NickGotts wrote:Paul also looked for infinite-growth patterns with small bounding boxes, and I think found one in a 5-by-5 box, which I don't have...
NickGotts wrote:Finally, here's [an] 8-glider slow salvo creating a glider-streamer out of a blinker - I'd forgotten this one until I prepared this post...
x = 301, y = 12, rule = B3/S23
6bo$5bobo287b2o2b2o$5bobo280b2o5b2ob2o$6bo281b2o10bo2$b2o$b2o5b2o$8b2o
4b2o276b2o$14b2o272b2o2b2o$2o6bo279b2o$2o5b2o$7bobo!
x = 15, y = 9, rule = B3/S23
2o$2o2$9b2o2b2o$9b2ob2o$14bo$2o4b2o$2o3bobo$5b2o!
NickGotts wrote:Thanks Dave. I agree that 8 is unlikely to be minimal, and the strategy you suggest is reasonable - I've actually kind of followed it rather unsystematically for the first couple of gliders. Here's the biggest mess you can make with a slow 2-salvo into a block or blinker...
dvgrn wrote:If just six gliders can produce these constellations from a honeyfarm, the beehive in the left-hand pattern might actually be a clue as to the honeyfarm's initial position. Now we just need an ambitious Slow Salvo Reverse Engineer...
x = 398, y = 266, rule = B3/S23
6bo132b2o$5bobo127b2o2b2o$5bobo127b2o$6bo2$b2o7b2o119b2o$o2bo5bo2bo
117bo2bo$b2o7b2o119b2o$136b2o$6bo13bobo113b2o$5bobo10bo5bo$5bobo$6bo
10bo2b3o2bo$20bo$17bo3bo3bo111b2o$137b2o$18bo5bo$20bobo19$33bobo$31bo
5bo2$30bo2b3o2bo$33bo$30bo3bo3bo2$31bo5bo$33bobo9$62b3o$62bo$63bo23$
84b3o$84bo$85bo183$396b2o$395b2o$397bo!
#C glider-streaming switch-engine, seven slow gliders from a block
x = 65, y = 67, rule = B3/S23
2o$2o4$3o$o$bo5$17bo$16b2o$16bobo6$25bo$24b2o$24bobo11$27bo$26b2o11b3o
$26bobo10bo$40bo10$48b3o$48bo$49bo16$63b2o$62b2o$64bo!
It may not be entirely clear to everyone why your best initial target is a blonk (block or blinker) rather than, say, a tub or a beehive. In the context of a Sparse Life early universe, blocks and blinkers will appear overwhelmingly often compared to any other still life
Unfortunately I suppose this recipe isn't really the most interesting kind, since the switch engine returns toward the gliders' source -- and there's quite likely to be some junk back in that direction that will stop the switch-engine, sooner rather than later (?).
of course, any such constructed salvo will have specific forward spacings between the gliders
NickGotts wrote:A standard collision sequence involves one glider or r-pentomino present at t=0, and a number of blocks and blinkers also present at t=0, but nothing else; and "minimal" refers to the number of such blonks (blocks or blinkers) involved.
NickGotts wrote:A standard collision sequence involves one glider or r-pentomino present at t=0, and a number of blocks and blinkers also present at t=0, but nothing else; and "minimal" refers to the number of such blonks (blocks or blinkers) involved. My best recipe so far involves 49 of them, although my guess is that the optimum is less than 10, perhpas quite a bit less (I can prove it's more than 2!).
x = 2034, y = 1103, rule = B3/S23
o2032bo$b2o2030bo$2o2031bo1094$1043bo$1044bo$1042b3o4$1046b3o!
NickGotts wrote:Here's the order-49 SCS (standard collision sequence). It doesn't use a slow salvo, but the synchonised pair plunging into a settled pi which I posted earlier - but setting this up is not easy.
NickGotts wrote:... before even trying to design a systematic search for a minimal SCS, I want to find a reasonably short one!
#C A block plus 12 slow gliders with no parity constraints makes a
#C 4-block seed. One more glider makes a glider-streaming switch engine.
