I did some soup search on several symmetries, but most extensively on D4_+1 and got some nice results.
Most importantly I found a new reflector (as part of an oscillator). Now we have 6 (of 2 general types) reflectors:
Code: Select all
x = 43, y = 101, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
8$26b2o$27bo$26b2o4$29bo$31bo$30b2o$28bo$35b2o$35bo$35b2o$28bo$30b2o$
31bo$29bo6$31b2o$31bo$30b2o$28bo$35b2o$35bo$35b2o$28bo$30b2o$31bo$31b
2o5$29bo$27b5o3b2o$27bo3bo3bo$23bo2b2obob2o2b2o$21b3o3bo3bo$21bo5b5o$
29bo10$29bo$27b5o3b2o$21bo5bo3bo3bo$23bo2b2obob2o2b2o$22b2o3bo3bo$27b
5o$29bo8$29bo$27b5o$27bo3bo3b2o$23bo2b2obob2o2bo$21b3o3bo3bo3b2o$21bo
5b5o$29bo10$29bo$27b5o$21bo5bo3bo3b2o$23bo2b2obob2o2bo$22b2o3bo3bo3b2o
$27b5o$29bo!
Most importantly, the new reflector(s) reflect(s) the glider colour preserving.
Thus, this reflector allows many nice things. E.g. the p39+4N gun (above) can be made much smaller:
Code: Select all
x = 69, y = 114, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
5$52b2o$53bo$53b2o3$54bo$52b5o$52bo3bo$51b2obob2o$54bo4$54bobo$54b3o
16$25b2o12b2o$16bo7bob2o10b2obo7bo$11bo13b2o12b2o$9b3o4bo32bo4b3o$9bo
44bobo4$54bo$51b2obob2o$52bo3bo$52b5o$54bo3$53b2o$53bo$52b2o3$52bo3bo$
49bo9bo$51bo5bo$50b2o5b2o$31bo$33bo$32b2o$30bo$38b2o$37b2obo7bo$38b2o$
30bo17bo4b3o$32b2o19bobo$33bo$31bo2$53bo$50b2obob2o$51bo3bo$51b5o$53bo
3$52b2o$52bo$54bo4$52bo3bo$49bo9bo$51bo5bo$50b2o5b2o2$30bo$32bo$31b2o$
29bo$38b2o$37b2obo7bo$38b2o$29bo18bo4b3o$31b2o20bobo$32bo$30bo2$53bo$
50b2obob2o$51bo3bo$51b5o$53bo3$52b2o$52bo$54bo!
But it also allows for small families of oscillators with adjustable an even period:
Code: Select all
x = 90, y = 34, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
5$5b2o2b2o12b2o3b2o20b2o4b2o14b2o6b2o$5bo4bo12bo5bo20bo6bo14bo8bo$4b2o
4b2o10b2o5b2o18b2o6b2o12b2o8b2o$2bo10bo6bo11bo14bo12bo8bo14bo$7b2o16b
2o22b2o6b2o13b2o6b2o$8bo17bo22bo8bo13bo8bo$7b2o16b2o22b2o6b2o13b2o6b2o
$2bo10bo6bo11bo14bo12bo8bo14bo$4b2o4b2o10b2o5b2o18b2o6b2o12b2o8b2o$5bo
4bo12bo5bo20bo6bo14bo8bo$5b2o2b2o12b2o3b2o20b2o4b2o14b2o6b2o3$4bo6bo
11bo7bo$6bo2bo15bo3bo$5b2o2b2o13b2o3b2o17bo10bo10bo12bo$3bo8bo9bo9bo
17bo6bo14bo8bo$8b2o17b2o20b2o6b2o12b2o8b2o$9bo18bo18bo12bo8bo14bo$8b2o
17b2o20b2o6b2o12b2o8b2o$3bo8bo9bo9bo16bo8bo12bo10bo$5b2o2b2o13b2o3b2o
18b2o6b2o12b2o8b2o$6bo2bo15bo3bo17bo12bo8bo14bo$4bo6bo11bo7bo17b2o6b2o
12b2o8b2o$50bo6bo14bo8bo$48bo10bo10bo12bo!
