The most known class of such block CA are detailed in this blog post (sourced from this forum post) by Nathaniel: http://www.njohnston.ca/2009/05/rectang ... automaton/
and are explored further in the following paper: http://www.njohnston.ca/wp-content/uplo ... 01/2x2.pdf
A starter list of known media:
muzik wrote: ↑January 10th, 2018, 12:33 pmMargolus rule being simulated by all five possible media (empty doesn't count) coexisting in a single rule:Code: Select all
x = 84, y = 12, rule = B2c3i4i5i/S2c3i4i5i 2o18b2o20bo19bo19bo$bo18b2o20bo40bo$2o18b2o20bo19bo19bo$bo18b2o20bo40b o$2o18b2o20bo19bo19bo$bo18b2o20bo40bo$2o18b2o20bo19bo19bo$bo18b2o20bo 40bo$2o18b2o20bo19bo19bo$bo18b2o20bo40bo$2o18b2o20bo19bo19bo$bo18b2o 20bo40bo!
bprentice wrote: ↑July 16th, 2016, 2:39 pmI'm surprised that the young members of the forum did not explore the rule introduced here:
http://www.conwaylife.com/forums/viewto ... 125#p32973
A beautiful period 4194302 oscillator:
Brian PrenticeCode: Select all
x = 48, y = 48, rule = B2ae3i/S .A.A3.A.A.A5.A.A.A7.A.A3.A5.A.A.A$A3.A.A5.A3.A5.A5.A3.A.A.A3.A5.A$9. A3.A.A3.A3.A3.A7.A.A.A3.A3.A$A3.A.A.A.A7.A.A3.A.A5.A3.A5.A.A$.A.A5. A.A.A.A.A.A.A9.A.A5.A.A.A.A.A$6.A3.A7.A.A.A.A.A3.A.A.A.A.A3.A.A$.A. A.A.A5.A.A3.A.A5.A.A.A.A9.A3.A$A5.A.A.A.A3.A3.A3.A5.A.A3.A.A7.A$3.A 3.A9.A5.A.A.A3.A3.A3.A3.A.A$A.A.A5.A.A5.A.A.A.A3.A5.A5.A.A$3.A.A.A. A3.A9.A5.A.A.A11.A$A3.A9.A3.A.A19.A.A.A.A$.A5.A.A5.A.A3.A.A5.A.A.A5. A5.A.A$2.A.A.A3.A13.A3.A5.A3.A3.A3.A$11.A3.A.A3.A3.A.A3.A3.A.A3.A.A $2.A.A.A5.A.A3.A.A.A7.A.A7.A.A.A.A$.A5.A13.A.A.A.A.A.A.A.A.A.A.A.A3. A$A3.A3.A3.A.A3.A3.A7.A.A7.A.A$3.A.A3.A.A3.A.A.A5.A.A3.A3.A.A3.A5.A $A.A.A.A11.A.A.A.A3.A5.A3.A7.A$3.A.A.A.A.A3.A3.A9.A.A.A5.A.A3.A$A3. A.A5.A.A.A5.A.A17.A.A$.A3.A3.A5.A.A.A.A3.A3.A.A.A5.A$2.A5.A.A.A3.A9. A.A5.A3.A.A.A.A$3.A.A.A.A3.A5.A.A9.A3.A.A.A5.A$8.A5.A.A.A3.A3.A.A.A .A5.A3.A3.A$3.A.A17.A.A5.A.A.A5.A.A3.A$2.A3.A.A5.A.A.A9.A3.A3.A.A.A .A.A$.A7.A3.A5.A3.A.A.A.A11.A.A.A.A$A5.A3.A.A3.A3.A.A5.A.A.A3.A.A3. A.A$5.A.A7.A.A7.A3.A3.A.A3.A3.A3.A$A3.A.A.A.A.A.A.A.A.A.A.A.A13.A5. A$.A.A.A.A7.A.A7.A.A.A3.A.A5.A.A.A$4.A.A3.A.A3.A3.A.A3.A3.A.A3.A$.A 3.A3.A3.A5.A3.A13.A3.A.A.A$A.A5.A5.A.A.A5.A.A3.A.A5.A.A5.A$.A.A.A.A 19.A.A3.A9.A3.A$2.A11.A.A.A5.A9.A3.A.A.A.A$5.A.A5.A5.A3.A.A.A.A5.A. A5.A.A.A$2.A.A3.A3.A3.A3.A.A.A5.A9.A3.A$.A7.A.A3.A.A5.A3.A3.A3.A.A. A.A5.A$A3.A9.A.A.A.A5.A.A3.A.A5.A.A.A.A$3.A.A3.A.A.A.A.A3.A.A.A.A.A 7.A3.A$A.A.A.A.A5.A.A9.A.A.A.A.A.A.A5.A.A$3.A.A5.A3.A5.A.A3.A.A7.A. A.A.A3.A$A3.A3.A.A.A7.A3.A3.A3.A.A3.A$.A5.A3.A.A.A3.A5.A5.A3.A5.A.A 3.A$2.A.A.A5.A3.A.A7.A.A.A5.A.A.A3.A.A!
