22da (Hexagonal Grid)

For discussion of other cellular automata.
c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 13th, 2014, 9:27 pm

@wildmyron: I certainly underestimated that M(S&M(S&M)) quite a bit. The smoking ship I'm trying to synthesize has been known to delete duoplets, but not much else, so I might need to use the old-fashioned rake convoys to delete all the other junk. However, there is some chance of finding one -- here is a way to make sideways and backwards rakes with periods long enough to make a true MMM. This could also be useful for the sawtooth.

Code: Select all

x = 2186, y = 1360, rule = 22da
2bo$b2o$ob3o$bobo2b2o$2bo3b3o$8bo2$7bobobo38$56bo$55bo6$58b2o$59bo$58b
o2bo$59bobo$59bo$62bo$59bobobo$62bo$61bobo$57bo$57bobo$7bo47b2ob2o$7b
2o45bob2o$8bo27bo18bobo$35bo20bo12bobo$7bobobo58bobo$69bobo2b2o2$66b2o
3bob2ob2o$66bo8bobo$64b2ob2o$63bob2o17bo$64bobo16bo$65bo10$16bo$15bo7$
64bo$63bo7$16bobo$15bob2o$17bobo$16b2o2b2o$18bob2obo$17bo3bo2bo$19b3o$
20b6o$20b3ob2o$22bo3bo$24bo2b2o$6bo16bob3o$4b2o2bo16bo2bo15bo$3b2o6bo
15bo15bo$7bo5bo$3b2ob2o4bobo$4bobo6bo$15bo46bo59bo59bo59bo59bo59bo59bo
59bo59bo59bo59bo59bo119bo119bo119bo2$62bo59bo59bo59bo59bo59bo59bo59bo
59bo59bo59bo59bo119bo119bo119bo$16bo47b2o58b2o58b2o58b2o58b2o58b2o58b
2o58b2o58b2o58b2o58b2o58b2o118b2o118b2o118b2o$13b2o47bo2b2o55bo2b2o55b
o2b2o55bo2b2o55bo2b2o55bo2b2o55bo2b2o55bo2b2o55bo2b2o55bo2b2o55bo2b2o
55bo2b2o115bo2b2o115bo2b2o115bo2b2o$12b2o3bo$16bo$12b2ob2o$13bobo1074b
o$1090b2o$1091bo2$1090bobobo4$666bo2b2o$669b2o$668bo2$670bo76$586bo2b
2o$589b2o$588bo2$590bo28$1090bo$1090b2o$1091bo2$1090bobobo44$506bo2b2o
$509b2o$508bo2$510bo61$198bo$197b2o$196bob3o$197bobo2b2o$198bo3b3o$
204bo2$203bobobo882bo$1090b2o$1091bo2$1090bobobo4$426bo2b2o$429b2o$
428bo2$430bo26$252bo$251bo6$254b2o$255bo$254bo2bo$255bobo$255bo$258bo$
255bobobo$258bo$257bobo$253bo$253bobo$203bo47b2ob2o$203b2o45bob2o$204b
o27bo18bobo$231bo20bo12bobo$203bobobo58bobo$265bobo2b2o2$262b2o3bob2ob
2o$262bo8bobo$260b2ob2o$259bob2o17bo$260bobo16bo$261bo10$212bo$211bo7$
260bo$259bo$346bo2b2o$349b2o$344bo3bo$343b2o$342bo3bo3bo$341bob3o$212b
obo125bo4bob2o$211bob2o124bo2b2obobo$213bobo122bobob2o2bo$212b2o2b2o
119b2obo4bo$214bob2obo120b3obo$213bo3bo2bo114bo3bo3bo$215b3o123b2o$
216b6o115bo3bo$216b3ob2o113b2o$218bo3bo112b2o2bo$220bo2b2o$202bo16bob
3o$200b2o2bo16bo2bo15bo$199b2o6bo15bo15bo$203bo5bo$199b2ob2o4bobo$200b
obo6bo$211bo46bo59bo2$258bo59bo$212bo47b2o58b2o$209b2o47bo2b2o55bo2b2o
$208b2o3bo108b2o$212bo110b2o$208b2ob2o111bo$209bobo$323bobobo762bo$
1090b2o$1091bo2$1090bobobo34$372bo$371bo6$374b2o$375bo$374bo2bo$375bob
o$375bo$378bo$375bobobo$378bo$377bobo$373bo$373bobo$323bo47b2ob2o698bo
2b2o$323b2o45bob2o703b2o$324bo27bo18bobo702bo$351bo20bo12bobo$323bobob
o58bobo689bo11bo$385bobo2b2o698b2o$1091bo$382b2o3bob2ob2o$382bo8bobo
696bobobo$380b2ob2o$379bob2o17bo$380bobo16bo$381bo10$332bo$331bo7$380b
o$379bo7$332bobo$331bob2o$333bobo$332b2o2b2o$334bob2obo$333bo3bo2bo$
335b3o$336b6o$336b3ob2o$338bo3bo$340bo2b2o$322bo16bob3o$320b2o2bo16bo
2bo15bo$319b2o6bo15bo15bo$323bo5bo$319b2ob2o4bobo$320bobo6bo$331bo46bo
59bo2$378bo59bo$332bo47b2o58b2o$329b2o47bo2b2o55bo2b2o$328b2o3bo107b2o
$332bo$328b2ob2o110bo$329bobo110b2o$441bob3o644bo$442bobo645b2o$443bo
647bo2$1090bobobo12$994bo2b2o$997b2o$996bo2$998bo7$2063bo$2063b2o$
2064bo2$2063bobobo29$1090bo$1090b2o$1091bo2$1090bobobo19$2047bo2b2o$
2050b2o$2049bo2$2051bo11bo$2063b2o$2064bo2$2063bobobo5$914bo2b2o$917b
2o$916bo2$918bo20$1090bo$1090b2o$1091bo2$1090bobobo23$2063bo$2063b2o$
2064bo2$2063bobobo10$606bo$605b2o$604bob3o1358bo2b2o$605bobo2b2o1358b
2o$606bo3b3o1356bo$612bo$1971bo$611bobobo8$834bo2b2o$837b2o$836bo2$
838bo251bo$1090b2o$1091bo2$1090bobobo22$660bo$659bo1403bo$2063b2o$
2064bo2$2063bobobo2$662b2o$663bo$662bo2bo$663bobo$663bo$666bo$663bobob
o$666bo$665bobo$661bo$661bobo$611bo47b2ob2o$611b2o45bob2o$612bo27bo18b
obo$639bo20bo12bobo$611bobobo58bobo$673bobo2b2o2$670b2o3bob2ob2o$670bo
8bobo$668b2ob2o$667bob2o17bo$668bobo16bo$669bo4$1090bo$1090b2o$1091bo$
1887bo2b2o$1090bobobo795b2o$1889bo$620bo$619bo1271bo7$668bo$667bo$754b
o2b2o$757b2o$752bo3bo$751b2o$750bo3bo3bo$749bob3o$620bobo125bo4bob2o$
619bob2o124bo2b2obobo$621bobo122bobob2o2bo$620b2o2b2o119b2obo4bo$622bo
b2obo120b3obo$621bo3bo2bo114bo3bo3bo1311bo$623b3o123b2o1312b2o$624b6o
115bo3bo1314bo$624b3ob2o113b2o$626bo3bo112b2o2bo1315bobobo$628bo2b2o$
610bo16bob3o$608b2o2bo16bo2bo15bo$607b2o6bo15bo15bo$611bo5bo$607b2ob2o
4bobo$608bobo6bo$619bo46bo59bo2$666bo59bo$620bo47b2o58b2o$617b2o47bo2b
2o55bo2b2o$616b2o3bo108b2o$620bo110b2o$616b2ob2o111bo$617bobo$731bobob
o12$1090bo$1090b2o$1091bo2$1090bobobo4$1579bo$1578b2o$1577bob3o$1578bo
bo2b2o$1579bo3b3o$1585bo2$1584bobobo8$1807bo2b2o$1810b2o$1809bo$780bo$
779bo1031bo251bo$2063b2o$2064bo2$2063bobobo2$782b2o$783bo$782bo2bo$
783bobo$783bo$786bo$783bobobo$786bo$785bobo$781bo$781bobo$731bo47b2ob
2o$731b2o45bob2o$732bo27bo18bobo$759bo20bo12bobo$731bobobo58bobo$793bo
bo2b2o2$790b2o3bob2ob2o$790bo8bobo$788b2ob2o840bo$787bob2o17bo823bo$
788bobo16bo$789bo4$1090bo544b2o$1090b2o544bo$1091bo543bo2bo$1636bobo$
1090bobobo541bo$1639bo$740bo895bobobo$739bo899bo$1638bobo$1634bo$1634b
obo$1584bo47b2ob2o$1584b2o45bob2o$1585bo27bo18bobo$788bo823bo20bo12bob
o$787bo796bobobo58bobo$1646bobo2b2o2$1643b2o3bob2ob2o$1643bo8bobo$
1641b2ob2o$1640bob2o17bo$740bobo898bobo16bo$739bob2o899bo$741bobo$740b
2o2b2o$742bob2obo$741bo3bo2bo1314bo$743b3o1317b2o$744b6o1314bo$744b3ob
2o$746bo3bo1312bobobo$748bo2b2o$730bo16bob3o841bo$728b2o2bo16bo2bo15bo
823bo$727b2o6bo15bo15bo$731bo5bo$727b2ob2o4bobo$728bobo6bo$739bo46bo
59bo2$786bo59bo794bo$740bo47b2o58b2o790bo$737b2o47bo2b2o55bo2b2o876bo
2b2o$736b2o3bo107b2o879b2o$740bo984bo3bo$736b2ob2o110bo872b2o$737bobo
110b2o871bo3bo3bo$849bob3o868bob3o$850bobo740bobo125bo4bob2o$851bo740b
ob2o124bo2b2obobo$1594bobo122bobob2o2bo$1593b2o2b2o119b2obo4bo$1595bob
2obo120b3obo$1594bo3bo2bo114bo3bo3bo$1596b3o123b2o$1597b6o115bo3bo$
1597b3ob2o113b2o$1599bo3bo112b2o2bo$1601bo2b2o$1090bo492bo16bob3o$
1090b2o489b2o2bo16bo2bo15bo$1091bo488b2o6bo15bo15bo$1584bo5bo$1090bobo
bo485b2ob2o4bobo$1581bobo6bo$1592bo46bo59bo2$1639bo59bo$1593bo47b2o58b
2o$1590b2o47bo2b2o55bo2b2o$1589b2o3bo108b2o$1593bo110b2o$1589b2ob2o
111bo$1590bobo$1704bobobo12$2063bo$2063b2o$2064bo2$2063bobobo22$1753bo
$1752bo6$1090bo664b2o$1090b2o664bo$1091bo663bo2bo$1756bobo$1090bobobo
661bo$1759bo$1756bobobo$1759bo$1758bobo$1754bo$1754bobo$1704bo47b2ob2o
$1704b2o45bob2o$1705bo27bo18bobo$1732bo20bo12bobo$1704bobobo58bobo$
1766bobo2b2o2$1763b2o3bob2ob2o$1763bo8bobo$1761b2ob2o$1760bob2o17bo$
1761bobo16bo$1762bo4$2063bo$2063b2o$2064bo2$2063bobobo2$1713bo$1712bo
7$1761bo$1139bo620bo$1138bo6$1141b2o570bobo$1142bo569bob2o$1141bo2bo
569bobo$1142bobo568b2o2b2o$1142bo572bob2obo$1145bo568bo3bo2bo$1142bobo
bo569b3o$1145bo571b6o$1144bobo570b3ob2o$1140bo578bo3bo$1140bobo578bo2b
2o$1090bo47b2ob2o560bo16bob3o$1090b2o45bob2o560b2o2bo16bo2bo15bo$1091b
o27bo18bobo559b2o6bo15bo15bo$1118bo20bo12bobo549bo5bo$1090bobobo58bobo
544b2ob2o4bobo$1152bobo2b2o542bobo6bo$1712bo46bo59bo$1149b2o3bob2ob2o$
1149bo8bobo598bo59bo$1147b2ob2o561bo47b2o58b2o$1146bob2o17bo542b2o47bo
2b2o55bo2b2o$1147bobo16bo542b2o3bo107b2o$1148bo564bo$1709b2ob2o110bo$
1710bobo110b2o$1822bob3o$1823bobo$1824bo5$1099bo$1098bo4$2063bo$2063b
2o$2064bo$1147bo$1146bo916bobobo7$1099bobo$1098bob2o$1100bobo$1099b2o
2b2o$1101bob2obo$1100bo3bo2bo$1102b3o$1103b6o$1103b3ob2o$1105bo3bo$
1107bo2b2o$1089bo16bob3o$1087b2o2bo16bo2bo15bo$1086b2o6bo15bo15bo$
1090bo5bo$1086b2ob2o4bobo$1087bobo6bo$1098bo46bo59bo2$1145bo59bo$1099b
o47b2o58b2o$1096b2o47bo2b2o55bo2b2o$1095b2o3bo107b2o$1099bo$1095b2ob2o
110bo$1096bobo110b2o$1208bob3o$1209bobo$1210bo21$2063bo$2063b2o$2064bo
2$2063bobobo38$2112bo$2111bo6$2114b2o$2115bo$2114bo2bo$2115bobo$2115bo
$2118bo$2115bobobo$2118bo$2117bobo$2113bo$2113bobo$2063bo47b2ob2o$
2063b2o45bob2o$2064bo27bo18bobo$2091bo20bo12bobo$2063bobobo58bobo$
2125bobo2b2o2$2122b2o3bob2ob2o$2122bo8bobo$2120b2ob2o$2119bob2o17bo$
2120bobo16bo$2121bo10$2072bo$2071bo7$2120bo$2119bo7$2072bobo$2071bob2o
$2073bobo$2072b2o2b2o$2074bob2obo$2073bo3bo2bo$2075b3o$2076b6o$2076b3o
b2o$2078bo3bo$2080bo2b2o$2062bo16bob3o$2060b2o2bo16bo2bo15bo$2059b2o6b
o15bo15bo$2063bo5bo$2059b2ob2o4bobo$2060bobo6bo$2071bo46bo59bo2$2118bo
59bo$2072bo47b2o58b2o$2069b2o47bo2b2o55bo2b2o$2068b2o3bo107b2o$2072bo$
2068b2ob2o110bo$2069bobo110b2o$2181bob3o$2182bobo$2183bo!
Towards the goal of omniperiodicity, here's a stable one-cell eater with an unbelievable recovery time. The best way to prove 22darealDLA omniperiodic would thus be to make a stable duplicator. (Interestingly enough, in 22da(realDLA) duplicators are easier to make than reflectors.)