So we have p12+4N oscillators (one glider version), such as p10+4N oscillators (two glider versions), as we have many known p2, p4, p6, p8 oscillators, we have oscillators for all even periods.
However, combining it with the odd reflector (colour changing reflector), we get p37+4N oscillators (with 1 glider), and p35+4N oscillators (with 2 gliders):
Code: Select all
x = 101, y = 63, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
3$42bo32bo$40bo32bo$40b2o31b2o$27bo15bo15bo16bo$25b5o2b2o23b5o2b2o$19b
o5bo3bo2bo18bo5bo3bo2bo$21bo2b2obob2ob2o19bo2b2obob2ob2o$20b2o3bo3bo
13bo8b2o3bo3bo14bo$25b5o10b2o15b5o11b2o$27bo12bo18bo13bo$42bo32bo4$41b
o$39bo34bo$27bo11b2o31bo$25b5o12bo16bo12b2o$19bo5bo3bo3b2o22b5o13bo$
21bo2b2obob2o2bo17bo5bo3bo3b2o$20b2o3bo3bo3b2o18bo2b2obob2o2bo$25b5o
12bo9b2o3bo3bo3b2o$27bo11b2o16b5o13bo$39bo19bo12b2o$41bo30bo$74bo5$7bo
39bo6bo41bo$9bo17bo17bo10bo18bo18bo$8b2o35b2o8b2o37b2o$6bo15bo9bo15bo
4bo16bo9bo16bo$15b2o3b5o2bo2b5o3b2o23b2o3b5o2bo2b5o3b2o$16bo3bo3bo5bo
3bo3bo25bo3bo3bo5bo3bo3bo$15b2o2b2obob2o3b2obob2o2b2o23b2o2b2obob2o3b
2obob2o2b2o$6bo13bo3bo5bo3bo13bo4bo14bo3bo5bo3bo14bo$8b2o10b5o2bo2b5o
10b2o8b2o11b5o2bo2b5o11b2o$9bo12bo9bo12bo10bo13bo9bo13bo$7bo39bo6bo41b
o$27bo47bo5$8bo18bo18bo8bo19bo19bo$10bo33bo12bo35bo$9b2o11bo9bo11b2o
10b2o12bo9bo12b2o$7bo12b5o2bo2b5o12bo6bo13b5o2bo2b5o13bo$15b2o3bo3bo5b
o3bo3b2o23b2o3bo3bo5bo3bo3b2o$16bo2b2obob2o3b2obob2o2bo25bo2b2obob2o3b
2obob2o2bo$15b2o3bo3bo5bo3bo3b2o23b2o3bo3bo5bo3bo3b2o$7bo12b5o2bo2b5o
12bo6bo13b5o2bo2b5o13bo$9b2o11bo9bo11b2o10b2o12bo9bo12b2o$10bo33bo12bo
35bo$8bo18bo18bo8bo19bo19bo!
