318bo$705bobo
316bobo$706b2o315bo3bo$1022bo5bo$744bo276bo7bo$743bobo276bo5bo$743b2o
278bo3bo$1024bobo$1025bo7$706bo288bo$664bo40bobo286bobo$663bobo40b2o
285bo3bo$662bo3bo325bo5bo$661bo5bo76bo246bo7bo$660bo7bo74bobo246bo5bo$
661bo5bo75b2o248bo3bo$662bo3bo327bobo$663bobo329bo$664bo6$706bo258bo$
705bobo256bobo$706b2o255bo3bo$962bo5bo$744bo216bo7bo$743bobo216bo5bo$
743b2o218bo3bo$964bobo$965bo7$706bo228bo$679bo25bobo226bobo$678bobo25b
2o225bo3bo$677bo3bo250bo5bo$676bo5bo61bo186bo7bo$675bo7bo59bobo186bo5b
o$676bo5bo60b2o188bo3bo$677bo3bo252bobo$678bobo254bo$679bo6$706bo198bo
$705bobo196bobo$706b2o195bo3bo$902bo5bo$744bo156bo7bo$743bobo156bo5bo$
743b2o158bo3bo$904bobo$905bo7$706bo168bo$694bo10bobo166bobo$693bobo10b
2o165bo3bo$692bo3bo175bo5bo$691bo5bo46bo126bo7bo$690bo7bo44bobo126bo5b
o$691bo5bo45b2o128bo3bo$692bo3bo177bobo$693bobo179bo$694bo6$845bo$844b
obo$843bo3bo$842bo5bo$744bo96bo7bo$743bobo96bo5bo$743b2o98bo3bo$844bob
o$704b2o139bo$703bobo$704bo5$815bo$781bo32bobo$780bobo30bo3bo$779bo2bo
29bo5bo$779bobo29bo7bo$778b2o2bo29bo5bo$780bobo30bo3bo$781bo32bobo$
692b2ob2ob2ob2ob2o76bo32bo$691bo2bo2bo2bo2bobo76bo$692bo3bo7bo76bo$
693b3o9bobo74bo$695bo10b2o74bo$781bo14bo$780bobo12bobo$779bob2o13b2o
21bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo$778bo39bobo12bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo$778b2o38b2o13b
2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o28$5bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo$4bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo$5b2o13b2o
13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o
13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o
13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o
13b2o13b2o$740b3o$740bobo$740bo2b2o$741bo2bo$742b3o$741bo57b2o13b2o13b
2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b
2o13b2o13b2o$740bo58bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo$738bobo59bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo$738b3o27$b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o
13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o
13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o
13b2o13b2o13b2o13b2o13b2o13b2o13b2o13b2o38b2o$obo12bobo12bobo12bobo12b
obo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bo
bo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo12bobo
12bobo12bobo12bobo12bobo12bobo12bobo39bo$bo14bo14bo14bo14bo14bo14bo14b
o14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo14bo
14bo14bo14bo21b2o13b2obo$683bobo12bobo$684bo14bo$698bo74b2o10bo$698bo
74bobo9b3o$699bo76bo7bo3bo$698bo76bobo2bo2bo2bo2bo$665bo32bo76b2ob2ob
2ob2ob2o$664bobo32bo$663bo3bo30bobo$662bo5bo29bo2b2o$661bo7bo29bobo$
662bo5bo29bo2bo$663bo3bo30bobo$664bobo32bo$665bo5$776bo$775bobo$635bo