Code: Select all

x = 7, y = 8, rule = 22darealDLA
2.A2$4.A$2.2A$2.2A2.A3$B!
@simsim314: Here's the same rule with "grey cells" (almost equivalent to the grey cells in the LifeHistory rule).

Code: Select all

@RULE 22daHistory


@TABLE

n_states:4
neighborhood:hexagonal
symmetries:rotate6reflect
var a={0,1,2,3}
var b={a}
var c={a}
var d={a}
var e={a}
var nl = {0,2}

var nl1 = {nl}
var nl2 = {nl}
var nl3 = {nl}
var nl4 = {nl}
var nl5 = {nl}
var nl6 = {nl}
1,a,b,c,d,e,3,0
nl,1,1,nl1,nl2,nl3,nl4,1
nl,1,nl1,1,nl2,nl3,nl4,1
nl,1,nl1,nl2,1,nl3,nl4,1
1,nl1,nl2,nl3,nl4,nl5,nl6,2
1,1,nl1,nl2,nl3,nl4,nl5,2
1,1,1,1,a,b,c,2
1,1,1,c,1,a,b,2
1,1,c,1,b,1,a,2
1,1,nl1,1,nl2,nl3,nl4,2
For the replicator, here's a three-glider synthesis for the p16.

Code: Select all

x = 14, y = 14, rule = 22da
11b2o$13bo$13bo7$2bo$bobo$3obo$2b2o$2bo!
wildmyron wrote:
simsim314 wrote:Is this "back puffer" known:

Code: Select all

x = 27, y = 18, rule = 22da
bo$2o$4bo$5bo$b2o2bob2o$2b2o2bo$o5bo4b2o$bo4b2o$bo3b2o6bo$4b2o9bo$7bo
5bo2bo$8bo7bo$11bobo2b5o$12bo2b2obo2b2o$19bo3b2o$20b2o$22b2ob2o$24bobo
!
That seems to be the rake produced by the synthesis above. I don't know how long ago it was found though and I didn't realise until looking at it again that the side rakes actually emit gliders in the forward directions rather than backward directions as in the rakes produced by the recently completed gun.
It was found March 23rd and was the first back puffer known. It was also a key component in the first backrake.

wildmyron
Posts: 1398
Joined: August 9th, 2013, 12:45 am

Re: 22da (Hexagonal Grid)

Post by wildmyron » May 13th, 2014, 11:22 pm

A dirty but compact p120 rake:

Code: Select all

x = 22, y = 50, rule = 22da
2o2$2obo$bobo27$11bo$9bo2b2o$11b2o$5bo3b5o$4bo6bo3b2o$3b2o2bo8b2o$2b2o
$6b2o$2b2ob2o$3bobo7bo2b2o$15b2o2bo$14bob2ob2o$18bo$19bobo$19b3o$14bo
5bo$14b2o3bo$13bo7bo$11b2o$11b2o!
Probably useless but surprising puffer interaction:

Code: Select all

x = 71, y = 71, rule = 22da
69b2o$69b2o$68bo$66b2o$61bo5bo$61bobo$63b2o$64b2o$55bo6bo$56b2o7b2o$
55bobo3$60b2o$61bo$60bobo$48bo2$49bo2$35bo$29bo4bobo15bo$28b2obo2b2obo
16bo$29b2o4b2o$30b4o6bo$34b2o$32bo8bo$32bo2$44bo$46bo3$48bo$47bobo$45b
ob2obo$45bo2b2o$46bo$43b2obo$46bobo$46b2o$16bo30b3o$18bo29bo10$28bo2$
29bo3$o$2bo5$6b2o$6b2o$5bo$3b2o$4bo$12bo2$13bo!
The gliders which are pulling the duoplets in this reaction are delayed by 2 gen every 2nd period of the duoplet puffer and when the trailing puffer catches up it is destroyed.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 14th, 2014, 5:43 pm

@wildmyron: Here's a clean 48-cell p60 backrake.

Code: Select all

x = 93, y = 93, rule = 22da
41b2o$41b2o6$49bo$48bo$46b2o3bo$46b2o25$o2$2bo$2o$2o2$83bo2$85bo$84bo$
8bo73b2o$7bo74b2o$5b2o3bo$5b2o2$91b2o$91b2o31$45bo2$47bo$46bo$44b2o$
44b2o$53bo2$55bo$53b2o$53b2o!
I don't think that the puffer interaction you found is useless. Here's a near-backrake that unfortunately can't be cleaned up.

Code: Select all

x = 103, y = 103, rule = 22da
100bo$99bobo$92bo6b2obo$94bo2b2ob2o$92b2o5bo$93b2o4bo$93bo$95bo$87b2o
8bobo$96b3o$86bo3bo7bobo$89bo$88bobobo$91bo$90bo3bo$94bo$80bo11bo2$81b
o3$84bo$86bo2$72bo2$73bo3$76bo$78bo2$64bo2$65bo3$68bo$70bo2$56bo2$57bo
3$60bo$62bo2$48bo2$49bo3$52bo$54bo2$40bo2$41bo3$44bo$46bo2$32bo$21bobo
$21bob2o8bo$19bo$19bo3b2o$18bobob2o12bo$17bo20bo$17bo3bo$18b4o$19bo3bo
$24bo4$28bo5bobo$29bo3b2ob2o$33bo$30b2o4b2o$30bo2bo$17bo11b2o3b2o$16bo
bo11bo2bo$15b3obo11b2o$17b2o$17bo2$o$2bo10$12bo2$13bo!
For the sawtooth, I found that p16s could do just as well as gliders for cleaning. (It's conceivable that rakes with a high enough period could pull a p16 at their own speed.)

Code: Select all

x = 131, y = 127, rule = 22da
obobo2$3bo$3b2o$4bo64$116bo2$118bo$116b2o$116b2o2bo6$126bo2$128bo$126b
2o$126b2o2bo14$120bo$120bo$81b2o2$78bo39bo$77bo39bo9$118b2o$119bo2$
119b3o10$102bo$102b2obo$105bo$105bo!
Although glider wicks have not been the most popular oscillator supporters, this one is irresistibly sparky and has an odd period.

Code: Select all

x = 171, y = 163, rule = 22da:T195,195
158bo$157bobo$156b3obo7bo$158b2o7b2o$158bo7bob3o$167bobo$168bo33$119bo
$118bobo$117b3obo7bo$119b2o7b2o$119bo7bob3o$128bobo$129bo2$23bo2$23bo$
25b2o$23bo2b2o27$80bo$79bobo$78b3obo7bo$80b2o7b2o$80bo7bob3o$89bobo$
90bo33$41bo$40bobo$39b3obo7bo$41b2o7b2o$41bo7bob3o$50bobo$51bo33$2bo$b
obo$3obo7bo$2b2o7b2o$2bo7bob3o$11bobo$12bo!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 15th, 2014, 5:48 pm

There may be small backrakes, but this forward rake has an astoundingly small size!

Code: Select all

x = 43, y = 44, rule = 22da
o2b2o$3b2o$2bo2$4bo$bo10b2o$3bo4bo3b2o$11bo$4bo5bo$4bobo2b2o$4bobo2bob
2o$6bo5$5bo$4bo$bo3bobo$3bo$3bo3bo$4bo2bo$5b2o2$6b2o$8bo$7b2o$7b3o2$8b
3o$36b2o$32bo3b2o$32bo2bo$13bo19b2o$13bobo16b2o$13bob3o18bo$15b2obo2b
2obo$18bobo10b3o$20bo3bobo$21bo3bo6b3o3bo2b2o$22b2o12bo4b2o$40bo$24bo
12bo$42bo!
For the sawtooth, here is a nice converter puffer.

Code: Select all

x = 244, y = 161, rule = 22da
41bo$35bo4bobo$40b2obo$34bo4bob2o$40bo$33bo2$36bo$35bo6bo$40bo$38bo2$
30bo$31bo4$26bo$25bo4$20bo$21bo4$16bo$15bo4$10bo$11bo4$6bo$5bo$188bobo
$187b2ob2o$186b2o$o189b2o$bo27b2o2bo25b2o2bo25b2o2bo25b2o2bo25b2o2bo
25b2o8b2o$30b2o28b2o28b2o28b2o28b2o28b2o2bo$33bo29bo29bo29bo29bo29b3o$
184b2o$33bo29bo29bo29bo29bo10bo$4bo158bo29bobo$193bob2o$5bo$170bo24b2o
$22bo$22b2o144bo$23bo2$22bobobo$154bo$153bo4$42bo$42b2o$43bo2$42bobobo
$144bo$143bo4$62bo$62b2o$63bo2$62bobobo$134bo12bobo$133bo12b2ob2o$145b
2o$149b2o$138b2o8b2o$82bo56b2o2bo$82b2o58b3o$83bo59b2o2$82bobobo65bobo
$152bob2o2$154b2o3$102bo$102b2o$103bo2$102bobobo5$201bo2b2o$122bo81b2o
$122b2o79bo$123bo$205bo$122bobobo86b2o$213b2o$208bo3bo$208b2obo$210b2o
$209b4o$142bo68bobo$142b2o$143bo2$142bobobo60b2o$205bo3bo$206bo$207bo
2$208b2o$162bo45b3o$162b2o$163bo45b3o2$162bobobo5$237b2o$182bo49bo4b2o
$182b2o13b2o34bo2bo$183bo13bobo20bo11b4o$220bobo10b2o$182bobo35bob2o3b
o5bobo$185bo12b4o20b2o4bo6b2o$225bo2bo$226bo$200bobo24bo11bo2b2o$201b
2o7bo31b2o$210b2o29bo$212bo$206bo5bo30bo$211bo2$194bo$192bo$192bo$177b
obo15bo$176b2o2b2o$177b5o12bobo$179b2o14b2o$180bo3$184b2o2$180bo$180bo
!