Thus, we have oscillators for all odd periods larger than 33 and all larger periods oscillators are known. For small periods, we know oscillators for all periods (smallest known example listed until p50):
Code: Select all
x = 179, y = 222, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
2$100bo$102bo3bo$66bo8bo25b2o26bo19bo19bo$64b3o6bo25bo13bo17bo35bo$64b
o8b2o33bo21b2o35b2o$39bo27bo37bob2o19bo20bo20bo$33b2o3b3o3b2o62bo28b2o
6bo7bo6b2o$10bo23bo4bo4bo22bo31bo13bo23bo23bo$32bo13bo17bo8b2o26b2o34b
2o6bo7bo6b2o$64b3o6bo28bo3bo21bo20bo20bo$66bo8bo24bo29b2o35b2o$131bo
35bo$129bo19bo19bo10$68b2o29bo11bo$68bo2bo29bo7bo26bo26bo$67b2ob2o28b
2o7b2o27bo22bo$11bo23bo7bo28bo25bo13bo24b2o22b2o$9b3o27bo67b2o26bo28bo
$9bo26bo2bo23bo3bo4bo2bo32bo39bo2bo$11bo27bo67b2o$10b2o23bo7bo28bo25bo
13bo35bo2bo$67b2ob2o28b2o7b2o24bo28bo$68bo2bo29bo7bo27b2o22b2o$68b2o
29bo11bo26bo22bo$136bo26bo10$37bo3bo59bo7bo52bo$34bo4bo4bo58bo3bo52bo$
36bo5bo31bo25bo9bo49b2o$35b2o2bo2b2o30b3o28bo57bo$5bo4b2o52bo11bo18bo
19bo41b2o$7bo2bo22bo5bo5bo27bo31bo31bo7bo11bo$6b2o4bo22bo7bo22bo37b3o
32bo17b2o$10b3o21b2o7b2o28bo31bo32b2o5bo17bo$10bo28bo24bo11bo18bo19bo
44b2o$37bo3bo32b3o28bo54bo$74bo25bo9bo51bo$103bo3bo$101bo7bo13$37bo29b
o3bo75bo3bo$13bo25bo99bo19bo$11bo26b2o97bo23bo$9bob2o21bo8bo16bo8bo8bo
53bo33bo$40bo58b2o4bo5b2o36bo$35bo30bobobobo27bo10bo23bobo23bobo$7b2ob
o29bo57bo6bo7bo35bo$8bo25bo8bo16bo8bo8bo53bo33bo$6bo31b2o97bo23bo$39bo
99bo19bo$37bo29bo3bo75bo3bo11$30b2o12bo$30bo13b3o$29b2o15bo56bo3bo$33b
o116bo$7bo3bo27bobobo56bo9bo41bo$9bo23bo40bo76b2o$4bo9bo49bo34bo2bo5bo
2bo33bo$6bo5bo20bo37bobo76bo$5b2o2bo2b2o51bo30bo5bo5bo5bo$74bo75bo$9bo
32bo23b2o31bo2bo5bo2bo33bo10bo$67bo83b2o$42bo22bo34bo9bo41bo$9bo22bobo
bo113bo$7bo3bo30bo60bo3bo$29bo15b2o$29b3o13bo$31bo12b2o10$101bo12bo36b
o3bo$35bo31b2o34bo8bo34bo11bo$37bo29bo2bo31b2o8b2o35bo7bo$11bo24b2o31b
2o29bo14bo32b2o7b2o$6bo56bo46b2o41bo$12bo23bo74bo$7bobo22bo3b2o3bo22bo
bo7bo35b2o36b2o3bo3b2o$36bo63bo14bo33bo7bo$6bo56bo38b2o8b2o33bo5bo5bo$
36b2o31b2o32bo8bo38bo3bo$37bo29bo2bo30bo12bo$35bo31b2o9$71bo$69bo$64bo
4b2o16bo18bo18bo41bo$66bo22bo33bo41bo$36bo28b2o6bo14b2o33b2o40b2o$38bo
47bo19bo19bo41bo$37b2o28bobobo22b2o6bo7bo6b2o44bo2bo$33bo60bo23bo22bo
7bo17bo$5bo5bo53b2o6bo20b2o6bo7bo6b2o24bo19bo2bo$36bobo2bo24bo19bo19bo