139b2o$634bobo$633bo3bo98b2o$632bo5bo96bobo$631bo7bo96bo$632bo5bo$633b
o3bo$634bobo$635bo6$786bo$605bo179bobo$604bobo177bo3bo$603bo3bo128b2o
45bo5bo$602bo5bo126bobo44bo7bo$601bo7bo126bo46bo5bo$602bo5bo175bo3bo$
603bo3bo165b2o10bobo$604bobo166bobo10bo$605bo168bo7$575bo$574bobo$573b
o3bo158b2o$572bo5bo156bobo$571bo7bo156bo$572bo5bo$573bo3bo195b2o$574bo
bo196bobo$575bo198bo6$801bo$545bo254bobo$544bobo252bo3bo$543bo3bo188b
2o60bo5bo$542bo5bo186bobo59bo7bo$541bo7bo186bo61bo5bo$542bo5bo250bo3bo
$543bo3bo225b2o25bobo$544bobo226bobo25bo$545bo228bo7$515bo$514bobo$
513bo3bo218b2o$512bo5bo216bobo$511bo7bo216bo$512bo5bo$513bo3bo255b2o$
514bobo256bobo$515bo258bo6$816bo$485bo329bobo$484bobo327bo3bo$483bo3bo
248b2o75bo5bo$482bo5bo246bobo74bo7bo$481bo7bo246bo76bo5bo$482bo5bo325b
o3bo$483bo3bo285b2o40bobo$484bobo286bobo40bo$485bo288bo7$455bo$454bobo
$453bo3bo278b2o$452bo5bo276bobo$451bo7bo276bo$452bo5bo$453bo3bo315b2o$
454bobo316bobo$455bo318bo6$831bo$425bo404bobo$424bobo402bo3bo$423bo3bo
308b2o90bo5bo$422bo5bo306bobo89bo7bo$421bo7bo306bo91bo5bo$422bo5bo400b
o3bo$423bo3bo345b2o55bobo$424bobo346bobo55bo$425bo348bo7$395bo$394bobo
$393bo3bo338b2o$392bo5bo336bobo$391bo7bo336bo$392bo5bo$393bo3bo375b2o$
394bobo376bobo$395bo378bo6$846bo$365bo479bobo$364bobo477bo3bo$363bo3bo
368b2o105bo5bo$362bo5bo366bobo104bo7bo$361bo7bo366bo106bo5bo$362bo5bo
475bo3bo$363bo3bo405b2o70bobo$364bobo406bobo70bo$365bo408bo7$335bo$
334bobo$333bo3bo398b2o$332bo5bo396bobo$331bo7bo396bo$332bo5bo$333bo3bo
435b2o$334bobo436bobo$335bo438bo6$861bo$305bo554bobo$304bobo552bo3bo$
303bo3bo428b2o120bo5bo$302bo5bo426bobo119bo7bo$301bo7bo426bo121bo5bo$
302bo5bo550bo3bo$303bo3bo465b2o85bobo$304bobo466bobo85bo$305bo468bo7$
275bo$274bobo$273bo3bo458b2o$272bo5bo456bobo$271bo7bo456bo$272bo5bo$
273bo3bo495b2o$274bobo496bobo$275bo498bo6$876bo$245bo629bobo$244bobo
627bo3bo$243bo3bo488b2o135bo5bo$242bo5bo486bobo134bo7bo$241bo7bo486bo
136bo5bo$242bo5bo625bo3bo$243bo3bo525b2o100bobo$244bobo526bobo100bo$
245bo528bo7$215bo$214bobo$213bo3bo518b2o$212bo5bo516bobo$211bo7bo516bo
$212bo5bo$213bo3bo555b2o$214bobo556bobo$215bo558bo6$891bo$185bo704bobo
$184bobo702bo3bo$183bo3bo548b2o150bo5bo$182bo5bo546bobo149bo7bo$181bo
7bo546bo151bo5bo$182bo5bo700bo3bo$183bo3bo585b2o115bobo$184bobo586bobo
115bo$185bo588bo7$155bo$154bobo$153bo3bo578b2o$152bo5bo576bobo$151bo7b
o576bo$152bo5bo$153bo3bo615b2o$154bobo616bobo$155bo618bo6$906bo$125bo
779bobo$124bobo777bo3bo$123bo3bo608b2o165bo5bo$122bo5bo606bobo164bo7bo
$121bo7bo606bo166bo5bo$122bo5bo775bo3bo$123bo3bo645b2o130bobo$124bobo
646bobo130bo$125bo648bo7$95bo$94bobo$93bo3bo638b2o$92bo5bo636bobo$91bo
7bo636bo$92bo5bo$93bo3bo675b2o$94bobo676bobo$95bo678bo6$921bo$65bo854b