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 16th, 2014, 1:08 pm

Here is a pure glider only way to clean the "mess":

Code: Select all

x = 81, y = 62, rule = 22da
21$58bobo$57b2ob2o$56b2o$60b2o$19b2o2bo25b2o8b2o$20b2o28b2o2bo$23bo29b
3o$54b2o$23bo10bo$33bo29bobo$63bob2o2$40bo24b2o2$38bo4$24bo$23bo4$o2b
2o$3b2o$2bo2$4bo$8bobo8bo2b2o$8bob2o10b2o$21bo$10b2o$23bo!
And inside the whole construction:

Code: Select all

x = 244, y = 161, rule = 22da
41bo$35bo4bobo$40b2obo$34bo4bob2o$40bo$33bo2$36bo$35bo6bo$40bo$38bo2$
30bo$31bo4$26bo$25bo4$20bo$21bo4$16bo$15bo4$10bo$11bo4$6bo$5bo$188bobo
$187b2ob2o$186b2o$o189b2o$bo27b2o2bo25b2o2bo25b2o2bo25b2o2bo25b2o2bo
25b2o8b2o$30b2o28b2o28b2o28b2o28b2o28b2o2bo$33bo29bo29bo29bo29bo29b3o$
184b2o$33bo29bo29bo29bo29bo10bo$4bo158bo29bobo$193bob2o$5bo$170bo24b2o
$22bo$22b2o144bo$23bo2$22bobobo$154bo$153bo4$42bo87bo2b2o$42b2o89b2o$
43bo88bo2$42bobobo87bo$138bobo8bo2b2o$138bob2o10b2o$151bo$140b2o$153bo
$62bo$62b2o$63bo2$62bobobo6$82bo$82b2o$83bo2$82bobobo6$102bo$102b2o$
103bo2$102bobobo5$201bo2b2o$122bo81b2o$122b2o79bo$123bo$205bo$122bobob
o86b2o$213b2o$208bo3bo$208b2obo$210b2o$209b4o$142bo68bobo$142b2o$143bo
2$142bobobo60b2o$205bo3bo$206bo$207bo2$208b2o$162bo45b3o$162b2o$163bo
45b3o2$162bobobo5$237b2o$182bo49bo4b2o$182b2o13b2o34bo2bo$183bo13bobo
20bo11b4o$220bobo10b2o$182bobo35bob2o3bo5bobo$185bo12b4o20b2o4bo6b2o$
225bo2bo$226bo$200bobo24bo11bo2b2o$201b2o7bo31b2o$210b2o29bo$212bo$
206bo5bo30bo$211bo2$194bo$192bo$192bo$177bobo15bo$176b2o2b2o$177b5o12b
obo$179b2o14b2o$180bo3$184b2o2$180bo$180bo!
Here is also a constalation of glider, that can reflect glider once if "needed".

Code: Select all

x = 114, y = 87, rule = 22da
13$107bo2$108bo24$81bo2$82bo24$20bo22bo2b2o7bo$19bobo24b2o$18b3obo22bo
10bo$20b2o$20bo26bo2$29bobo$29bob2o2$31b2o!
EDIT I've noticed that this constellation of gliders also clean the smoke from this puffer:

Code: Select all

x = 66, y = 57, rule = 22da
63bo$57bo4bobo$62b2obo$56bo4bob2o$62bo$55bo2$58bo$57bo6bo$62bo$60bo2$
52bo$53bo4$48bo$47bo4$42bo$43bo4$38bo$37bo4$32bo$33bo4$28bo$27bo4$22bo
$23bo3$2bo$bobo$3obo$2b2o$2bo$21bo$6bo2b2o9bobo$9b2o8b3obo$8bo12b2o$
21bo$10bo!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 16th, 2014, 4:06 pm

@simsim314: How did that glider constellation escape my notice?! I was looking for that for a long time and will need to look for ways that it might improve my syntheses.

The previous converter puffer would have been good for a breeder. This one should be better for a smoking ship backrake, if I can get the gliders close enough together.

Code: Select all

x = 194, y = 255, rule = 22da
16bo2b2o$19b2o$18bo2$20bo$28b2o$28b2o$23bo3bo$23b2obo$25b2o$24b4o$26bo
bo4$22b2o$20bo3bo$21bo$22bo2$23b2o$23b3o2$24b3o6$53b2o$48bo4b2o$16b2o
31bo2bo$15bo2bo17bo11b4o$18b2o16bobo10b2o$36bob2o3bo5bobo$38b2o4bo6b2o
$41bo2bo$16bo25bo$43bo11bo2b2o$58b2o$57bo$19b2o$19bo3bo35bo$20bo2bo$
23bo2bo$23bo3bo$26b2o$7b2o100bobo$7bo2bo98bob2o$8bo4bo$111b2o$11b2o$
118bobo$117b2ob2o$117bo$120b2o$119b2o$119bo$3bo19bo90b2o$3bo20bo89b3o$
26b2o87bo$24bo2b2o$8b2o106bo$2o4b4o106b2o$7b2obo106bo$8bo$8b3o$9bo6$
109bo2$107bo2$34bo2$34bo78bo$36b2o74bo$34bo2b2o7$71bobo$71bob2o28bo$
102bo10bobobo$73b2o$116bo$80bobo33b2o$79b2ob2o33bo$79bo$82b2o$44bo36b
2o$81bo$44bo31b2o15bo$46b2o28b3o13bo$44bo2b2o28bo2$78bo$78b2o$79bo4$
83bo$82bo7$54bo2$54bo$56b2o55bobobo$54bo2b2o$116bo$116b2o$117bo13$64bo
2$64bo$66b2o$64bo2b2o9$113bobobo2$116bo$116b2o$117bo3$74bo2$74bo$76b2o
$74bo2b2o16$84bo2$84bo$86b2o25bobobo$84bo2b2o$116bo$116b2o$117bo8$157b
o$150bobo3bobo$151b2ob4obo$154b5o$155b3o$94bo61b2o2$94bo62b2o$96b2o59b
o$94bo2b2o59bo$148bo$149bo$185bobo$184b2ob2o$183b2o$144bo42b2o$143bo2b
2o2bo25b2o8b2o$147b2o28b2o2bo$113bobobo32bo29b3o$181b2o$116bo21bo11bo
10bo$116b2o21bo20bo29bobo$117bo72bob2o2$167bo24b2o$104bo$165bo$104bo$
106b2o$104bo2b2o$128bo22bo$129bo20bo9$118bo22bo$119bo20bo9$131bo12bobo
$130bo12b2ob2o$142b2o$146b2o$135b2o8b2o$136b2o2bo$139b3o$140b2o2$149bo
bo$149bob2o2$151b2o!
In 22darealDLA, the most promising result is this 2-cell pattern which spews out four pieces of junk after being fed a glider.

Code: Select all

x = 15, y = 16, rule = 22darealDLA
10.A2$12.A$10.2A$10.2A2.A6$B5$2.B!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 17th, 2014, 10:01 pm

It looks like I will need to use higher-period rakes for this -- it seems nearly impossible for a glider to make the maneuver required.

Code: Select all

x = 224, y = 412, rule = 22da
22bo$21bobo$20b3obo$22b2o$22bo$31bo$30bobo$30b2obo$29bob2o$26bobobo$
27b2o$27bo2$29bobo$29b2o$31bo10$22bo$23bo$20bo2bo$22bo$56bo$55bobo$48b
obo4b2obo$23b2o24bo4bob2o$24bobo22b2o4bo$23b2o28b2o$26b2o2bo21b2o$26b
2o26bo$27bo$61bo$29bo6b2o22bobo$29b2o4bo2bo20b3obo$29b3o29b2o$18bo17bo
24bo$18bo2$17bo$16bo2bo$20bo$23bo87bo2b2o$15bob2o3bo91b2o$16bobo94bo$
20b2o$17b2o3b4o89bo$17bo6b2obo95b2o$25bobo95b2o$27bo94bo$23bo95b3o$
121bo$8b3o101bo7b2o$8bo2bo110bo$11b2o99b3o$10bo104bo4$2bo2$o112bo2bo$
114bo2bo$4bo109bo2bo$o2bobo104bo$33bo78bo2bobo$34b2o$33b3obo77bo$35bob
o80bo$37bo77b2obo$118b2o2$118bo$117bobo$118b2o$118b3o2$119b3o3$109bo$
110bo2$73bo2b2o$76b2o$43bo31bo$44b2o$43b3obo29bo$45bobo37b2o$47bo37b2o
$84bo14bo$81b3o16bo$83bo$74bo7b2o$84bo$74b3o$77bo4$89bo$90bo2$117bobo$
118b2o$53bo64b3o$54b2o$53b3obo61b3o$55bobo$57bo16$63bo$64b2o$63b3obo$
65bobo$67bo4$117bobo$118b2o$118b3o2$119b3o8$73bo$74b2o$73b3obo$75bobo$
77bo14$117bobo$118b2o$83bo34b3o$84b2o$83b3obo31b3o$85bobo$87bo16$93bo$
94b2o$93b3obo61bobo$95bobo55bo4b2ob2o$97bo54b7o$154bo2bo3b2o$154b2obo
2b2o$156bob3o$117bobo35b3o2bo$118b2o36bobobo$118b3o37b3o$160b2o$119b3o
38bo$150bo$151bo38b2o$190b2o$185bo3bo$161bo24b3o$146bo14bobo22bobo$
145bo15bob3o2bo19bo$103bo59b2obob3o$104b2o59bo7bob2o$103b3obo61bo7bo$
105bobo61bobobo9bo8bo2b2o$107bo67b2o7bo10b2o$177bo6bo9bo$173bo10bobo$
196bo$136bo20bo16bo$135bo22bo9$117bobo6bo20bo$118b2o5bo22bo$113bo4b3o$
114b2o$113b3obob3o$115bobo$117bo4$116bo20bo$115bo22bo3$149b2o$149b2o
30bo2b2o$108bo35bo3bo35b2o$108bo36b3o35bo$145bobo$147bo37bo$106bo86b2o
$105bo6bo75bo4b2o$112b2o75bo2bo$113bo28bo8bo2b2o32b4o$143bo10b2o33b2o$
112bobobo26bo9bo35bobo$143bobo45b2o$155bo2$182bobo2$132bo$132b2o$133bo
2$132bobobo46bo2bo3$180bo4bo$180bobob2obo$183bo2bo$152bo32bo$152b2o$
153bo$189bo$152bobobo60b2o$189bo27b2o$186bo2bo22bo3bo$186b3o23b2obo$
189bo2bo21b2o$187bo6bo18b4o$170b2ob2o15bob2o21bobo$170bo4bo15bo7bo$
172bobo23bo4bo$171b2o2b2o20bob2o18bo2b2o$171bo2bo2bo21bo9bo12b2o$170b
3o4b3o18bo4bo17bo$172bo2bo2bob2o17bo9bo$173b2o3bo3bo40bo$175bo2bobo18b
2o$174bo9bo$175b2o2bob2o$181bo5$165b3o$165bo$166bo$167b2o3$157b2o$158b
obo$159bo$155bo42$78bo2b2o$81b2o$80bo2$82bo$90b2o$9bo75bo4b2o$9b2o75bo
2bo$10bo74b4o$86b2o$9bobobo72bobo$88b2o3$79bobo2$29bo$29b2o$30bo2$29bo
bobo46bo2bo3$77bo4bo$77bobob2obo$80bo2bo$49bo32bo$49b2o$50bo$86bo$49bo
bobo60b2o$86bo27b2o$83bo2bo22bo3bo$83b3o23b2obo$86bo2bo21b2o$84bo6bo
18b4o$67b2ob2o15bob2o21bobo$67bo4bo15bo7bo$69bobo23bo4bo$68b2o2b2o20bo
b2o18bo2b2o$68bo2bo2bo21bo9bo12b2o$67b3o4b3o18bo4bo17bo$69bo2bo2bob2o
17bo9bo$70b2o3bo3bo40bo$72bo2bobo18b2o$71bo9bo$72b2o2bob2o$78bo5$62b3o
$62bo$63bo$64b2o3$54b2o$55bobo$56bo$52bo$54bo$55b2o$55bo!
22darealDLA still hasn't been proven omniperiodic, but there is a stable glider duplicator.

Code: Select all

x = 41, y = 40, rule = 22darealDLA
40.B7$24.B4$21.B6$27.B2$15.A2$17.A6.B$9.B5.2A$15.2A2.A3$6.B6$12.B4$9.
B3$B!