19bo15b2o5bo18bo$3bo8bo51bo4b2o17b2o33b2o40b2o$6bobobo22bo35bo19bo33bo
41bo$37b2o32bo15bo18bo18bo41bo$38bo$36bo9$107bo$63bo10bo34bo$65bo6bo
38b2o33bo15bo$64b2o6b2o38bo35bo11bo$8bo53bo12bo36b3o32b2o11b2o$6bo26bo
6bo29b2o31bo10bo30bo17bo$6b2o3bo59bo86b2o$34bobobo31b2o32bo5bobo46bo$
9bo2bo49bo12bo82b2o$33bo6bo23b2o6b2o29bo10bo30bo17bo$9bo55bo6bo39b3o
32b2o11b2o$63bo10bo37bo35bo11bo$111b2o33bo15bo$109bo$107bo6$68bo3bo$
70bo2$68bo3bo2$7bo3b2o47bo19bo37bo11bo21bo21bo$9bo2bo19bo29bo15bo37bo
15bo39bo$8b3ob2o20bo6bo19b2o15b2o36b2o13b2o39b2o$33b2o6bo2bo74bo9bo22b
o22bo$12bo28bo23bobobobobobo36b2o26b2o6bo7bo6b2o$45bo48bo7bo9bo27bo23b
o$61b2o15b2o16bo15b2o26b2o6bo7bo6b2o$62bo15bo16b2o5bo16bo9bo22bo22bo$
60bo19bo35b2o13b2o39b2o$116bo15bo39bo$68bo3bo45bo11bo21bo21bo2$70bo$
68bo3bo7$136bo30bo$105bo3bo28bo26bo$66bo31bo17bo20b2o26b2o$10bo57bo27b
o21bo16bo32bo$8b3o25bo30b2o22bo15bo15bo26bo2bo$8bo54bo12bo30bo$42bo51b
obo21bobo29bo2bo$31bo32bo3bo4bobo31bo27bo32bo$9bo2bo20bobobobo51bo15bo
15bo13b2o26b2o$8b3o21b2o29bo12bo19bo21bo19bo26bo$67b2o29bo17bo19bo30bo
$68bo36bo3bo$7bo3bo54bo!
Moreover, some other discoveries, a small direct p61, p45, p36 and two p19 guns (all not adjustable, the 10 cell gun was already known):
Code: Select all
x = 25, y = 97, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
3$14bo$16bo$12bo2b2o$10b3o$10bo$13bo2$13bo$10bo$10b3o$12bo2b2o$16bo$
14bo5$13b2o$10bo3bo$12bob2o$11b2o$7bo2$8bobo6bo2$7bo$11b2o$12bob2o$10b
o3bo$13b2o5$15b2o$13bo2bo$13b2ob2o$7bo7bo2$11bobo2$7bo7bo$13b2ob2o$13b
o2bo$15b2o7$17bo$14bo2$15bo2$15bo2$11bo3bo4$11bo3bo2$15bo2$15bo2$14bo$
17bo5$15b2o$15bo2bo$17b2o3$10bobobo2$9bo2$16bo5$10bobo$10b3o!
EDIT1:
Another colour changing reflector with just 8 cells (see top):
Code: Select all
x = 20, y = 110, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
2$11bo$9bo$4bo$14b2o$7bo2bo3bo$14b2o$4bo$9bo$11bo7$5b2o$6bo$5b2o4$8bo$
10bo$9b2o$7bo$14b2o$14bo$14b2o$7bo$9b2o$10bo$8bo6$10b2o$10bo$9b2o$7bo$
14b2o$14bo$14b2o$7bo$9b2o$10bo$10b2o5$8bo$6b5o3b2o$6bo3bo3bo$2bo2b2obo
b2o2b2o$3o3bo3bo$o5b5o$8bo10$8bo$6b5o3b2o$o5bo3bo3bo$2bo2b2obob2o2b2o$
b2o3bo3bo$6b5o$8bo8$8bo$6b5o$6bo3bo3b2o$2bo2b2obob2o2bo$3o3bo3bo3b2o$o
5b5o$8bo10$8bo$6b5o$o5bo3bo3b2o$2bo2b2obob2o2bo$b2o3bo3bo3b2o$6b5o$8bo!