#C Two trivial variants are shown -- there are many others.
x = 1291, y = 213, rule = Life
1093b2o$1093b2o3$1094bo$1093b2o$1093bobo14$1102bo$1101b2o$1101bobo3$
1115bo$5bo1108b2o$2o2b2o1108bobo$2o2bobo$1130bo$1129b2o$1129bobo8$
1141bo$1140b2o$1140bobo$12bo$11b2o$11bobo3$25bo10bo$24b2o9b2o$24bobo8b
obo5$1137bo$1136b2o$1136bobo6$43bo$42b2o$42bobo7$1148bo$1147b2o$51bo
1095bobo$50b2o$50bobo2$67bo$66b2o1096bo$66bobo1094b2o$1163bobo18$1182b
o$1181b2o$74bo1106bobo$73b2o$73bobo16$1207bo$1206b2o$92bo1113bobo$91b
2o$91bobo16$1224bo$1223b2o$117bo1105bobo$116b2o$116bobo16$1232bo$1231b
2o$134bo1096bobo$133b2o$133bobo18$142bo$141b2o$141bobo6$1289bo$1288b2o
$1288bobo20$199bo$198b2o$198bobo!
It looks as if it ought to be simpler to avoid synchronization problems and do everything with a slow salvo -- but I'm sure there are complications there as well.
those to the north-west, negative
NickGotts wrote:A standard collision sequence involves one glider or r-pentomino present at t=0, and a number of blocks and blinkers also present at t=0, but nothing else; and "minimal" refers to the number of such blonks (blocks or blinkers) involved. My best recipe so far involves 49 of them, although my guess is that the optimum is less than 10, perhpas quite a bit less (I can prove it's more than 2!)
Does the bolded bit imply you've surveyed all possible ways that an R-pentomino or a glider can collide with 2 blonks?
x = 243, y = 166, rule = B3/S23
8bo$8bo$8bo4$b2o$obo$2bo155$241b2o$240b2o$242bo!
x = 72, y = 92, rule = B3/S23
o$b2o$2o22$42b3o31$69b3o16$71bo$71bo$71bo18$21b3o!
Scorbie wrote:Here's a glider+4blinker solution. I'm not sure if it's a valid one though...
x = 6109, y = 544, rule = B3/S23
2966bo$2967bo$2965b3o31$1122bo879bo$1120bobo877bobo$1121b2o878b2o2$
1123b3o877b3o6$4335bo$4334bo$4334b3o32$117bo$115b2o$116b2o4$5603bo$
5604bo$5602b3o124$3bo$2bo$2b3o$o$o$o52$964b2o$965b2o$964bo32$2207b3o$
2207bo$2208bo11$3279b3o2$3282b2o$3282bobo$3282bo59$4000bo$4000bo$4000b
o$3996b3o$3998bo$3997bo158$6106bo$6106bobo$6106b2o2$6103b3o!
x = 777, y = 809, rule = B3/S23
76$634bo$632b2o$633b2o557$86bo$84bobo$85b2o2$87b3o!
x = 98, y = 77, rule = B3/S23
97bo$95b2o$96b2o69$4bo$3bo$3b3o$bo$2o$obo!
x = 307, y = 284, rule = B3/S23
138b5o$138bo4b2obo4b5o$138bo5bobo4bo4b2obo$139bo4bo6bo5bobo$141bob3o6b
o4bo$143b3o8bob3o$156b3o$141b2o$139b2o13b2o$139bo2bo9b2o$139bo12bo2bo$
140b2o10bo$145bo7b2o52b2o$142bo15bo47b2ob2o$143b2o10bo51b4o20b2o$156b
2o9b3o15b3o20b2o20b2ob2o$137b7obo20b5o13b5o42b4o$122b2o13bo7bo4b7obo6b
2ob3o12b2ob3o43b2o$99b2o19bo4bo11bo7bo4bo7bo7b2o16b2o$98b2ob3o15bo18bo