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 18th, 2014, 9:11 am

Here is clean back-rake, based on gliders cleaning method, and the known "back rake/puffer":

Code: Select all

x = 99, y = 99, rule = 22da
97b2o$97b2o$92bo3bo$90bob2obo$86bo2bo$85bo4bo4bo$80bo8b2obo2b2o$79bo$
84bo7b2obo$79b4obo7bobo$80b5o3bo$79bo4bo2bo$79bo2bo2b2o7bo$78b2o5b2o6b
o$87b4o$88bo$78b2o6bob2o$54bo2b2o18bobobo6b2o$57b2o29b2o2bo$56bo21b2ob
2o2b3obobo$79bo2bo2bo$58bo22bo2$61b2o$62bo$61bo2bo$62bobo2$68bo$65bo2b
2o$63bo4b3o$64b3o$64bob2o$67bobo$66b2o4b2o$68bo$72bob2o$73bobo3$77bo2b
2o$80b2o$79bo2$81bo2$6bo2b2o$9b2o$8bo35bo$23bobo$10bo3bo2b2o4bob2o17b
2o2bo$17b2o14bo7b2o4bo$16bo8b2o5bo9b2o2bo$48bo$o17bo25bo3bobo$2bobo2b
2o37bo$2bobo2b2o33bo3b2o$6bo34bo5bo2$8bo2$12bo$11bobo$10b3obo$12b2o$
12bo34bo$46bo6$46bobo$18bobo25bob2o2$48b2o3$17b3o5bo$17bo2bo$18bobo4bo
18bo2b2o$15b2o2b2o26b2o$17bo28bo$17bo$35bo12bo$34bobo$33b3obo$35b2o$
35bo12bo2b2o$51b2o$39bo2b2o6bo$42b2o$41bo10bo2$42b2o2$42b2o2$44bo!
It's currently uses 12 gliders.

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 18th, 2014, 2:04 pm

Here is a bunch of recipes on deleting one of the p2s with two gliders:

Code: Select all

x = 1749, y = 119, rule = 22da
54$883bobo$883bob2o$959bobo83bobo$158bo88bo80bo80bo475b2o72bob2o82bob
2o$157bobo86bobo78bobo78bobo$156b3obo84b3obo76b3obo76b3obo549b2o84b2o$
158b2o87b2o79b2o79b2o$158bo88bo80bo80bo$471bo635bobo80bobo$93bo2b2o75b
o2b2o75bo2b2o75bo2b2o75bo2b2o52bobo20bo2b2o52bo22bo2b2o75bo2b2o75bo2b
2o75bo2b2o75bo2b2o75bo2b2o75bo2b2o49bob2o22bo2b2o52bob2o19bo2b2o75bo2b
2o155bo2b2o75bo2b2o75bo2b2o75bo2b2o$96b2o78b2o78b2o78b2o78b2o51b3obo
22b2o51bobo24b2o78b2o78b2o78b2o78b2o78b2o78b2o78b2o78b2o78b2o158b2o78b
2o78b2o78b2o$95bo79bo79bo79bo79bo55b2o22bo52b3obo22bo79bo79bo79bo79bo
79bo79bo53b2o24bo56b2o21bo79bo159bo79bo79bo79bo$471bo78b2o$97bo79bo79b
o79bo79bo79bo52bo26bo79bo5bo73bo79bo79bo79bo79bo79bo79bo79bo159bo79bo
79bo79bo$662bobo38bo$61bo2b2o33bo79bo79bo79bo79bo79bo79bo79bob3obo36bo
bo34bo79bo79bo79bo79bo79bo79bo41bobo35bo44bo22bo2b2o7bo79bo79bo79bo79b
o$64b2o597b2o36b3obo555bob2o78bobo24b2o$63bo36bo79bo79bo79bo79bo79bo
79bo79bo2bo39b2o35bo79bo79bo79bo79bo79bo79bo79bo41b3obo22bo10bo79bo79b
o79bo79bo$703bo559b2o79b2o$65bo1278bo26bo$805bo$804bobo546bobo$803b3ob
o545bob2o$805b2o$805bo549b2o86bobo$1443bob2o2$1445b2o72bobo$1519bob2o
76bobo$1599bob2o$1521b2o$1601b2o71bobo$1674bob2o2$1676b2o!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 18th, 2014, 9:03 pm

@simsim314: That makes my decision easy! My earlier objection was that the gliders were too close to each other to be continually produced by backrakes, but since the gliders are so far from each other here, I won't need any crazy manuevers, and since the smoking ship backrake is becoming a mess, this seems like my best alternative.
I noticed that you didn't offer any cleanup reactions for duoplets in the other orientation. Here's a (perhaps cramped) two-glider cleanup reaction for this type of duoplet.

Code: Select all

x = 14, y = 14, rule = 22da
o2b2o$3b2o$2bo2$4bo2$6bo$7bo2$11bo$10bobo$9b3obo$11b2o$11bo!
While trying to clean up the debris of the back puffer, I came upon a tiny O(n log n) growth pattern.

Code: Select all

x = 14, y = 24, rule = 22da
b2o$b2o9$5bo2$3bo2bo3b2o$10b2o$4bo3$3b2o6bo$2bo2bo7bo$b2o3bo2bo$2o4bo
4bo$4b2o$2ob2o$bobo!
Here's a 5-cell infinite growth pattern that perhaps explains why the puffer produced is so common.

Code: Select all

x = 4, y = 4, rule = 22da
bo$obo$3bo$2bo!

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 20th, 2014, 1:34 pm

c0b0p0 wrote:I noticed that you didn't offer any cleanup reactions for duoplets in the other orientation.
Well you can notice that all my cleaning operations are made to this orientation. But first I use one glider to change the orientation and then I use any of the two gliders in the recipe to clear it. But yes I definitely didn't looked for two gliders cleanup for this orientation, nice job!

-----
c0b0p0 wrote:O(n log n) growth pattern

It's probably something more like O(n) +O(log^2(n)) which is still O(n). There is no "multiplication" in this "binary adder". But yes it's nice.

----
Looking for 11 cells quadratic, I'm almost certain that 12 is the minimum. At least as two linear growth combination are considered.

Here is another 12 cells quadratic:

Code: Select all

x = 19, y = 7, rule = 22da
bo$obo13bo$3bo10bobo$2bo$18bo$17b2o$18bo!
And here is a new much more dense way to grow quadratic (14 cells):

Code: Select all

x = 44, y = 51, rule = 22da
41bo$39bobo2$43bo$42b2o$43bo40$2bo$obo2$4bo$3b2o$4bo!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 20th, 2014, 6:33 pm

@simsim314: Given the 5-cell infinite growth pattern, it could easily be as low as 9, since it's easy to transform a duoplet puffer into any of the other two common puffers. However, unless there is another breeder, which is unlikely, the limit will probably stand at 12.

Code: Select all

x = 35, y = 6, rule = 22da
33bo2$3bo13bo16bo$2bo13bo16bo$2o3bo8b2o15b2o$2o12b2o15b2o!
My post in this thread on March 21st included another binary counter of a similar type that I decided was O(n log n). Here's a reduction of the earlier "binary adder" (previously it was 34 cells; now it is 33 cells) which makes it look more synthesizable than it really is.

Code: Select all

x = 14, y = 24, rule = 22da
b2o$b2o9$5bo2$3bo2bo3bo$10b2o$4bo3$3b2o6bo$2bo2bo7bo$b2o3bo2bo$2o4bo4b
o$4b2o$2ob2o$bobo!
For the sawtooth, this demonstrates an approach that can make pairs of gliders that are very close to each other.

Code: Select all

x = 276, y = 262, rule = 22da
257bo2b2o$260b2o$259bo2$194bo66bo$204bobo$196bo9bo$194b2o10bo$194b2o2b
o8bo$268bo$267bobo$266b3obo$202bo65b2o$202bobo63bo$202b3o$201bo3bo$
199b2o$199b2o3$211bo$212bo9$201bo$202bo8$230bo$191bo25bo2b2o7bo$175bo
16bo27b2o7bo2bo$153bo65bo9bo2bo$163bobo10bo53b2o$155bo9bo6bo48bo8bobo$
153b2o10bo7b2o59bo$153b2o2bo8bo9bobobo51b2o$172bo7bo52bobob2o$173b2obo
7bo29bo21bo$179b3obob2o28b2o18b2o3bo$161bo19bo2b3obo25b3obo18b3o$161bo
bo22bobo27bobo$161b3o24bo29bo$160bo3bo$158b2o$158b2o6$227b3o2$228b3o$
229b2o$229bobo2$258bo$259bo4$271bo$272b3o$264bo$265b2o7bo$265bo$248bo
16b3o$249bo14bo$262b2o$177bo2b2o80b2o$180b2o89bo$179bo$273bo$181bo89b
2o$271b2o2bo2$238bo$239bo3$227b3o2$228b3o$229b2o$229bobo$230bo2$229b2o
$230bob2o$230bo$233bo2$231bobo2bo$238bo$231bo2bo$231bo2bo$232bo2bo6$
233bo$234b3o$226bo$227b2o7bo$227bo$227b3o$226bo$137bo2b2o82b2o$140b2o
82b2o$139bo93bo2$141bo93bo$233b2o$233b2o2bo34$97bo2b2o$100b2o$99bo2$
101bo3$41b2o2$41b2obo$42bobo13bo$48b2o8bo2b2o$48bo7b2obo2bo$51bo$49bo
13bo$47b2obo12bo$46b2o3bo$50b2o$46b2ob2o$47bobo6$55bo$56bo9$45bo$46bo
2$57bo28b2o$89b2o$60b2o28bo$60b2o$89bo$90b2o$63bo25bo$2o33bo39bo13bo$
36bo39bo$2obo14b2o25b3o$bobo13bo26bob2obo$7b2o8b2o25bo2b2o$7bo7b2o67b
2o2bo$10bo10b2o22bo3bo33b2obo$8bo15b2o20bo3bo2bo28b2o3bo2bo$6b2obo15b
2o20bo4bo33bo2b2o$5b2o3bo36b2o3b3o27b2ob2o$9b2o38bo3b2o10bo17bobo$5b2o
b2o40bo3bo11bo$6bobo43b2o37b2o2$91b2obo$92bobo5$55bo$56bo9$48bo$48b2o$
49bo2$50bo$50bo2$54bo$52bobo$52b2o$51bo$51bo5$46b2o2bo$45b2obo$44b2o3b
o2bo$48bo2b2o$44b2ob2o$45bobo2$53b2o2$53b2obo$54bobo!
Unless I get a denser duoplet killer, however, it seems that 10 cleanup gliders will be required.

A p16 has a stellar reputation for eating, even being able to eat another p16. However, it seems that the smallest p16 eater is a duoplet.

Code: Select all

x = 8, y = 8, rule = 22da
2bo$b2o$4bo$4b2o2$6b2o$bo4bo$o!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 21st, 2014, 5:21 pm

This reaction converts a duoplet to a glider. Combining this with simsim314's technology, it should be possible to make a more efficient backrake.

Code: Select all

x = 111, y = 113, rule = 22da
109bo$110bo11$97bo$98bo11$85bo$86bo11$73bo$74bo11$61bo$62bo11$49bo$50b
o11$37bo$38bo11$25bo$26bo5$7bo2b2o$10b2o$obo6bo$ob2o$11bo$2b2o$13bo$
14bo2$18bo$17bobo$16b3obo$18b2o$18bo5$16bo2b2o$19b2o$18bo2$20bo!
 

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 21st, 2014, 7:10 pm

c0b0p0 wrote:it should be possible to make a more efficient backrake
Here is a back rake along those lines (I only checked the regular douplet puffer + 2 glider in your constellation).

Code: Select all

x = 60, y = 59, rule = 22da
56bobo$53b2obob2o$50bo$52b2o4b2o$54bo$55bo2bo$56bobo$39bo2b2o12bo$42b
2o$41bo15bo$49bo$39b2obo5bo$21b2o$17bo3b2o17b2ob2o$18bobo21bo$15bobo
23bo$14bo2bo2bo25bo3bo$18b2obo9b2o12b3obobo$12bob2o15bo15bob2obo$13bo
2bo2bo11b2obo7b2o4bob2o$16bobo12b3o16bo$13bobo16b2o2bo6bo$11b2o3bo14bo
bobo7b2o$11b2o28bo2bo$42b3o$41b2obo$45bo$42bo3bo$44b2o2$18bo$30bo$19bo
$29bo3bo3$29bo2bo$31b2o3bo$31bo3bo$17bobo$17bob2o15bo$37bo$19b2o4$33bo
2b2o$36b2o$o2b2o14bo2b2o11bo$3b2o17b2o$2bo18bo15bo2$4bo18bo$8bobo$8bob
2o2$10b2o4bo2$17bo!
It's really not so optimized, it uses 3 gliders for back shoot, and 5 for cleaning. But it proves that glider+douplet puffer can create a clean back rake. Considering the fact it's almost gliders only the "theoretical" synthesis of such back rake is trivial. Probably it can be optimized to have 3-4 back glider.