This allows now for ridiculously small oscillators of period p29+4N (2gliders shuttle, with population 14!) and p31+4N (1 glider shuttle):
Code: Select all
x = 68, y = 37, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
4$21bo21bo$15bo3bo16bo4bo$19b2o20b2o$8bo13bo6bo14bo2$9bobo4bo13bobo4bo
2$8bo13bo6bo14bo$19b2o20b2o$15bo3bo16bo4bo$21bo21bo11$11bo8bo26bo10bo
2$4bo22bo12bo24bo2$5bobo4bo6bo4bobo14bobo4bo8bo4bobo2$4bo22bo12bo24bo
2$11bo8bo26bo10bo!
So some of the minimal oscillators above, have a smaller version. Also some guns can be made smaller using this technology.
EDIT1.2:
The complete list of known 180° G reflectors:
Code: Select all
x = 32, y = 98, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
6$17b2o$18bo$17b2o4$21bo$19b5o$19bo3bo$18b2obo$19bo$17bo7b2o$17b3o5bo$
19bo5b2o$19b2o4$19bo$21bo$20b2o$18bo$25b2o$25bo$25b2o$18bo$20b2o$21bo$
19bo5$20bo$16bo5bo$14b3o4b2o$14bo$25b2o$16bo8bo$25b2o$14bo$14b3o4b2o$
16bo5bo$20bo7$22bo$20bo$15bo$25b2o$18bo2bo3bo$25b2o$15bo$20bo$22bo8$
19bo$17b5o$11bo5bo3bo3b2o$13bo2b2obob2o2bo$12b2o3bo3bo3b2o$17b5o$19bo
7$19bo$17b5o3b2o$11bo5bo3bo3bo$13bo2b2obob2o2b2o$12b2o3bo3bo$17b5o$19b
o!
The upper one is p2, the other ones are stable. The p2 is very fast, the turning reaction requires only 4 ticks, so it allows for a p8 glider shuttle:
Code: Select all
x = 12, y = 13, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
4bo$2b5o$2bo3bo$b2obo$2bo5b2o$o5bo2bo$3o6b3o$2bo3bo4bo$2b2o5bo$7bob2o$
5bo3bo$5b5o$7bo!
EDIT2:
As mentioned by danny for the synthesis of the 12 glider 2c/19 spaceship, it seems that synthesis of still lifes is hard, as no still life (except 1 single cell) can be created by two gliders.
However, I gathered a few synthesis of objects:
Code: Select all
x = 147, y = 219, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
8$31bo$30bobo$30b3o$31bo6b2o29b2o$37b2obo27b2obo$19b2o17b2o29b2o$20bo$
19b2o$30b3o24b3o21b2o3b2o$30bobo24bobo21bo4bo$59bo23bo2b2o14$88b2o3bo$
87bob2o$88b2o$16bobo54b2o5b2o11bo2b2o$16b3o39bobo13bo5bo15bo$40b2o16b
3o12b2o5b2o14b2o$33b2o5bo52bo$32bob2o4b2o$33b2o61bo$19bo39bo20bo11b2o$
18b3o70bob2o$18bobo14bo56b2o3bo$19bo34b2o25bo$37bo17bo3bo38bo$54b2o26b
o$61bo2$98bo$97b3o$97bobo$98bo2$25b2o$18b2o4b2obo$19bo5b2o$18b2o10$21b
o$20bobo$20b3o$21bo2$38b2o5b2o$39bo4b2obo11b2o$38b2o5b2o13bo7b2o$23b2o
34b2o8bo$16b2o4b2obo42b2o5b2o4b2o$17bo5b2o49b2obo3bo$16b2o22bo34b2o4b
2o$39b3o$39bobo$40bo8$39bo$17b2o18bobo$18bo18b3o$17b2o36bobo$25b3o27b
3o$25bo15bo$25b2o3$52bobo$52b3o4$18b2o34bo$19bo32b5o$18b2o32bo3bo$24bo
26b2obo$22bo29bo$22b2o28b2o6$26bobo$26b3o4$40b2o$41bo5bo$40b2o$23b2o3b