obo$64bobo852bo3bo$63bo3bo668b2o180bo5bo$62bo5bo666bobo179bo7bo$61bo7b
o666bo181bo5bo$62bo5bo850bo3bo$63bo3bo705b2o145bobo$64bobo706bobo145bo
$65bo708bo7$35bo$34bobo$33bo3bo698b2o$32bo5bo696bobo$31bo7bo696bo$32bo
5bo$33bo3bo735b2o$34bobo736bobo$35bo738bo6$936bo$5bo929bobo$4bobo927bo
3bo$3bo3bo728b2o195bo5bo$2bo5bo726bobo194bo7bo$bo7bo726bo196bo5bo$2bo
5bo925bo3bo$3bo3bo765b2o160bobo$4bobo766bobo160bo$5bo768bo9$736b2o$
735bobo$736bo2$773b2o$773bobo$774bo6$951bo$950bobo$949bo3bo$736b2o210b
o5bo$735bobo209bo7bo$736bo211bo5bo$949bo3bo$773b2o175bobo$773bobo175bo
$774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$774bo6$966bo$965bobo$964b
o3bo$736b2o225bo5bo$735bobo224bo7bo$736bo226bo5bo$964bo3bo$773b2o190bo
bo$773bobo190bo$774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$774bo6$
981bo$980bobo$979bo3bo$736b2o240bo5bo$735bobo239bo7bo$736bo241bo5bo$
979bo3bo$773b2o205bobo$773bobo205bo$774bo9$736b2o$735bobo$736bo2$773b
2o$773bobo$774bo6$996bo$995bobo$994bo3bo$736b2o255bo5bo$735bobo254bo7b
o$736bo256bo5bo$994bo3bo$773b2o220bobo$773bobo220bo$774bo9$736b2o$735b
obo$736bo2$773b2o$773bobo$774bo6$1011bo$1010bobo$1009bo3bo$736b2o270bo
5bo$735bobo269bo7bo$736bo271bo5bo$1009bo3bo$773b2o235bobo$773bobo235bo
$774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$774bo6$1026bo$1025bobo$
1024bo3bo$736b2o285bo5bo$735bobo284bo7bo$736bo286bo5bo$1024bo3bo$773b
2o250bobo$773bobo250bo$774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$
774bo6$1041bo$1040bobo$1039bo3bo$736b2o300bo5bo$735bobo299bo7bo$736bo
301bo5bo$1039bo3bo$773b2o265bobo$773bobo265bo$774bo9$736b2o$735bobo$
736bo2$773b2o$773bobo$774bo6$1056bo$1055bobo$1054bo3bo$736b2o315bo5bo$
735bobo314bo7bo$736bo316bo5bo$1054bo3bo$773b2o280bobo$773bobo280bo$
774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$774bo6$1071bo$1070bobo$
1069bo3bo$736b2o330bo5bo$735bobo329bo7bo$736bo331bo5bo$1069bo3bo$773b
2o295bobo$773bobo295bo$774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$
774bo6$1086bo$1085bobo$1084bo3bo$736b2o345bo5bo$735bobo344bo7bo$736bo
346bo5bo$1084bo3bo$773b2o310bobo$773bobo310bo$774bo9$736b2o$735bobo$
736bo2$773b2o$773bobo$774bo6$1101bo$1100bobo$1099bo3bo$736b2o360bo5bo$
735bobo359bo7bo$736bo361bo5bo$1099bo3bo$773b2o325bobo$773bobo325bo$
774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$774bo6$1116bo$1115bobo$
1114bo3bo$736b2o375bo5bo$735bobo374bo7bo$736bo376bo5bo$1114bo3bo$773b
2o340bobo$773bobo340bo$774bo9$736b2o$735bobo$736bo2$773b2o$773bobo$
774bo6$1131bo$1130bobo$1129bo3bo$736b2o390bo5bo$735bobo389bo7bo$736bo
391bo5bo$1129bo3bo$773b2o355bobo$773bobo355bo$774bo9$736b2o$735bobo$
736bo2$773b2o$773bobo$774bo!
#C [[ GRAPH ]]
So what function does the population plot show now?
I believe it is a ruler function.