11bo7bo$99b5o15bo5bo14b2o9bo$100b3o16b6o28b2o$104bo$104bo$102bo$101bo
3bo$97b2o2bo3bo$96b2ob2o2bo20bo$97b2o3bo17b2obo2b3o$98b2o2bo5bo3bo3bo
3b2ob2ob3o$103bo4bo3bo3bo2bo$98b2o2bo5bo3bo3bo3b2ob2ob3o112b2o$97b2o3b
o17b2obo2b3o111b2ob3o$96b2ob2o2bo20bo116b5o$97b2o2bo3bo136b3o$101bo3bo
$102bo$104bo$104bo$100b3o16b6o28b2o11b2o23b2o$99b5o15bo5bo14b2o9bo12bo
4bo20b2ob4o$98b2ob3o15bo18bo11bo7bo4bo27b6o$99b2o19bo4bo11bo7bo4bo7bo
4bo5bo12b6o4b4o$122b2o13bo7bo4b7obo4b6o13bo5bo$137b7obo36bo$156b2o25bo
4bo$143b2o10bo29b2o$142bo15bo$145bo7b2o$140b2o10bo$139bo12bo2bo$139bo
2bo9b2o$139b2o13b2o$141b2o$156b3o$143b3o8bob3o$141bob3o6bo4bo$139bo4bo
6bo5bobo$138bo5bobo4bo4b2obo$138bo4b2obo4b5o$138b5o10$47b3o$46b6o8b3o$
45b2ob5o6b6o$46b2o4bo5b2ob5o$59b2o4bo$50bo$50b2obo9bo$50b3o10b2obo$48b
2o13b3o$47b2obo10b2o$46b2o12b2obo$47bobo9b2o$48bo11bobo$49bo11bo52b4o$
51b2o9bo51bo3bo$51bo12b2o10bo17bo19bo23b4o$46b4o14bo9bo3bo13bo3bo18bo
2bo19bo3bo$45b6obo6b4o10bo17bo46bo$44b2ob4o2b2o3b6obo7bo4bo12bo4bo42bo
2bo$6b5o34b2o10b2ob4o2b2o5b5o13b5o$6bo4bo15b2o29b2o$6bo19b2ob4o$7bo19b
6o$9bobo16b4o$11bo2$9b2o$4b4ob2obo$4bo2b4o24bo$4bo3b4o16b2obo2bobo$5b
3o2b2o15bobob4obo$10b2o3b3ob3ob3obo$5b3o2b2o15bobob4obo111b5o153bo$4bo
3b4o16b2obo2bobo111bo4bo150b2o$4bo2b4o24bo112bo156b2o$4b4ob2obo136bo3b
o$9b2o140bo2$11bo$9bobo16b4o$7bo19b6o65b6o$6bo19b2ob4o65bo5bo$6bo4bo
15b2o29b2o11b2o18b4o3bo$6b5o34b2o10b2ob4o2b2o2b2ob4o13b6o3bo4bo$44b2ob
4o2b2o3b6obo5b6o12b2ob4o5b2o$45b6obo6b4o9b4o14b2o$46b4o14bo$51bo12b2o$
51b2o9bo$49bo11bo$48bo11bobo$47bobo9b2o$46b2o12b2obo$47b2obo10b2o$48b
2o13b3o$50b3o10b2obo$50b2obo9bo$50bo$59b2o4bo$46b2o4bo5b2ob5o$45b2ob5o
6b6o$46b6o8b3o$47b3o41$213bo$212bo$212b3o$210bo$209b2o$209bobo41$45bo$
43bo14bo$42bo6bo6bo$42bo6bo5bo6bo$42b6obo5bo6bo$55b6obo$47b2o$46bo13b
2o$49bo9bo$44b2o16bo$43bo13b2o$43bo2bo9bo$43b2o11bo2bo$45b2o9b2o$58b2o
$47b3o$44b2ob3o10b3o$42bo5bo8b2ob3o7b2o$41bo6bobo4bo5bo6bo4bo12b6o$4b
3o34bo5b2obo3bo6bobo3bo18bo5bo$3b5o33b6o7bo5b2obo3bo5bo12bo$2b2ob3o15b
6o25b6o7b6o14bo4bo2b2o$3b2o18bo5bo59b2o3b2ob4o$23bo71b6o$7bo16bo4bo66b
4o$7bo18b2o$7bo$2b2ob4o$b4o$2o30bo112b2o$bo23b2obo2bobo110b2ob3o$2b4o
3bo3bo3bo3bob2obob4o113b5o$6bo2bo3bo3bo3bo2bo121b3o$2b4o3bo3bo3bo3bob
2obob4o$bo23b2obo2bobo$2o30bo$b4o$2b2ob4o$7bo$7bo18b2o$7bo16bo4bo$23bo
$3b2o18bo5bo$2b2ob3o15b6o25b6o11b3o15b3o$3b5o33b6o7bo5b2obo6b5o13b5o$
4b3o34bo5b2obo3bo6bobo5b2ob3o12b2ob3o$41bo6bobo4bo5bo8b2o16b2o45b2o$
42bo5bo8b2ob3o71b2ob2o$44b2ob3o10b3o48b2o22b4o$47b3o60b2ob2o21b2o$58b
2o51b4o$45b2o9b2o54b2o$43b2o11bo2bo$43bo2bo9bo$43bo13b2o$44b2o16bo$49b
o9bo$46bo13b2o$47b2o$55b6obo$42b6obo5bo6bo$42bo6bo5bo6bo$42bo6bo6bo$
43bo14bo$45bo!