EDIT Just for fun here are couple of quadratics along the same lines:

Code: Select all

x = 46, y = 53, rule = 22da
7$29bobo$25b2ob2ob2o$25bo$31b2o$31bo$27bo$31bo$12bo2b2o13b2o$15b2o$14b
o7bo$23bo$15b2o$16bo$15bo$18bo$17bo$19bo3bo$8bo7bo5bobo$7bobo11b3obo$
7bo6bo2bo5b2o$23bo$10bo4bobo$7bobo7bo$17bobo6bo$7b2o16bobo$8bo11bo4b2o
bo$9b2obo7bo3bob2o$10b2o10bo2b2o$21bob2o$8bo3bo10bo$13bo$12bo2$7bo12b
2o$7bo3$15bo!

Code: Select all

x = 52, y = 40, rule = 22da
7$40b2o$32bob2o4b2o$34bo4bo$38bo$33bo$33bo$24bo9bo5bo$23bobo8b2o3b2o$
11bo2b2o6b3obo9b2o$14b2o8b2o14bo$13bo10bo$30bo$15bo13bo4$31bobo$31bob
2o2$33b2o!
Last edited by simsim314 on May 22nd, 2014, 4:07 pm, edited 1 time in total.

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 22nd, 2014, 4:07 pm

Here is a sawtooth recipe, it's built having the parabolic sawtooth in mind:

Code: Select all

x = 371, y = 348, rule = 22da
370bo$369bo15$355bo2b2o$358b2o$357bo2$359bo3$337bobo$337bob2o2$339b2o
5$318bobo$318bob2o2$320b2o17$312bo2b2o$315b2o$314bo2$316bo12$291bo2b2o
$294b2o$293bo2$295bo14$265bo2b2o$268b2o$267bo2$269bo24$260bo$259bobo$
258b3obo$260b2o$260bo4$238bo2b2o$241b2o$240bo2$242bo4$219bo2b2o$222b2o
$221bo2$223bo15$217bo$216bobo$215b3obo$217b2o$217bo12$196bo$195bobo$
194b3obo$196b2o$196bo18$154bo2b2o$157b2o$156bo2$158bo2$152bobo$152bob
2o2$154b2o10$135bo2b2o$138b2o$137bo2$139bo2$133bobo$133bob2o2$135b2o
10$116bo2b2o$119b2o$118bo2$120bo2$114bobo$114bob2o2$116b2o10$97bo2b2o$
100b2o$99bo2$101bo2$95bobo$95bob2o2$97b2o10$78bo2b2o$81b2o$80bo2$82bo
2$76bobo$76bob2o2$78b2o10$59bo2b2o$62b2o$61bo2$63bo2$57bobo$57bob2o2$
59b2o10$40bo2b2o$43b2o$42bo2$44bo2$38bobo$38bob2o2$40b2o10$21bo2b2o$
24b2o$23bo2$25bo2$19bobo$19bob2o2$21b2o10$2bo2b2o$5b2o$4bo2$6bo2$obo$o
b2o2$2b2o!
Now it's only a question of correct gun placing.

For reference here is parabolic sawtooth:

Code: Select all

#N Parabolic sawtooth
#O Dean Hickerson
#C A sawtooth with parabolic envelope and minimum repeating population
#C that repeats in quadratic (as opposed to exponential) time.
#C www.conwaylife.com/wiki/index.php?title=Parabolic_sawtooth
x = 126, y = 144, rule = B3/S23
34b2o11b2o36b2o18b2o19b$34bo12bo37bo19bo20b6$16b2o16bo91b$16bo16b3o90b
$33b3o36b2o29bo5bo16b$72bo11b3o16b2o3b2o16b$31b2o3b2o6b2o3b2o32bo3bo
38b$31bo5bo44bo5bo16b3o18b$45bo3bo32bo5bo16b3o18b$46b3o57bo19b$46b3o
24bo10bo41b$35bo35b2ob2o7b2o41b$34bo91b$34b3o33bo5bo49b$14b5o107b$13bo
b3obo50b2o3b2o5b3o41b$14bo3bo26bo5bo30b3o41b$15b3o15bo5bo4b3o5bo28bo3b
o40b$16bo16bo5bo4b3o3b3o73b$34bo3bo41b2o3b2o20b3o6b2o8b$35b3o4b2o3b2o
57bo3bo5bo9b$42bo5bo56bo5bo14b$5b2o7bo90bo5bo14b$5bo8bo111b$13bobo110b
$12b2ob2o99b3o7b$11bo5bo98b3o7b$14bo23b2o7b2o23b2o3b2o36bo3bo6b$11b2o
3b2o20bo8bo24bo5bo47b$5bo33b3o6b3o31b2o23b2o5b2o3b2o5b$4b3o27b2o5bo8bo
4b2o16bo3bo4bo24bo18b$4b3o28bo19bo18b3o21b2o26b$35bobo5bo9bobo42bo27b$
2b2o3b2o27b2o4bobo8b2o71b$2bo5bo32bob2o81b$40b2ob2o81b$13b2o26bob2o13b
o67b$13bo9b2o17bobo12bo40bo27b$4bo15bo4b4o14bo13b3o14b2o4bobo13b2ob2o
25b$5bo13b2o2b2ob3o36b2o7bo5b2o44b$3b3o17bo37b4o4b2o10bo13bo5bo24b$61b
3ob2o2bo18bo2bo34b$66bo16b2o2b2o3bo2b2o3b2o14bo5bo3b$83bo8bo23b2o3b2o
3b$o5bo81b4o34b$o5bo111b3o5b$bo3bo21bo15bo74b3o5b$2b3o22b2o15bo74bo6b$
26bobo13b3o81b3$34bo91b$34b3o89b$37bo88b$36b2o55b2o3b2o2b2o22b$25b2o
66bo5bo2bo23b$26bo32bo9b2o51bo3b$57bobo10bo23bo3bo22b3o2b$23bo2bo31b2o
10bobo5bo16b3o22b5ob$3b2o3b2o14bo2bo43b2o3b4o39b2o3b2o$3b2o3b2o15bobo
8bo5bo34bob2o9b2o34b$4b5o17bo9bo5bo32bobob3o8bo35b$5bobo29bo3bo35bob2o
45b$25b2o11b3o35b4o32b2o12b$5b3o17bo30bo21bo33bobo11b$57b2o37b2o11b2ob
obo11b$56b2o38bo12bobobo12b$111bo14b$111b2o13b$8bo43b2o57b3o12b$7bobo
42bo23bo34b3o3b2o3b2o2b$6bo3bo63bobo34b3o3b2o3b2o2b$7b3o28b2o35b2o34b
2o5b5o3b$5b2o3b2o26bo15b2o55bo7bobo4b$54bo32b2o20bobobo12b$45b2o5bobo
32bo21b2obobo4b3o4b$44b3o5b2o19bo38bobo11b$32bo8bob2o29bo37b2o12b$32bo
bo6bo2bo27b3o51b$20b2o11bobo5bob2o81b$20bo12bo2bo7b3o79b$33bobo9b2o63b
2o7b2o5b$32bobo75bo8bo6b$32bo93b$8b2o33b2o81b$8bo34bo12b2o51b3o14b$55b
o2bo50b2o15b$47b2o6bo56b2o12b$48b2o5bo55b3o12b$47bo7bob2o51bobo13b$57b
o52b2o14b3$56b2o68b$56bo69b2$28bobo95b$28bo3bo93b$18b2o12bo10b2o81b$
18bo14bo7bo2bo21b2o42b2o14b$32bo7bo11b2o12bo43bo15b$28bo3bo7bo11bo73b$
28bobo9bo85b$41bo2bo20b3o58b$43b2o20b2o59b$68b2o56b$34bo32b3o56b$34bob
o29bobo57b$17b2o18b2o4b2o21b2o41b2o15b$19bo17b2o4bo65bo16b$20bo16b2o9b
3o23bo51b$9b2o9bo8bo4bobo13bo22b2o51b$9bo10bo9bo3bo14bo7b2o13b2o8b2o
42b$19bo8b3o26b3o11b3o8bo43b$17b2o40b2obo9b2o52b$59bo2bo10b2o51b$59b2o
bo11bo51b$50b2o5b3o66b$49bobo5b2o67b$49bo44bo31b$48b2o40b2o2b2ob3o26b$
90bo5b4o26b$86b2o6b2o30b$85bobo18b2o18b$22b2o60b3o19bo19b$24bo59b2o21b
3o16b$14b2o9bo13bo47b2o20bo16b$14bo10bo13bobo44b3o37b$25bo16b2o4b2o12b
2o62b$24bo17b2o4bo13b3o61b$22b2o18b2o9b2o9b2obo11bo6b2o38b$39bobo11bo
10bo2bo10b2o6bo39b$39bo24b2obo9b2o47b$62b3o11b3o47b$62b2o13b2o47b$78b
2o5b2o39b$79bo5bobo38b$87bo38b$87b2o!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 22nd, 2014, 9:26 pm

@simsim314: A one-glider pulling reaction is known, and was used in my growing spaceship:

Code: Select all

x = 411, y = 412, rule = 22da
409bo2$410bo21$333bo2$333b2o$332bo$324bo2bo6bo$326bo6bob2o$337b2o$330b
2o7bo$324bo5bobo2bobobo$323b2o9bobo3bo$322b2o11bobo2bo$326b2o5b2obo4bo
bo$322b2ob2o7bo5bo2bobo$323bobo11bo4bo$338bo$337b2o$369bobo$369bob2o$
334bo6bo$333b2o5bo30b2o$332b2o$336b2o3bo$332b2ob2o$333bobo10$328bo2$
330bo$328b2o$328b2o2bo6$376bo2$376b2o$375bo$367bo2bo6bo$369bo6bob2o$
380b2o$373b2o7bo$367bo5bobo2bobobo$366b2o9bobo3bo$365b2o11bobo2bo$369b
2o5b2obo4bobo$365b2ob2o7bo5bo2bobo$351bo14bobo11bo4bo$381bo$353bo26b2o
$351b2o$351b2o2bo$377bo6bo$323bobo50b2o5bo$323bob2o48b2o$379b2o3bo$
325b2o48b2ob2o$376bobo27$234bo2$234b2o$233bo$225bo2bo6bo$227bo6bob2o$
238b2o$231b2o7bo$225bo5bobo2bobobo$224b2o9bobo3bo$223b2o11bobo2bo$227b
2o5b2obo4bobo$223b2ob2o7bo5bo2bobo$224bobo11bo4bo$239bo$238b2o2$275bob
o$235bo6bo32bob2o$234b2o5bo$233b2o42b2o$237b2o3bo$233b2ob2o$234bobo11$
230bo$229b2o$228bob3o$229bobo$230bo11$283bo2$283b2o$282bo$274bo2bo6bo$
276bo6bob2o$287b2o$280b2o7bo$274bo5bobo2bobobo$273b2o9bobo3bo$272b2o
11bobo2bo$276b2o5b2obo4bobo$272b2ob2o7bo5bo2bobo$273bobo11bo4bo$259bo
28bo$258b2o27b2o$227bobo27bob3o$227bob2o27bobo$259bo24bo6bo$229b2o52b
2o5bo$212bo69b2o$211bo74b2o3bo$282b2ob2o$283bobo$202bo$201bo9$226bo$
225bo9$188bo33bo$187bo33bo3$178bo$177bo9$202bo$201bo5$179bobo$179bob2o
2$181b2o$164bo33bo$163bo33bo3$154bo$153bo9$178bo$177bo7$2bo$b2o$ob3o
135bo33bo$bobo135bo33bo$2bo2$130bo$129bo9$154bo$153bo$14bo$14bobo$14bo
b3o$16b2o$18bo112bobo$131bob2o2$133b2o$116bo33bo$115bo33bo3$106bo$105b
o9$130bo$129bo9$92bo33bo$91bo33bo3$82bo$81bo3$96b2o$91bo6bo$90bo7bo2$
93bo$94bo$106bo$97bo7bo$38bo57bo$38bobo$38bob3o$40b2o$42bo2$81bobo$81b
ob2o$102bo$83b2o16bo2$71b2o$58bo11bobobo$57bo12b2o2b2o$65bo8b3o$64bo
10b3o$73bo2b3o$73b2o$78b2o$77bobo$77b2o2$68bo$67bo2$76bo$75bo2$43bobo
2$44bo4b4obo$45bobo5bo$47bo3b2ob3o21bo$52bobobo20bo$49bo2bo2b4o$47bobo
2bo3bobo$47b2o3bobo2b2obo$44bo2bo2b3o6bo$46bo5b7obo$45bobo5bo4bobo$48b
obo2bo6bo$48bo6b2o3bo$49b2o3bo$51bob3o2b2o$52bo$51bo7bo2bo$53bo6bo$62b
o$86bobo$33bo5bo47b2o$32bo5b2o47b3o$37bob3o$40bo47b3o$37bobo$30b3ob3o$
29bob2ob3o$29bo4b3o$33bo7bo$35b2o3bo$28b2o5b2o$27b2o7bo$31bo2b2o$27b2o
b2o$28bobo9$134bobo$135b2o$135b3o2$136b3o10$154bo$153b2o$152bob3o$153b
obo$154bo!
Unfortunately, it doesn't work for duoplets in that orientation.
simsim314 wrote:Probably it can be optimized to have 3-4 back glider.
The "back puffer" certainly can be optimized to use no more than 3-4 cleanup gliders. Here's the smallest backrake predecessor I could make, which breaks the record for the smallest backrake. Since the puffer can be made by making a constellation of duoplets and then synthesizing a DDP (double duoplet puffer) in front, it shouldn't be difficult to synthesize it.