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Re: Thread for basic questions

Post by Schiaparelliorbust » January 4th, 2021, 2:12 am

MathAndCode wrote:
January 3rd, 2021, 11:55 pm
The crystal sequence includes a traffic light, so it only works if the glider stream has even period. What are the crystal analog(s) for when a glider stream of odd period is fired at some junk?
I asked a similar question earlier:
Schiaparelliorbust wrote:
December 30th, 2020, 9:57 am
Are there any known crystals other than the basic beehive one?
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Re: Thread for basic questions

Post by Hunting » January 4th, 2021, 5:35 am

Schiaparelliorbust wrote:
January 4th, 2021, 2:12 am
MathAndCode wrote:
January 3rd, 2021, 11:55 pm
The crystal sequence includes a traffic light, so it only works if the glider stream has even period. What are the crystal analog(s) for when a glider stream of odd period is fired at some junk?
I asked a similar question earlier:
Schiaparelliorbust wrote:
December 30th, 2020, 9:57 am
Are there any known crystals other than the basic beehive one?
...Yes, obviously. There are a full collection of them.

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Re: Thread for basic questions

Post by Schiaparelliorbust » January 4th, 2021, 5:43 am

Hunting wrote:
January 4th, 2021, 5:35 am
...Yes, obviously. There are a full collection of them.
The wiki only shows one example.
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Re: Thread for basic questions

Post by Hunting » January 4th, 2021, 5:51 am

Schiaparelliorbust wrote:
January 4th, 2021, 5:43 am
Hunting wrote:
January 4th, 2021, 5:35 am
...Yes, obviously. There are a full collection of them.
The wiki only shows one example.
That's because the term crystal usually refers to only that particular crystal. That one's slow and thus more common than those requiring a specific period. I believe Dean Hickerson have a collection of non-standard crystals.

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Re: Thread for basic questions

Post by bubblegum » January 4th, 2021, 12:53 pm

Schiaparelliorbust wrote:
January 4th, 2021, 5:43 am
The wiki only shows one example.
It only needs to show one example; that's the most common one for gliders.
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Re: Thread for basic questions

Post by MathAndCode » January 4th, 2021, 2:04 pm

bubblegum wrote:
January 4th, 2021, 12:53 pm
It only needs to show one example; that's the most common one for gliders.
Is there not a single common crystal for odd periods, or are odd-period glider streams simply not as common?
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Re: Thread for basic questions

Post by bubblegum » January 4th, 2021, 2:15 pm

MathAndCode wrote:
January 4th, 2021, 2:04 pm
Is there not a single common crystal for odd periods, or are odd-period glider streams simply not as common?
To be honest I have no idea either. (Odd-period glider streams do seem less common though.)
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Re: Thread for basic questions

Post by Schiaparelliorbust » January 4th, 2021, 2:18 pm

Hunting wrote:
January 4th, 2021, 5:51 am
That's because the term crystal usually refers to only that particular crystal. That one's slow and thus more common than those requiring a specific period. I believe Dean Hickerson have a collection of non-standard crystals.
I only found this other one there:

Code: Select all

x = 229, y = 225, rule = B3/S23
31$111bo$109b3o11bo$108bo14b3o$108b2o16bo14bo$125b2o12b3o$85bo52bo$71b
o13b3o50b2o$69b3o16bo$43b2o23bo18b2o29b2o$44bo23b2o47b2o18b2o$44bobo
71b2o17b2o$45b2o2b2o68b3o$49b2o70bo$121bo2$81bobo$81bo3bo$81bo3bo35b2o
$83bo17b2o19bo10b3o$101bobo15b3o10bo3bo$103bo15bo11bo$91b2o10b2o19b2o$
91bo33bo5bo3b2o$43b2o36b2o9b3o27b3o7b3o$42bobo16b2o19bo11bo27bo$42bo
18bobo17bo$41b2o20bo17b2o$57b2o4b2o$57bobo80b2o$59bo80bobo$50b2o7b2o
81bo$50b2o90b2o7$40b2o90b2o$41bo90b2o$41bobo$42b2o79b2obo$123bob2o2$
134b2o$61bo70b2o2bo6b2o$59b3o70b2obo7bo$58bo72bob2o6bobo$58b2o81b2o3$
127b2o3b2o$126bobo$126bo$125b2o$63b2o$63bo$61bobo$61b2o3$47b2o81b2o$
46bobo82bo$46bo81b3o$45b2o81bo3$63b2obo73bo$63bob2o72b3o$138b2o2bo$56b
2o82b3o$56b2o5$136bo2b3o$136bob2o2bo$46b2o90bo3b2o$47bo81b2o12bo$47bob
o80bo9bo2bo$48b2o80bobo7bo2bo$125b2o4b2o8b2o$107b2o17bo20b2o$108bo17bo
bo18bo$67bo27bo11bo19b2o16bobo$65b3o27b3o9b2o36b2o$64bo33bo$64b2o19b2o
10b2o32bo$70bo15bo44b2o$68b3o15bobo40b2o2bo$67bo19b2o38bo4b2o$67b2o41b
2o15b3o$110b2o15b2o4$139b2o$70b2o67b2o2b2o27b2o$51b2o17b2o71bobo4b2o
20b2o$51b2o67b2o23bo4b2o$101b2o18bo23b2o$101bo16b3o$50b2o50b3o13bo$51b
o52bo$48b3o12b2o$48bo14bo16b2o$64b3o14bo$66bo11b3o$78bo!
It's still even period, so it doesn't satisfy MathAndCode's question.
Edit: Added link.
Last edited by Schiaparelliorbust on January 4th, 2021, 2:49 pm, edited 1 time in total.
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Re: Thread for basic questions