2o$24bo2b2obo6b2o5bo$23b2o3b2o8bo$37b2o2$51bo$47b2o$24bo23bo$22bo23bo$
22b2o22b2o4$102bobo$102b3o3$99bobo$99b3o3$13bobo$13b3o$59bobo35bo$59b
3o20b2o5b2o$26bo2bo2bo17bo2bo2bo10bo2bo2bo3bo4bo6bo16bo$82b2o5b2o$98b
2o25b2o$13b3o37bo16bo28bo26bo$13bobo35b5o12b5o3bo20b5o9b2o11b5o$20b2o
29bo3bo2b3o7bo3bo24bo3bo8bob2o10bo3bo$21bo7b2o19b2obo4bobo6b2obo25b2ob
o11b2o5b2o3b2obo$20b2o8bo20bo16bo28bo21bo4bo$29b2o5b2o4b2o7b2o15b2o27b
2o19b2o4b2o$35b2obo3bo$36b2o4b2o2$117bobo$117b3o3$114bobo$114b3o3$13bo
bo$13b3o$60bobo49bo$60b3o23b2o5b2o5b2o$31bo2bo2bo12bo2bo2bo15bo2bo2bo
4bo2bo6bo6bo20bo$86b2o5b2o5b2o$113b2o$13b3o37bo21bo13b2o23bo$13bobo35b
5o17b5o4bo6bo22b5o$42b2o7bo3bo3b3o11bo3bo11b2o21bo3bo$33b2o7bo10bob2o
2bobo13bob2o35bob2o$33bo8b2o11bo21bo38bo$20b2o4b2o5b2o19b2o20b2o37b2o$
21bo3bob2o$20b2o4b2o13$125b2o$66bobo57bo$66b3o56b2o2$130bo$15bobo$15b
3o$31bo20bo14bo32bo$118b2o$25bobo91bo2bo7b2o$25b3o15b2o26b2o45b2o10bo$
30bo13bo2bo3bo11bo2bo3b2obo16b2o4b2o3b2o20bo4b3ob2o$14b3o26b2o26b2o18b
o5bo2b2obo24bo3bo$14bobo73b2o4b2o3b2o19bo7b3o$61bo68bo$46bo$24b3o94b3o
$24bobo94bobo2$45b3o$45bobo!
We have 4 gliders for the p4 spaceship (the R) and 12 gliders for the c/6 (p12) diagonal spaceship.
3 gliders for a snowflake and a 1/2-snowflake which is optimal.
4 gliders for the 3/4 snowflake, 5 gliders (1G+1R) for the 4 cell eater, 6 gliders for the 5 cell eater (the Z) and 10 gliders for the carrier.
12 gliders for the 'extended' 3/4 snowflake, and 14 for the 7-bit still life (the W heptomino). 8 gliders for the second most common 7bit still life (point symmetric 4-bit still life). And 8 gliders for a quite complex still life: two stacked W.
Everything which requires more than 3 gliders might be improved.
EDIT3:
A clean p12 R-rake and a p24 c/2 ship (with a relative large spark, based on a p12 Z-puffer):
Code: Select all
x = 60, y = 80, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
15$24bo$23b3o2bo$22bo2bob3o$27bobo$28bo$30b3o$27bo2bobo$32bo$26bo$25b
3o$26bo5$30b3o$32bo$24bo6b2o2$19b3o$19bobo5b3o$19bo7bobo$29bo19$47bo$
6bo16b3o3bo11b3o2b3o$5b3o2b3o10bobo2b3o10bobobo2bo$5bo2bobobo12bo2bobo
$29bo2b3o$32bobo11b3o$5b3o20bo5bo8bo2bobo$5bobo2bo16b3o18bo$5bo22bo11b
2o$12b2o26bo$13bo26b2o$12b2o12b2o$26bo9b2o$16b2o7b2o9bo$17bo18b2o$16b
2o$32b2o$20b2o4b2o4bo$21bo4bo5b2o$20b2o3b2o$28b2o$28bo$28b2o!
and a p2 wickstretcher, laying 1/2-snowflakes close to each other so that they become p2 oscillating:
Code: Select all
x = 46, y = 14, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
3$3b2o$4bo$3b2o$10b2o$11bo$5bobo2b2o2$11b2o$12bo$10b3o!