Here are some 2 gliders + blinker -> switch engine interactions (one of them was the basis for the 24 cell quadratic
simsim314 wrote:Here is a surprise! 3 glider synthesis of switch engine (3 gliders infinite growth).
x = 284, y = 251, rule = B3/S23
236b3o14$282bo$281bobo$282bo232$bo$3o$2bo!
x = 30142, y = 152, rule = B3/S23
15063bo$15062bobo$15064bo10066bobo$15065bo10066b2o$25133bo6$30141bo$
30140bo$30138bobo$30139bo65$20111bo$20110bo$20111b2o$20113bo4$2bo$bo$
3o6$79bo4999bo4999bo4999bo4999bo4999bo4999bo$79b3o4997b3o4997b3o4997b
3o4997b3o4997b3o4997b3o$80bo4999bo4999bo4999bo4999bo4999bo4999bo9$
5024bo$5025bo$5025bobo$5026bo42$10053bo$10054bo$10053b3o!
x = 377, y = 162, rule = B3/S23
233bo$231bobo$232b2o66$o$b2o$2o89$56b2o317b2o$55b2o317b2o$56bo318bo!
x = 4795, y = 85, rule = LifeHistory
4794.A$4794.A$4794.A15$4747.3A$4745.A$4746.A$4747.A$4746.A$4745.A2$
2179.A$2179.A$2179.A12$2188.A$2188.A$2185.A2.A$2184.A.A$2183.A3.A24$
3.3A$.A$2.A$3.A$2.A$.A12$2A$2A!
x = 24128, y = 101, rule = LifeHistory
4018.2A$4018.2A15$4033.3A2$8.A3999.A3999.A$8.A3999.A3999.A$8.A3999.A
3999.A4$.2A3998.2A3998.2A$A.A3997.A.A3997.A.A$2.A3999.A3999.A13$15.A$
15.A$15.A17567.A3999.A$17583.A3999.A$17583.A3999.A$7984.A36.A$7984.A
36.A9560.3A3997.3A$7984.A36.A3$31.2A15376.3A$31.2A11373.3A$15393.2A$
15393.2A5$24106.3A$17597.A3999.A$11419.A3999.A2177.A3999.A$11408.3A8.
A3999.A2177.A3999.A$11419.A3999.A3$17590.2A3998.2A$11412.2A3998.2A
2175.A.A3997.A.A$11411.A.A3997.A.A2177.A3999.A$11413.A3999.A13$24127.
A$24127.A$24127.A4$24120.2A$24119.A.A$24121.A12$24094.3A!
x = 654089, y = 4149, rule = LifeHistory
654087.2A$654087.2A168$603918.2A$603918.2A362$553555.2A$553555.2A190$
503364.2A$503364.2A168$453195.2A$453195.2A362$402832.2A$402832.2A190$
352641.2A$352641.2A168$302472.2A$302472.2A362$252109.2A$252109.2A190$
201918.2A$201918.2A3$151914.2A$151914.2A164$101749.2A$101749.2A333$
51415.2A$51415.2A28$1386.2A$1386.2A1412$14.A49999.A49999.A49999.A
49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.
A$15.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A
49999.A49999.A49999.A49999.A$15.A.A49997.A.A49997.A.A49997.A.A49997.A
.A49997.A.A49997.A.A49997.A.A49997.A.A49997.A.A49997.A.A49997.A.A
49997.A.A49997.A.A$16.A49999.A49999.A49999.A49999.A49999.A49999.A
49999.A49999.A49999.A49999.A49999.A49999.A49999.A29$.A49999.A49999.A
49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.A49999.
A49999.A$2A49998.2A49998.2A49998.2A49998.2A49998.2A49998.2A49998.2A
49998.2A49998.2A49998.2A49998.2A49998.2A49998.2A$.2A49998.2A49998.2A
49998.2A49998.2A49998.2A49998.2A49998.2A49998.2A49998.2A49998.2A
49998.2A49998.2A49998.2A!
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