Post by dvgrn » January 4th, 2021, 2:37 pm

Schiaparelliorbust wrote:
January 4th, 2021, 2:18 pm
Hunting wrote:
January 4th, 2021, 5:51 am
That's because the term crystal usually refers to only that particular crystal. That one's slow and thus more common than those requiring a specific period. I believe Dean Hickerson have a collection of non-standard crystals.
I only found this other one there...
("There" meaning in Dean Hickerson's web pages)

Yes, I hope Hunting can provide a link to a bigger collection of crystal reactions. I don't remember seeing anything like that.

Odd-period glider streams might be considered to be "less common" just because when people were first studying crystallization reactions, there weren't any known odd-period guns yet. The first odd-period gun only showed up in 1995, right at the halfway point between the discovery of Conway's Life and today.

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Re: Thread for basic questions

Post by wwei23 » January 4th, 2021, 9:57 pm

Each 2c/3 signal is made up of two half-signals that can be separated from each other by an arbitrary number of ticks.
I don't see the half-signals, can anyone provide an example?

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Re: Thread for basic questions

Post by MathAndCode » January 4th, 2021, 11:55 pm

wwei23 wrote:
January 4th, 2021, 9:57 pm
Each 2c/3 signal is made up of two half-signals that can be separated from each other by an arbitrary number of ticks.
I don't see the half-signals, can anyone provide an example?
Maybe it's referring to a double-length signal?
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Re: Thread for basic questions

Post by Scorbie » January 5th, 2021, 12:29 am

MathAndCode wrote:
January 4th, 2021, 11:55 pm
wwei23 wrote:
January 4th, 2021, 9:57 pm
Each 2c/3 signal is made up of two half-signals that can be separated from each other by an arbitrary number of ticks.
I don't see the half-signals, can anyone provide an example?
Maybe it's referring to a double-length signal?
No, a single-length signal.

Code: Select all

x = 86, y = 24, rule = B3/S23
7b2o28b2o28b2o$7b2o28b2o28b2o2$5b6o24b6o24b6o$4bo6bo22bo6bo22bo6bo$bo
2bo2bob3o19bo2bo2bob3o19bo2bo2bob3o$obobobobo5bo15bobobobobo5bo15bobob
obobo5bo$bo2bobo2b6o16bo2bobobo2b4o16bo2bobobo2b4o$4bobobo25bobobobo
23bobobobo$5b2obo2b6o18b2obobob5o18b2obobo2b4o$8bobo6bo20bobo6bo20bobo
bo4bo$8bobo2b5o20bobo2b5o20bobobo2b3o$9b2obo7bo18b2obo7bo18b2obobo5bo$
12bo2b6o21bo2b6o21bobob5o$12bobo8bo18bobo8bo18bobo8bo$11b2obo2b7o17b2o
bo2b7o17b2obo2b7o$14bobo27bobo27bobo$14bobo2b5o20bobo2b5o20bobo2b5o$
15b2obo4bo21b2obo4bo21b2obo4bo$18bo2bo26bo2bo26bo2bo$18bobob4o22bobob
4o22bobob4o$17b2obo4bo21b2obo4bo21b2obo4bo$21b3o27b3o27b3o$23b2o28b2o
28b2o!

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Re: Thread for basic questions

Post by Donald K Trump » January 5th, 2021, 2:09 am

I've been watching ColorfulGalaxy's activity lately, and there's something that I really don't understand.
What's "minimum covering convex polygon"?

His wiki articles also listed the unstablised wick "xq1_3cc3z3cc3z" and "xp0_196609966099660".
Do unstabilized wicks have apgcodes?
Also, "xp0_14" leads to "MWSS spark". But the MWSS doesn't have this spark.

Also, can tagalong be made up of gliders?
The Wiki said that the tagalong is not a spaceship.

What should a person do to become a Life enthusiast?
Will ColorfulGalaxy become a Life Enthusiast in the future?

By the way, how did he get the pixel characters and the fake stub message?

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Re: Thread for basic questions

Post by bubblegum » January 5th, 2021, 12:46 pm

Donald K Trump wrote:
January 5th, 2021, 2:09 am
I've been watching ColorfulGalaxy's activity lately, and there's something that I really don't understand.
What's "minimum covering convex polygon"?