Code: Select all

x = 64, y = 64, rule = 22da
39bo$38bobo$39bobo$40bo14$14b2o2$14b2obo$15bobo2$61bo$60bobo$61bobo$
62bo21$43b2o2$43b2obo$44bobo4$2bo2$3bo$6bo$7bo2$3bo$3b2o3bo$2bo7bo$2o$
2o!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 23rd, 2014, 8:15 pm

This shaves off two gliders from the projected back-puffer synthesis and is relatively clean, so it should be good enough for a nice small sawtooth.

Code: Select all

x = 26, y = 33, rule = 22da
obobo2$3bo$3b2o$4bo21$22bo$24bo2$21bo3bo$21b2o$20bo$18b2o$18b2o!
A 17-cell O(n log n) growth pattern:

Code: Select all

x = 10, y = 25, rule = 22da
bo$o$bobo$2bo12$3bo2$4bo3$3bo3bo$3b2o4bo$2bo$2o$2o!

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 24th, 2014, 8:10 am

c0b0p0 wrote:O(n log n) growth pattern
I've already mentioned it's not O(n log n) because there is no "logn multiplier" of factor N. To show it more clearly here is population graph (I've made it up to about 182 millions):

Code: Select all

x = 588, y = 536, rule = 22da
266b4o3b3o2b4o2bo3bobo6b3o2b5o2b3o3b3o2bo3bo7b4o2bo6b3o2b5o$266bo3bobo
3bobo3bobo3bobo5bo3bo3bo5bo3bo3bob2o2bo7bo3bobo5bo3bo3bo$266bo3bobo3bo
bo3bobo3bobo5bo3bo3bo5bo3bo3bobobobo7bo3bobo5bo3bo3bo$266b4o2bo3bob4o
2bo3bobo5b5o3bo5bo3bo3bobo2b2o7b4o2bo5bo3bo3bo$266bo5bo3bobo5bo3bobo5b
o3bo3bo5bo3bo3bobo3bo7bo5bo5bo3bo3bo$266bo5bo3bobo5bo3bobo5bo3bo3bo5bo
3bo3bobo3bo7bo5bo5bo3bo3bo$266bo6b3o2bo6b3o2b5obo3bo3bo4b3o3b3o2bo3bo
7bo5b5o2b3o4bo8$bo4b3o3b3o3b3o3b3o5bo4bo4b3o2b5o$2o3bo3bobo3bobo5bo3bo
3b2o3b2o3bo3bobo$bo3bo3bo5bobo5bo3bo2bobo4bo7bobo$bo4b3o5bo2b4o3b3o2bo
2bo4bo6bo3b3o10bo498bo$bo3bo3bo3bo3bo3bobo3bob5o3bo5bo7bo9bo498bo$bo3b
o3bo2bo4bo3bobo3bo4bo4bo4bo4bo3bo9bo498bo$3o3b3o2b5o2b3o3b3o5bo3b3o2b
5o2b3o10bo498bo$61bo495bo2bo$61bo495bo2bo$61bo495bo2bo$61bo492bo2bo2bo
$61bo492bo2bo2bo$61bo492bo2bo2bo$61bo489bo2bo2bo2bo$61bo489bo2bo2bo2bo
$61bo489bo2bo2bo2bo$61bo486bo2bo2bo2bo2bo$61bo486bo2bo2bo2bo2bo$61bo
486bo2bo2bo2bo2bo$61bo483bo2bo2bo2bo2bo2bo$61bo483bo2bo2bo2bo2bo2bo$
61bo483bo2bo2bo2bo2bo2bo$61bo480bo2bo2bo2bo2bo2bo2bo$61bo480bo2bo2bo2b
o2bo2bo2bo$61bo480bo2bo2bo2bo2bo2bo2bo$61bo477bo2bo2bo2bo2bo2bo2bo2bo$
61bo477bo2bo2bo2bo2bo2bo2bo2bo$61bo477bo2bo2bo2bo2bo2bo2bo2bo$61bo474b
o2bo2bo2bo2bo2bo2bo2bo2bo$61bo474bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo474bo
2bo2bo2bo2bo2bo2bo2bo2bo$61bo471bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo471b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo471bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo
468bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo468bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo$61bo468bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo465bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo$61bo465bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo
465bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$61bo462bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo$61bo462bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b2o$61bo
462bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobobo$61bo459bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bobobo$61bo459bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob
o$61bo459bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2obo$61bo456bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bobob2obo$61bo456bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2b3ob2obo$61bo456bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2obo$
61bo453bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2obo$61bo453bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2obo$61bo453bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bobob2ob2ob2obo$61bo450bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2b3ob2ob2ob2obo$61bo450bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob
2obo$61bo450bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2obo$61bo
447bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2obo$61bo447bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2obo$61bo447bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2obo$61bo444bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2obo$61bo444bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bobob2ob2ob2ob2ob2ob2obo$61bo444bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bobob2ob2ob2ob2ob2ob2obo$61bo441bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2b3ob2ob2ob2ob2ob2ob2obo$61bo441bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob
2ob2ob2ob2ob2ob2ob2obo$61bo441bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob
2ob2ob2ob2ob2ob2obo$61bo438bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob
2ob2ob2ob2ob2ob2obo$61bo438bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2o
b2ob2ob2ob2ob2ob2obo$61bo438bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2obo$61bo435bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2o
b2ob2ob2ob2ob2ob2ob2obo$61bo435bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob
2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo435bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
3ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo432bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo432bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo432bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo429bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo
429bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2obo$61bo429bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2obo$61bo426bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo426bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo426bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo423bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61b
o423bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2o$61bo423bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2obo$61bo420bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo420bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo420bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo417bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$61bo417bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2obo$61bo417bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo414bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo414bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo414bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo
411bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2obo$61bo411bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$61bo411bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo408bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo408bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo408bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo405b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$61bo405bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$61bo405bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo402bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo402bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo402bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo399bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo399b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
o$61bo399bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$61bo396bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2obo$61bo396bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo396bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo393bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo393bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo393bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo390bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
61bo390bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2o$61bo390bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2obo$61bo387bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2o$61bo387bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo387bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo384bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo384bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo384bo2bo2bo2bo2bo
2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo381bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo
381bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
61bo381bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$61bo378bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2obo$61bo378bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$61bo378bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo375bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo375bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo375bo2bo2bo2bo2bo2bo2bo2bo2bo2bob
ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo372bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo372bo2bo2bo2bo2bo2bo2bo2b
o2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo372bo2bo2bo2bo2bo2bo
2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo369bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo369bo2bo2bo
2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo369bo2b
o2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo366bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo
366bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$
61bo366bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
$61bo363bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2obo$61bo363bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2o$61bo363bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$61bo360bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2obo$61bo360bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$61bo360bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2o$61bo357bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$61bo357bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$61bo357bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2obo$61bo354bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo354bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo354bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2o$61bo351bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo351bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2obo$61bo351bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2o$61bo348bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo348bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2obo$61bo348bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo345bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo345bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo345bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo342bo2bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo342bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo342bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2obo$61bo339bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo339bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2o$61bo339bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2obo$61bo336bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$61bo336bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o
b2ob2ob2ob2obo$61bo336bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$61bo333bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2o$61bo333bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2obo$61bo333bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2o$61bo330bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$61bo330bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
61bo330bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo
327bo2bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo
327bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo327b
o2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo324bo2bo
2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo324bo2bo2bo
2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo324bo2bo2bo2bo
2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo321bo2bo2bo2bo2bo2bo
2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo321bo2bo2bo2bo2bo2bo2bo
2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo321bo2bo2bo2bo2bo2bo2bo2bo
2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo318bo2bo2bo2bo2bo2bo2bo2bo2bobob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo318bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob
2ob2ob2ob2ob2ob2ob2ob2obo$61bo318bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$61bo315bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$61bo315bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o
b2ob2obo$61bo315bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o
$61bo312bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo
312bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo312bo2bo
2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo309bo2bo2bo2bo2b
o2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo309bo2bo2bo2bo2bo2bo
2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo309bo2bo2bo2bo2bo2bo2bo2bobo
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo306bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo306bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2o
b2ob2ob2ob2ob2o$61bo306bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob
2ob2obo$61bo303bo2bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o