Some O(n/log(n)) growth:
Code: Select all
x = 23, y = 13, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
2bo$bo$2o19bo$b2o16bo$19b2o$22bo$b2o2bobo3b2o$bo10bo$b2o8b2o$6bo15bo$
5bo13b2o$4b2o13bo$5b2o14bo!
a quadratic growth pattern:
Code: Select all
x = 59, y = 62, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
30bo$24b3o2b3o$24bobo2bo2bo2$21bo$20b3o$20bo2bo$44bo$46bo$45b2o5$42b2o
3b2o$43bobobo$43b5o$45bo$31b3o$31bobo16b3o$41b2o6b2ob2o2b2o$41bo7bo3bo
2bo$41b2o6b2ob2o4bo$50b3o2$43b3o$19bo11b3o9bobo$18b3o9b2ob2o$18bobo9bo
3bo$19bo10b2ob2o$31b3o2$42b2o3b2o$32b2o9bobobo$33bo9b5o$31bo13bo3$45b
2o$46bo$44bo3$19bo$18b3o$8bo9bobo5bo$6b3o5b2o3bo4b3o$o5bo6bob2o7bo8bo$
2bo2bobo6b2o7bobo5bo$b2o3bo17bo6b2o$6b3o15b3o$8bo10bo6bo$17b5o$17bo3bo
$16b2obob2o$17bo3bo$17b5o$19bo2$19b2o$20bo$18bo!
and a natural (C4_4 soup) O(sqrt(n)) pattern with 28 cells:
Code: Select all
x = 42, y = 42, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
32bo$28bo2$28bo3$26bo$28bo2$o4$bobo3bo4bobo12bobo2$6bo11$35bo2$12bobo
12bobo4bo3bobo4$41bo2$13bo$15bo3$13bo2$13bo$9bo!
EDIT4:
A G to 2G signal converter (a splitter), unfortunately not a stable one, only a p191:
Code: Select all
x = 81, y = 97, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
71bo$69b5o$69bo3bo$64b2o2b2obob2o$65bo3bo3bo$63bo5b5o$71bo2$8bo$6b5o$
6bo3bo$b2o2b2obob2o$2bo3bo3bo$o5b5o$8bo3$38bo3bo3$22b2o16bo$23bo$23b2o
12bo5bo$40bo$36bo7bo$24bo$22b5o$22bo3bo$21b2obob2o$22bo3bo$22b5o$24bo
14bobo$39b3o$18b2o$17bob2o$18b2o6$57bo$55b5o6bo3bo$55bo3bo3bo9bo$54b2o
bob2o2b3o5bo$55bo3bo5bo5b2o$55b5o$14bo42bo$12b5o$12bo3bo$11b2obob2o13b
o$12bo3bo12bo$12b5o2b2o8b2o$14bo5bo$18bo4bo2$14b2o$14bo4b2o$16bo3bo$
18bo$23b2o$24bo6bo$22bo6b5o$29bo3bo$24b2o2b2obob2o$25bo3bo3bo$23bo5b5o
$31bo19bo$36b2o5b2o4b5o$37bo5bo5bo3bo$35bo9bo2b2obob2o$38bo3bo6bo3bo$
49b5o$51bo2$59bo$51b2o4b5o$51bo5bo3bo$50b4o2b2obob2o$53bo3bo3bo$51bo5b
5o$59bo17bo$75b5o$75bo3bo$68bo5b2obob2o$67b3o5bo3bo$67bobo5b5o$68bo8bo
2$64bo7bo$68bo8b2o$65bo5bo5bo$79bo$68bo3$66bo3bo!
However, signal converter with other (larger) periods are possible. For a stable G to 2G we require at least either a stable 90° R reflector, or a stable R to G converter.