His wiki articles also listed the unstablised wick "xq1_3cc3z3cc3z" and "xp0_196609966099660".
Do unstabilized wicks have apgcodes?
Also, "xp0_14" leads to "MWSS spark". But the MWSS doesn't have this spark.

Also, can tagalong be made up of gliders?
The Wiki said that the tagalong is not a spaceship.

What should a person do to become a Life enthusiast?
Will ColorfulGalaxy become a Life Enthusiast in the future?

By the way, how did he get the pixel characters and the fake stub message?
A MCCP is the smallest convex polygon (a shape with only straight sides and angles less than 180°) that completely covers the pattern.

No.
It does, but the MWSS is moving up.

A tagalong is a spaceship component that can be attached to the side or back of another spaceship to create a larger spaceship without interfering with the base. Yes, if the tagalong glider(s) is modified somewhat during the interaction each period, otherwise it's just considered an interaction.

They need to be interested in cellular automata.
They are already.

The pixel characters are in Braille and the fake stub message was copied and modified from the real template.
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Re: Thread for basic questions

Post by MathAndCode » January 6th, 2021, 12:25 am

What is the minimum integer n so that for any period p so that p≥n, there is an oscillator of period p whose minimum phase has p or fewer cells?
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Re: Thread for basic questions

Post by mniemiec » January 6th, 2021, 7:02 am

MathAndCode wrote:
January 6th, 2021, 12:25 am
What is the minimum integer n so that for any period p so that p≥n, there is an oscillator of period p whose minimum phase has p or fewer cells?
There is a simple upper bound of 228 on n, as a four-Snark glider loop can be created for any period ≥43 (and thus any ≥228) with that many cells. Some smaller still-life reflector-based loops with larger reset times might reduce this number.

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Re: Thread for basic questions

Post by Hunting » January 6th, 2021, 7:51 am

How does Nicolay's modification of WLS work?

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Re: Thread for basic questions

Post by dvgrn » January 6th, 2021, 2:17 pm

mniemiec wrote:
January 6th, 2021, 7:02 am
MathAndCode wrote:
January 6th, 2021, 12:25 am
What is the minimum integer n so that for any period p so that p≥n, there is an oscillator of period p whose minimum phase has p or fewer cells?
There is a simple upper bound of 228 on n, as a four-Snark glider loop can be created for any period ≥43 (and thus any ≥228) with that many cells. Some smaller still-life reflector-based loops with larger reset times might reduce this number.
Offhand I can't come up with a pair of 180-degree reflectors that can improve on a four-Snark glider loop to get an easy universal answer lower than 228. It's close, though. I can get ≥246 easily enough:

Code: Select all

x = 262, y = 253, rule = B3/S23
31bo11b2o$30bobo10b2o$22bo3b2o2bobo$21bobo2bo2b2ob2o$8bo12bobo3bobo$8b
3o11bob4o2bob2o$11bo12bo3bobob2o$10b2o11bo3bobo$22bo3bobo$22b2o3bo3$
39b3o$41bo$3b2o34b3o$3b2o45b2o$49bo2bo$50b2obo$53bo$53b2o$38b2o$39bo$
2obob2o29b3o$ob2ob2o17b2o10bo$24bobo$26bo$18b2o6b2o$7bo10bo$6bobo10b3o
$7bo13bo25$38bo$39b2o$38b2o17$99b2o$98b2o$100bo41$99bobo$100b2o$100bo
16$161bo$160b2o$160bobo41$161bo$162b2o$161b2o17$222b2o$221b2o$223bo25$
240bo13bo$240b3o10bobo$243bo10bo$234b2o6b2o$235bo$235bobo$225bo10b2o
17b2ob2obo$223b3o29b2obob2o$222bo$222b2o$207b2o$208bo$208bob2o$209bo2b
o$210b2o45b2o$220b3o34b2o$220bo$220b3o3$234bo3b2o$233bobo3bo$232bobo3b
o11b2o$228b2obobo3bo12bo$228b2obo2b4obo11b3o$232bobo3bobo12bo$228b2ob
2o2bo2bobo$229bobo2b2o3bo$217b2o10bobo$217b2o11bo!
Obviously you can remove four, six, or seven gliders in many (but not all) cases, shorten up the loop, and still get an oscillator with the right period, and a lower population than 228. Here's p226, for example:

Code: Select all

x = 129, y = 120, rule = B3/S23
31bo11b2o$30bobo10b2o$22bo3b2o2bobo$21bobo2bo2b2ob2o$8bo12bobo3bobo$8b
3o11bob4o2bob2o$11bo12bo3bobob2o$10b2o11bo3bobo$22bo3bobo$22b2o3bo3$
39b3o$41bo$3b2o34b3o$3b2o45b2o$49bo2bo$50b2obo$53bo$53b2o$38b2o$39bo$
2obob2o29b3o$ob2ob2o17b2o10bo$24bobo$26bo$18b2o6b2o$7bo10bo$6bobo10b3o
$7bo13bo20$33bo$34b2o$33b2o17$94b2o$93b2o$95bo20$107bo13bo$107b3o10bob
o$110bo10bo$101b2o6b2o$102bo$102bobo$92bo10b2o17b2ob2obo$90b3o29b2obob
2o$89bo$89b2o$74b2o$75bo$75bob2o$76bo2bo$77b2o45b2o$87b3o34b2o$87bo$
87b3o3$101bo3b2o$100bobo3bo$99bobo3bo11b2o$95b2obobo3bo12bo$95b2obo2b
4obo11b3o$99bobo3bobo12bo$95b2ob2o2bo2bobo$96bobo2b2o3bo$84b2o10bobo$
84b2o11bo!
There's a p227 oscillator with a population of 200, and it's easy to find p225 oscillators with population below 225, so that lowers the minimum to 224 at most. Not sure how much lower we can go with one-off solutions like this.

Code: Select all

#C p227 oscillator, population 200
x = 82, y = 51, rule = B3/S23
34bob2o$34b2obo$58bob2o$58b2obo$21bo45b2o$21b3o34b3o5bobo$24bo33bo2bo
4bo$7b2o14b2o11b2o22b2o3b2o$7b2o27b2o34b2o$72bo$70bobo$b2o22b3o42b2o$b
2o20bo4bo$5b2o18bob2o$5b2o15b3o$21bo$77b2o$47b2o28bo$2o44bobo26bobo$2o
44bo28b2o$45b2o2$57b2o$42bo15bo$36b2o4b3o10b3o$26bo9bo8bo9bo$24b3o10b
3o4b2o$23bo15bo$23b2o2$35b2o$5b2o28bo44b2o$4bobo26bobo44b2o$4bo28b2o$
3b2o$60bo$57b3o15b2o$53b2obo18b2o$53bo4bo20b2o$10b2o42b3o22b2o$9bobo$
9bo$8b2o34b2o27b2o$15b2o3b2o22b2o11b2o14b2o$15bo4bo2bo33bo$13bobo5b3o
34b3o$13b2o45bo$20bob2o$20b2obo$44bob2o$44b2obo!

Code: Select all

#C p225 oscillator, population 223
x = 66, y = 50, rule = B3/S23
15bo2bo2bo$15b7o$55bo$15b7o32b3o$15bo2bo2bo31b5o7$12b2o39b5o$12b2o4b2o
7b2o7bo6bo10b3o$17b2o3bo4b2o6b2o6b2o10bo$19b2obo11b3o6b3o$21bo13b2o6b
2o$36bo6bo$13b2o11bo$2ob2o10bo10b2o$bobo10bo10bobo6bo$bobo8bobo10bo6bo
bo8b2o$2ob2o7b2o10bo8b2o9bo$bobo9bo11b2o17bobo$bobo41b2o15b2o$2ob2o13b
o31bo11bobo$17bob2o28bobo12bo$11b2o4bo3b2o26bobo12b2o$11b2o7b2o4b2o22b
o$26b2o2$44bo$45b2o$44b2o3$18bo2bo2bo4bo2bob2obo2bo$18b7o4b4ob2ob4o$
29bo2bob2obo2bo14b2o$18b7o30bobo$18bo2bo2bo32bo$48b2o7b2o$48b2o6$46bo
4bo$44b2ob4ob2o$46bo4bo!