$61bo303bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo
303bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo300bo2bo
2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo300bo2bo2bo2bo2b
o2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo300bo2bo2bo2bo2bo2bo2bo2b
obob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo297bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo297bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2ob2obo$61bo297bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o
b2ob2o$61bo294bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2obo$
61bo294bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo294bo
2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo291bo2bo2bo2bo
2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo291bo2bo2bo2bo2bo2bo2bo
2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo291bo2bo2bo2bo2bo2bo2bo2b3ob2ob2o
b2ob2ob2ob2ob2ob2obo$61bo288bo2bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o
b2ob2ob2o$61bo288bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o$
61bo288bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2obo$61bo285bo2bo
2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2o$61bo285bo2bo2bo2bo2bo2b
o2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o$61bo285bo2bo2bo2bo2bo2bo2bo2b3ob
2ob2ob2ob2ob2ob2ob2ob2o$61bo282bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2ob2o$61bo282bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob
2obo$61bo282bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2o$61bo279bo
2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2ob2o$44b7o10bo279bo2bo2b
o2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2obo$47bo13bo279bo2bo2bo2bo2bo
2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2o$46bo14bo276bo2bo2bo2bo2bo2bo2bo2bob
ob2ob2ob2ob2ob2ob2ob2ob2obo$45bo15bo276bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob
2ob2ob2ob2ob2ob2o$44b7o10bo276bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob
2ob2ob2o$61bo273bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2obo$
45b5o11bo273bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2o$44bo5bo
10bo273bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2obo$44bo5bo10bo
270bo2bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2o$44bo5bo10bo270bo
2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2o$45b5o11bo270bo2bo2bo2bo
2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2obo$61bo267bo2bo2bo2bo2bo2bo2bo2bobo
b2ob2ob2ob2ob2ob2ob2ob2o$61bo267bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob
2ob2ob2obo$44bo5bo10bo267bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob
2o$44b7o10bo264bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2ob2o$44bo5b
o10bo264bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2obo$61bo264bo2bo2b
o2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2o$61bo261bo2bo2bo2bo2bo2bo2bo2b
3ob2ob2ob2ob2ob2ob2ob2ob2o$44bo16bo261bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob
2ob2ob2ob2ob2o$44bo16bo261bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob
2o$44b7o10bo258bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2obo$44bo16b
o258bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2o$44bo16bo258bo2bo2bo
2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2o$61bo255bo2bo2bo2bo2bo2bo2bo2b3o
b2ob2ob2ob2ob2ob2ob2o$45b6o10bo255bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2ob2o$44bo2bo13bo255bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2obo
$44bo2bo13bo252bo2bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o$44bo2bo
13bo252bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2o$45b6o10bo252bo2b
o2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2obo$61bo249bo2bo2bo2bo2bo2bo2bo2b
3ob2ob2ob2ob2ob2ob2ob2o$50bo10bo249bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob
2ob2ob2obo$50bo10bo249bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o$50bo
10bo246bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2ob2o$50bo10bo246bo2bo
2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2obo$44b7o10bo246bo2bo2bo2bo2bo2bo
2b3ob2ob2ob2ob2ob2ob2ob2o$61bo243bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2o
b2ob2obo$44b6o11bo243bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$50bo
10bo243bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o$50bo10bo240bo2bo2bo
2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2obo$50bo10bo240bo2bo2bo2bo2bo2bo2b3o
b2ob2ob2ob2ob2ob2ob2o$44b6o11bo240bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o
b2ob2o$61bo237bo2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$45b2o14bo
237bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o$44bo2bo13bo237bo2bo2bo2b
o2bo2bobob2ob2ob2ob2ob2ob2ob2obo$44bo2bo13bo234bo2bo2bo2bo2bo2bo2bobob
2ob2ob2ob2ob2ob2ob2o$44bo2bo13bo234bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob
2ob2ob2o$44b7o10bo234bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$61bo231b
o2bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$45b5o11bo231bo2bo2bo2bo2bo
2bo2b3ob2ob2ob2ob2ob2ob2obo$44bo5bo10bo231bo2bo2bo2bo2bo2bobob2ob2ob2o
b2ob2ob2ob2o$44bo5bo10bo228bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2ob2o$
44bo5bo10bo228bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2obo$45b5o11bo228bo
2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$61bo225bo2bo2bo2bo2bo2bo2b3ob2o
b2ob2ob2ob2ob2obo$45b2o14bo225bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2o$
44bo2bo13bo225bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$44bo2bo13bo222b
o2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2obo$44bo2bo13bo222bo2bo2bo2bo2bo
2bobob2ob2ob2ob2ob2ob2ob2o$44b7o10bo222bo2bo2bo2bo2bo2bobob2ob2ob2ob2o
b2ob2obo$61bo219bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2o$61bo219bo2bo2b
o2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$61bo219bo2bo2bo2bo2bo2bobob2ob2ob2ob
2ob2ob2obo$61bo216bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2o$61bo216bo2bo
2bo2bo2bo2bobob2ob2ob2ob2ob2ob2obo$61bo216bo2bo2bo2bo2bo2b3ob2ob2ob2ob
2ob2ob2o$61bo213bo2bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2o$61bo213bo2bo2b
o2bo2bo2bobob2ob2ob2ob2ob2ob2obo$61bo213bo2bo2bo2bo2bo2b3ob2ob2ob2ob2o
b2ob2o$61bo210bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2ob2o$61bo210bo2bo2bo
2bo2bo2bobob2ob2ob2ob2ob2ob2o$61bo210bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o
b2o$61bo207bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2obo$61bo207bo2bo2bo2bo
2bo2bobob2ob2ob2ob2ob2ob2o$61bo207bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2ob2o
$61bo204bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2obo$61bo204bo2bo2bo2bo2bo
2b3ob2ob2ob2ob2ob2ob2o$61bo204bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2obo$61bo
201bo2bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2o$61bo201bo2bo2bo2bo2bo2b3ob2ob
2ob2ob2ob2ob2o$61bo201bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2obo$61bo198bo2bo
2bo2bo2bo2bobob2ob2ob2ob2ob2ob2o$61bo198bo2bo2bo2bo2bo2b3ob2ob2ob2ob2o
b2obo$61bo198bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2o$61bo195bo2bo2bo2bo2bo
2bobob2ob2ob2ob2ob2ob2o$61bo195bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2obo$61b
o195bo2bo2bo2bo2bobob2ob2ob2ob2ob2ob2o$61bo192bo2bo2bo2bo2bo2bobob2ob
2ob2ob2ob2obo$61bo192bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o$61bo192bo2bo2bo
2bo2bobob2ob2ob2ob2ob2ob2o$61bo189bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2obo$
61bo189bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o$61bo189bo2bo2bo2bo2bobob2ob2o
b2ob2ob2ob2o$61bo186bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o$61bo186bo2bo2bo
2bo2bobob2ob2ob2ob2ob2ob2o$61bo186bo2bo2bo2bo2bobob2ob2ob2ob2ob2obo$
61bo183bo2bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o$61bo183bo2bo2bo2bo2bobob2ob2o
b2ob2ob2ob2o$61bo183bo2bo2bo2bo2bobob2ob2ob2ob2ob2obo$61bo180bo2bo2bo
2bo2bo2b3ob2ob2ob2ob2ob2o$61bo180bo2bo2bo2bo2bobob2ob2ob2ob2ob2obo$61b
o180bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o$61bo177bo2bo2bo2bo2bo2b3ob2ob2ob2ob
2ob2o$61bo177bo2bo2bo2bo2bobob2ob2ob2ob2ob2obo$61bo177bo2bo2bo2bo2b3ob
2ob2ob2ob2ob2o$61bo174bo2bo2bo2bo2bo2b3ob2ob2ob2ob2obo$61bo174bo2bo2bo
2bo2bobob2ob2ob2ob2ob2o$61bo174bo2bo2bo2bo2b3ob2ob2ob2ob2ob2o$61bo171b
o2bo2bo2bo2bobob2ob2ob2ob2ob2obo$61bo171bo2bo2bo2bo2bobob2ob2ob2ob2ob
2o$61bo171bo2bo2bo2bo2b3ob2ob2ob2ob2obo$61bo168bo2bo2bo2bo2bobob2ob2ob
2ob2ob2o$61bo168bo2bo2bo2bo2bobob2ob2ob2ob2ob2o$61bo168bo2bo2bo2bo2b3o
b2ob2ob2ob2obo$61bo165bo2bo2bo2bo2bobob2ob2ob2ob2ob2o$61bo165bo2bo2bo
2bo2b3ob2ob2ob2ob2ob2o$61bo165bo2bo2bo2bo2b3ob2ob2ob2ob2o$61bo162bo2bo
2bo2bo2bobob2ob2ob2ob2ob2o$61bo162bo2bo2bo2bo2b3ob2ob2ob2ob2obo$61bo
162bo2bo2bo2bobob2ob2ob2ob2ob2o$61bo159bo2bo2bo2bo2bobob2ob2ob2ob2ob2o
$61bo159bo2bo2bo2bo2b3ob2ob2ob2ob2obo$61bo159bo2bo2bo2bobob2ob2ob2ob2o
b2o$61bo156bo2bo2bo2bo2bobob2ob2ob2ob2obo$61bo156bo2bo2bo2bo2b3ob2ob2o
b2ob2o$61bo156bo2bo2bo2bobob2ob2ob2ob2ob2o$61bo153bo2bo2bo2bo2b3ob2ob
2ob2ob2obo$61bo153bo2bo2bo2bo2b3ob2ob2ob2ob2o$61bo153bo2bo2bo2bobob2ob
2ob2ob2obo$61bo150bo2bo2bo2bo2b3ob2ob2ob2ob2o$61bo150bo2bo2bo2bo2b3ob
2ob2ob2ob2o$61bo150bo2bo2bo2bobob2ob2ob2ob2obo$61bo147bo2bo2bo2bo2b3ob
2ob2ob2ob2o$61bo147bo2bo2bo2bobob2ob2ob2ob2obo$61bo147bo2bo2bo2bobob2o
b2ob2ob2o$61bo144bo2bo2bo2bo2b3ob2ob2ob2ob2o$61bo144bo2bo2bo2bobob2ob
2ob2ob2obo$61bo144bo2bo2bo2bobob2ob2ob2ob2o$61bo141bo2bo2bo2bo2b3ob2ob
2ob2ob2o$61bo141bo2bo2bo2bobob2ob2ob2ob2o$61bo141bo2bo2bo2b3ob2ob2ob2o
b2o$61bo138bo2bo2bo2bo2b3ob2ob2ob2obo$61bo138bo2bo2bo2bobob2ob2ob2ob2o
$61bo138bo2bo2bo2b3ob2ob2ob2ob2o$61bo135bo2bo2bo2bobob2ob2ob2ob2o$61bo
135bo2bo2bo2bobob2ob2ob2ob2o$61bo135bo2bo2bo2b3ob2ob2ob2obo$61bo132bo
2bo2bo2bobob2ob2ob2ob2o$61bo132bo2bo2bo2bobob2ob2ob2ob2o$61bo132bo2bo
2bo2b3ob2ob2ob2obo$61bo129bo2bo2bo2bobob2ob2ob2ob2o$61bo129bo2bo2bo2b
3ob2ob2ob2obo$61bo129bo2bo2bo2b3ob2ob2ob2o$61bo126bo2bo2bo2bobob2ob2ob
2ob2o$61bo126bo2bo2bo2b3ob2ob2ob2obo$61bo126bo2bo2bo2b3ob2ob2ob2o$61bo
123bo2bo2bo2bobob2ob2ob2obo$61bo123bo2bo2bo2b3ob2ob2ob2o$61bo123bo2bo
2bobob2ob2ob2ob2o$61bo120bo2bo2bo2bobob2ob2ob2obo$61bo120bo2bo2bo2b3ob
2ob2ob2o$61bo120bo2bo2bobob2ob2ob2ob2o$61bo117bo2bo2bo2bobob2ob2ob2o$
61bo117bo2bo2bo2b3ob2ob2ob2o$61bo117bo2bo2bobob2ob2ob2obo$61bo114bo2bo
2bo2b3ob2ob2ob2o$61bo114bo2bo2bo2b3ob2ob2ob2o$61bo114bo2bo2bobob2ob2ob
2o$61bo111bo2bo2bo2b3ob2ob2ob2o$61bo111bo2bo2bobob2ob2ob2obo$61bo111bo
2bo2bobob2ob2ob2o$61bo108bo2bo2bo2b3ob2ob2ob2o$61bo108bo2bo2bobob2ob2o
b2obo$61bo108bo2bo2bobob2ob2ob2o$61bo105bo2bo2bo2b3ob2ob2obo$61bo105bo
2bo2bobob2ob2ob2o$61bo105bo2bo2b3ob2ob2ob2o$61bo102bo2bo2bo2b3ob2ob2ob
o$61bo102bo2bo2bobob2ob2ob2o$61bo102bo2bo2b3ob2ob2obo$61bo99bo2bo2bo2b
3ob2ob2o$61bo99bo2bo2bobob2ob2ob2o$61bo99bo2bo2b3ob2ob2obo$61bo96bo2bo
2bobob2ob2ob2o$61bo96bo2bo2bobob2ob2obo$61bo96bo2bo2b3ob2ob2o$61bo93bo
2bo2bobob2ob2ob2o$61bo93bo2bo2bobob2ob2obo$61bo93bo2bo2b3ob2ob2o$61bo
90bo2bo2bobob2ob2ob2o$61bo90bo2bo2b3ob2ob2o$61bo90bo2bo2b3ob2ob2o$61bo
87bo2bo2bobob2ob2obo$61bo87bo2bo2b3ob2ob2o$61bo87bo2bobob2ob2ob2o$61bo
84bo2bo2bobob2ob2obo$61bo84bo2bo2b3ob2ob2o$61bo84bo2bobob2ob2obo$61bo
81bo2bo2bobob2ob2o$61bo81bo2bo2b3ob2ob2o$61bo81bo2bobob2ob2obo$61bo78b
o2bo2b3ob2ob2o$61bo78bo2bo2b3ob2obo$61bo78bo2bobob2ob2o$61bo75bo2bo2b
3ob2ob2o$61bo75bo2bo2b3ob2obo$61bo75bo2bobob2ob2o$61bo72bo2bo2b3ob2obo
$61bo72bo2bobob2ob2o$61bo72bo2bobob2ob2o$61bo69bo2bo2b3ob2obo$61bo69bo
2bobob2ob2o$61bo69bo2bobob2ob2o$61bo66bo2bo2b3ob2o$61bo66bo2bobob2ob2o
$61bo66bo2b3ob2obo$61bo63bo2bo2b3ob2o$61bo63bo2bobob2ob2o$61bo63bo2b3o
b2obo$61bo60bo2bobob2ob2o$61bo60bo2bobob2obo$61bo60bo2b3ob2o$61bo57bo
2bobob2ob2o$61bo57bo2bobob2obo$61bo57bo2b3ob2o$61bo54bo2bobob2obo$61bo
54bo2b3ob2o$61bo54bo2b3ob2o$61bo51bo2bobob2obo$61bo51bo2b3ob2o$61bo51b
o2b3obo$61bo48bo2bobob2o$61bo48bo2b3ob2o$61bo48bobob2obo$61bo45bo2bobo
b2o$61bo45bo2b3ob2o$61bo45bobob2o$61bo42bo2bobob2o$61bo42bo2b3obo$61bo
42bobob2o$61bo39bo2b3ob2o$61bo39bo2b3obo$61bo39bobob2o$61bo36bo2b3obo$
61bo36bobob2o$61bo36bobob2o$61bo33bo2b3obo$61bo33bobob2o$61bo33bobobo$
61bo30bo2b3o$61bo30bobob2o$61bo30b3obo$61bo27bo2b3o$61bo27bobobo$61bo
27b3o$61bo24bo2b3o$61bo24bobobo$61bo24b3o$61bo21bobob2o$61bo21bobo$61b
o21b3o$61bo18bobobo$61bo18b3o$61bo18b3o$61bo15bobo$61bo15b3o$61bo15b2o
$61bo12bobo$61bo12b3o$61bo11bobo$61bo9bobo$61bo9b2o$61bo8bo$61bo6bobo$
61bo6b2o$61bo5bo$43bo3b5o9bo3b2o$42b2o7bo9bo3bo$43bo6bo10bo2bo$43bo5bo
11b3o$43bo4bo12b501o$43bo3bo$42b3o2bo8$59b3o188b3o2b5obo3bob5ob4o3b3o
2b5o2b3o3b3o2bo3bo10bo33b3o4bo4b3o3bo166bo4b3o4bo4b3o2b5o2b3o3b3o3b3o
3b3o$58bo3bo186bo3bobo5b2o2bobo5bo3bobo3bo3bo5bo3bo3bob2o2bo9bo11bo21b
o3bo2bobo2bo7bo164b2o3bo3bo2b2o3bo3bo5bobo3bobo3bobo3bobo3bo$58bo2b2o
186bo5bo5bobobobo5bo3bobo3bo3bo5bo3bo3bobobobo9bo4b4ob5o2b3o2b4o2b5obo
3bobo3bobo7bo165bo7bo3bo3bo2b2o4bo6bobo2b2obo2b2obo2b2o$58bobobo186bo
2b2ob3o3bo2b2ob3o3b4o2b5o3bo5bo3bo3bobo2b2o9bo3bo7bo3bo3bobo3bo8b3o8b
4o4bo165bo5b2o4bo3bobobo3bo6bo2bobobobobobobobobo$58b2o2bo186bo3bobo5b
o3bobo5bo2bo2bo3bo3bo5bo3bo3bobo3bo9bo4b3o4bo3b5obo3bob5obo3bo7bo3bo3b
o165bo7bo3bo3b2o2bo2bo6bo3b2o2bob2o2bob2o2bo$58bo3bo186bo3bobo5bo3bobo
5bo3bobo3bo3bo5bo3bo3bobo3bo9bo7bo3bo3bo5bo3bo7bo3bo7bo3bo3bo165bo3bo
3bo3bo3bo3bobo6bo4bo3bobo3bobo3bo$59b3o188b3o2b5obo3bob5obo3bobo3bo3bo
4b3o3b3o2bo3bo10bo2b4o5b2o2b4ob4o9b3o9b3o3bo165b3o3b3o3b3o3b3o2bo5b5o
2b3o3b3o3b3o$339bo$339bo!
Notice that the fluctuations are also linear (you can use the "draw-lines" script to check it out).

The only thing this special pattern influences is the growing fluctuations in population, but it will always remain in some linear bounds.

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 24th, 2014, 9:52 pm

Here's a backrake much easier to synthesize than the other one, since it's made of components that are known to be synthesizable.

Code: Select all

x = 68, y = 70, rule = 22da
57bo2$59bo$58bo$56b2o$56b2o3$67bo$65b2o$65b2o49$bo2$3bo$2bo$2o$2o$9bo
2$11bo$9b2o$9b2o!
For reference here is the sawtooth that I'm basing my sawtooth on.

Code: Select all

x = 618, y = 10, rule = circleoflife
2.B.B.B3.B.B39.B$B7.B3.B37.B3.B41.B45.B.B7.B55.B55.B$B.B7.B41.B.B11.B
3.B23.B27.B3.B19.B3.B27.B3.B23.B27.B3.B23.B302.B39.B.B3.B.B.B$8.B7.B.
B.B45.B17.B9.B27.B17.B.B.B.B.B29.B27.B27.B27.B.B88.B55.B55.B7.B.B45.B
41.B3.B37.B3.B7.B$22.B45.B17.B37.B55.B55.B118.B23.B3.B27.B23.B3.B27.B
3.B19.B3.B27.B23.B3.B11.B.B41.B7.B.B$B.B3.B3.B3.B7.B55.B.B.B3.B57.B.B
3.B202.B.B27.B27.B27.B29.B.B.B.B.B17.B27.B9.B17.B45.B.B.B7.B$B.B5.B.B
9.B63.B63.B232.B55.B55.B37.B17.B45.B$18.B63.B61.B.B320.B3.B.B57.B3.B.
B.B55.B7.B3.B3.B3.B.B$469.B63.B63.B9.B.B5.B.B$471.B.B61.B63.B!

User avatar
simsim314
Posts: 1766
Joined: February 10th, 2014, 1:27 pm

Re: 22da (Hexagonal Grid)

Post by simsim314 » May 25th, 2014, 8:04 pm

c0b0p0 wrote:Here's a backrake much easier to synthesize than the other one
Nice! It's also the smallest known, by far the best back rake we got so far.

Here is p96 glider gun using 3 reflectors (instead of 6 + 4 circulating gliders):

Code: Select all

x = 107, y = 111, rule = 22da
39bo$41bo9$37b3o4b3o$37bo2bo$38bobo4b3o$38bo2bo4b2o$38bobobo3bobo2$39b
obobo$41b2o4$48bobo$46b3obo$45bob3o$48bo3$46b2o$46bo2bob2o$46bo4bo$47b
2o3bo3$18b3o$18bo2bo$19bobo$19bo2bo$19bobobo2$20bobobo$22b2o27bo$50bo
2bo$50b2o2bo$53bob2o$51bo5bo$53b3obo$56b2o2$71bo$70bo2bo$21b2o47b2o2bo
$19b2o52bob2o$bo16b2o3bo47bo5bo$o22bo6b3o40b3obo$18b2obo8bo2bo42b2o$
19bobo9bobo$31bo2bo$31bobobo2$32bobobo$34b2o7$16bo$15bo2bo$15bo2b2o$
14b2obo$2b2o10bo5bo$15bob3o$16b2o$66bo9b3o$65bo2bo$65bo2b2o7b3o$54bo9b
2obo10b2o$64bo5bo7bobo$54bo10bob3o$56b2o8b2o$54bo2b2o3$82bo$80bo4bo$
58bo$57bo2bo20bob2obo$57bo2b2o22bo$56b2obo22bo4bo$56bo5bo22bo8bo$57bob
3o21bob2obo4bo2bo$58b2o33b2o2bo$84bo4bo6bob2o$87bo6bo5bo$96b3obo$99b2o
4$89bobo$90b2o$90b3o2$91b3o12bo$105bo4$94bo$96bo!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 26th, 2014, 9:35 pm

@simsim314: Unless somone finds a more efficent glider duplicator, this is probably the smallest gun there is. Slightly modifying it makes a 58-cell gun predecessor, by far the smallest gun known.

Code: Select all

x = 83, y = 83, rule = 22da
23bo2bo$25bo$25b2o$26bo20$4bo2bo$6bo$6b2o$7bo3$36b2obo$37b2o2$39bo5$
56b2obo$57b2o2$59bo3$16bo2bo$18bo$18b2o$19bo10$ob2o$2b2o2$3bo4$33b2o
15bob2o$34b2o16b2o2$53bo9$42bob2o$44b2o2$45bo$79b2obo$80b2o2$82bo!
The backrake is also the easiest to synthesize. This synthesis does not assume that the gliders come from infinity, but it can easily be modified to assume this.

Code: Select all

x = 138, y = 155, rule = 22da
obobo2$3bo$3b2o$4bo107bo2$114bo$112b2o$112b2o2bo$121bo2$123bo$121b2o$
121b2o2bo11$84bo$83bobo$82b3obo$84b2o$84bo35$56bo2$58bo$56b2o$56b2o2bo
$65bo2$67bo$65b2o$65b2o2bo11$28bo$27bobo$26b3obo$28b2o$28bo13$133bo$
133b2o$134bo2$133bobobo46$74bo$74b2o$75bo2$74bobobo!

wildmyron
Posts: 1398
Joined: August 9th, 2013, 12:45 am

Re: 22da (Hexagonal Grid)

Post by wildmyron » May 27th, 2014, 5:20 am

c0b0p0 wrote:22darealDLA still hasn't been proven omniperiodic, but there is a stable glider duplicator.

Code: Select all

x = 41, y = 40, rule = 22darealDLA
40.B7$24.B4$21.B6$27.B2$15.A2$17.A6.B$9.B5.2A$15.2A2.A3$6.B6$12.B4$9.
B3$B!
Here is a reflector with faster recovery time than duplicator + dot:

Code: Select all

x = 16, y = 16, rule = 22darealDLA
11.B$8.B2$7.A$6.A8.B$9.A$7.A2.A$14.B$.B7.A2.A$11.A$2.3A$B.A2.A$3.A.A$
4.2A$7.B$4.B!
And here is a variation which gives 2 for 1. Interestingly, the above reflector can also give 1 for 2:

Code: Select all

x = 25, y = 25, rule = 22darealDLA
20.B$17.B3$24.B3$23.B4$9.A2$4.B6.A$3.B5.2A$9.2A2.A2$.B3$B10.B$10.B2$
7.B$4.B!
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 27th, 2014, 9:56 pm

@wildmyron: Unfortunately, this does not prove 22darealDLA omniperiodic, since their recovery times are both 0 (mod 2). It would be nice if there was a reflector with a recovery time of 1 (mod 2).

Code: Select all

x = 39, y = 40, rule = 22darealDLA
34.B$31.B3$38.B$30.A.A$30.A.2A$37.B$32.2A14$9.B4$6.B6$12.B4$9.B3$B!
Since the construction time of the rake was literally impossible to bear, I decided to use some known cleanup reactions, thus knocking off a bit less than one-third of an order of magnitude from the projected size of the sawtooth.

Code: Select all

x = 180, y = 139, rule = Marked22da
A.A.A2$3.A$3.2A$4.A6$94.A2$96.A$94.2A$94.2A2.A$103.A2$105.A$103.2A$
103.2A2.A17$60.B$59.B.B$58.3B.B$60.2B$60.B3$44.A.A$45.2A$45.3A2$46.3A
3$51.A$51.A.A$51.A.3A$53.2A$55.A5$48.A2$50.A$48.2A$48.2A2.A$57.A2$59.
A$57.2A$57.2A2.A3$28.A$27.A.A$26.3A.A$28.2A$28.A15$152.2A2.A$153.2A$
156.A2$156.A8$175.2A2.A$176.2A$179.A2$179.A28$66.A$66.2A$67.A2$66.A.A
.A!

c0b0p0
Posts: 645
Joined: February 26th, 2014, 4:48 pm

Re: 22da (Hexagonal Grid)

Post by c0b0p0 » May 28th, 2014, 9:05 pm

This knocks one-quarter of an order of magnitude off the projected size of the sawtooth, and I am pretty confident that the projected size cannot be made much smaller.

Code: Select all

x = 281, y = 293, rule = Marked22da
110.A.A$111.2A$111.3A2$112.3A79$A$124.A.A.A$A$2.2A123.A$A2.2A122.2A$
128.A6$218.A2$220.A$218.2A$218.2A2.A$227.A2$229.A$227.2A$227.2A2.A17$
184.B$183.B.B$182.3B.B$184.2B$184.B3$168.A.A$169.2A$169.3A2$170.3A2$
164.B$163.B11.A$175.A.A$175.A.3A$177.2A$179.A5$172.A2$174.A$172.2A$
172.2A2.A$181.A2$183.A$181.2A$181.2A2.A3$152.A$151.A.A$150.3A.A$152.
2A$152.A15$276.2A2.A$277.2A$280.A2$280.A40$190.A$190.2A$191.A2$190.A.
A.A66$240.A$240.2A$241.A2$240.A.A.A!

bprentice
Posts: 674
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Re: 22da (Hexagonal Grid)

Post by bprentice » May 29th, 2014, 2:15 pm

A Java CA Simulator that uses a hexagonal grid was introduced here:

viewtopic.php?f=11&t=1027&start=0

A new family of two state hexagonal rules has recently been added. This family includes Paul Callahan's rule which is documented here:

http://psoup.math.wisc.edu/mcell/files/hexrule.txt

and the rule discussed in this thread.

The program supports the generation and exploration of other members of the family. To generate a new member rule, repeatedly hit the N key until an interesting one is found.

The file 'Hexagonal Cell.zip' contains the Java source code and executable jar file and the file 'Hexagonal Grid.zip' contains some examples. These files are here:

http://bprentice.webenet.net/Hexagonal%20Cell/

I will probably add more examples from time to time.

Brian Prentice

Post Reply