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Re: Thread for basic questions

Post by toroidalet » January 6th, 2021, 7:09 pm

Here's a smaller p225 (not like it really matters):

Code: Select all

x = 60, y = 50, rule = B3/S23
15bo2bo2bo$15b7o2$15b7o$15bo2bo2bo7$12b2o$12b2o4b2o7b2o7bo6bo$17b2o3bo
4b2o6b2o6b2o$19b2obo11b3o6b3o$21bo13b2o6b2o14bo$36bo6bo13b3o$13b2o11bo
29bo$2ob2o10bo10b2o28b2o$bobo10bo10bobo6bo$bobo8bobo10bo6bobo8b2o$2ob
2o7b2o10bo8b2o9bo$bobo9bo11b2o17bobo$bobo41b2o$2ob2o13bo31bo$17bob2o
28bobo$11b2o4bo3b2o26bobo$11b2o7b2o4b2o22bo$26b2o2$44bo$45b2o$44b2o3$
18bo2bo2bo4bo2bob2obo2bo$18b7o4b4ob2ob4o$29bo2bob2obo2bo14b2o$18b7o30b
obo$18bo2bo2bo32bo$48b2o7b2o$48b2o6$46bo4bo$44b2ob4ob2o$46bo4bo!
We can get evens ≥208 by taking half the gliders out of the snark loop, and a pair of rectifiers can get us periods of the form 4n+1 ≥133:

Code: Select all

x = 73, y = 51, rule = B3/S23
4b2obo$4bob2o2$5b5o$2o2bo4bo20b2o$o2bo2bo23bo$bobob2o21bobo$2obo5bo18b
2o$3bo4bobo$3b2o2bo2bo$8b2o$39b2o$39bo$37bobo$37b2o2$19b2o$19b2o$43bo$
42bobo$42bobo$43bo$29b2o$28b2o$30bo2$42bo$43b2o$42b2o$29bo$28bobo$28bo
bo$29bo$52b2o$52b2o2$34b2o$33bobo$33bo$32b2o$63b2o$62bo2bo2b2o$62bobo
4bo$43b2o18bo5bob2o$42bobo21b2obobo$42bo23bo2bo2bo$41b2o20bo4bo2b2o$
63b5o2$65b2obo$65bob2o!
Using tubs and 6 gliders in the loop, we can get all odd periods ≥143:

Code: Select all

x = 149, y = 127, rule = B3/S23
8bo$7bobo$8bo2$6b5o$5bo4bo20b2o$4bo2bo23bo$bo2bob2o21bobo$obobo5bo18b
2o$bo2bo4bobo$4b2o2bo2bo$9b2o$40b2o$40bo$38bobo$38b2o2$20b2o$20b2o7$
33bo$32b2o$32bobo8bo$44b2o$43b2o$30bo$29bobo$29bobo$30bo28$68b2o$68bob
o$68bo11bo$78bobo$79b2o28$118bo$117bobo$117bobo$118bo$104b2o$103b2o$
105bo8bobo$115b2o$115bo7$127b2o$127b2o2$109b2o$108bobo$108bo$107b2o$
138b2o$137bo2bo2b2o$137bobo4bo2bo$118b2o18bo5bobobo$117bobo21b2obo2bo$
117bo23bo2bo$116b2o20bo4bo$138b5o2$140bo$139bobo$140bo!
Now the upper bound on n is 206, which could be improved by using rectifiers more or maybe boojums (booja?).
Any sufficiently advanced software is indistinguishable from malice.

wwei23

Re: Thread for basic questions

Post by wwei23 » January 6th, 2021, 9:22 pm

The pentadecathalon works for P15 and the caterer on figure eight works for P24, although the caterer on figure eight is boring. I will admit that it's one of the less-trivial interactions though.
Edit: For P30, there's the queen bee shuttle.
Edit 2: For P36, there's 22P36.
Edit 3: For P40, there's Beluchenko's P40.
Edit 4: For P46, there's the twin bees shuttle and Kazyan's p46.

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Moosey
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Re: Thread for basic questions

Post by Moosey » January 6th, 2021, 10:50 pm

MathAndCode wrote:
January 6th, 2021, 12:25 am
What is the minimum integer n so that for any period p so that p≥n, there is an oscillator of period p whose minimum phase has p or fewer cells?
related question: does there exist an n such that for any period p:p>=n, there exists an oscillator of period p whose stator contains exactly p cells? I feel like for large enough p there'd be some kind of UCC that makes sure the rotor covers p cells
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Re: Thread for basic questions

Post by MathAndCode » January 6th, 2021, 10:54 pm

wwei23 wrote:
January 6th, 2021, 9:22 pm
The pentadecathalon works for P15 and the caterer on figure eight works for P24, although the caterer on figure eight is boring. I will admit that it's one of the less-trivial interactions though.
Edit: For P30, there's the queen bee shuttle.
Edit 2: For P36, there's 22P36.
Edit 3: For P40, there's Beluchenko's P40.
Edit 4: For P46, there's the twin bees shuttle and Kazyan's p46.
Yes, but what about all of the cases in between?
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