Code: Select all
x = 64, y = 10, rule = B2e/S
63bo$42bobo17bo$25bobo13bo3bo15bo$12bobo9bo3bo11bo5bo13bo$3bobo5bo3bo
7bo5bo9bo7bo11bo$obo3bo3bo5bo5bo7bo7bo9bo9bo$7bobo7bo3bo9bo5bo11bo7bo$
18bobo11bo3bo13bo5bo$33bobo15bo3bo$52bobo!
wwei47 wrote: ↑March 29th, 2021, 10:46 pmFor margolus media that can have the cool oscillators, I know of three other types.Code: Select all
x = 91, y = 77, rule = B2i3ai4qt5i/S1e2ik3ij4w5i 4o17bo3bo14b12o9bo3bo3bo3bo3bo3bo$4o16b3ob3o13b12o8b3ob3ob3ob3ob3ob3o$ 21bo3bo35bo3bo3bo3bo3bo3bo18$8o13bo3bo3bo3bo$8o12b3ob3ob3ob3o$21bo3bo 3bo3bo8$40b16o5bo3bo3bo3bo3bo3bo3bo3bo$40b16o4b3ob3ob3ob3ob3ob3ob3ob3o $61bo3bo3bo3bo3bo3bo3bo3bo8$8o13bo3bo3bo3bo$8o12b3ob3ob3ob3o$8o13bo3bo 3bo3bo$8o15bo7bo$21bo3bo3bo3bo$20b3ob3ob3ob3o$21bo3bo3bo3bo24$40b16o5b o3bo3bo3bo3bo3bo3bo3bo$40b16o4b3ob3ob3ob3ob3ob3ob3ob3o$40b16o5bo3bo3bo 3bo3bo3bo3bo3bo$40b16o7bo7bo7bo7bo$61bo3bo3bo3bo3bo3bo3bo3bo$60b3ob3ob 3ob3ob3ob3ob3ob3o$61bo3bo3bo3bo3bo3bo3bo3bo!
Code: Select all
x = 266, y = 10, rule = B2en3ijq4w6aen/S2cek3aceny4ejqr5jk6a b2o4b2o22b2o4b2o4b2o4b2o20b2o4b2o4b2o4b2o20b2o4b2o4b2o4b2o4b2o4b2o18b 2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o16b2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o$o2bo2b o2bo20bo2bo2bo2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 14bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo20bo2bo2bo 2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo2bo2bo2bo2bo2b o2bo2bo16bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo14bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b2o4b2o22b2o4b2o4b2o4b2o20b2o4b2o 4b2o4b2o20b2o4b2o4b2o4b2o4b2o4b2o18b2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o16b 2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o3$71b2o4b2o4b2o4b2o130b2o4b2o4b2o4b2o4b 2o4b2o4b2o4b2o$70bo2bo2bo2bo2bo2bo2bo2bo128bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo$70bo2bo2bo2bo2bo2bo2bo2bo128bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo$71b2o4b2o4b2o4b2o130b2o4b2o4b2o4b2o4b2o4b 2o4b2o4b2o!
muzik wrote: ↑January 6th, 2020, 9:36 pmOther media that can support M10:
Code: Select all
x = 55, y = 25, rule = DeficientSeeds A.A19.A.A27.A.A6$A.A19.A.A27.A.A6$22.A.A27.A.A6$22.A.A27.A.A6$52.A.A!
Code: Select all
x = 25, y = 9, rule = B1c/S1c|B2a/S1c2e 24bo$21bo$18bo$15bo$12bo$9bo$6bo$3bo$o!
The following is a non-totalistic rule that can simulate these block CA at twice the speed:muzik wrote: ↑January 30th, 2020, 5:04 pmHere's another rule that exhibits that same kind of Margolus behaviour:
Code: Select all
x = 48, y = 48, rule = R2,C0,M0,S5..5,B3..3,NN bo$obo$bo$4bo$3bobo$4bobo$5bobo$6bo$9bo$8bobo$9bobo$10bobo$11bobo$12bo bo$13bo$16bo$15bobo$16bobo$17bobo$18bobo$19bobo$20bobo$21bobo$22bo$25b o$24bobo$25bobo$26bobo$27bobo$28bobo$29bobo$30bobo$31bobo$32bobo$33bo$ 36bo$35bobo$36bobo$37bobo$38bobo$39bobo$40bobo$41bobo$42bobo$43bobo$ 44bobo$45bobo$46bo!
AbhpzTa wrote: ↑June 30th, 2016, 12:53 pmB3i4int5ey6k7e/S1e2k3ey4irt5iEDIT:Code: Select all
x = 319, y = 95, rule = B3i4int5ey6k7e_S1e2k3ey4irt5i 17b2o19b2o54b2o23b2o25b2o71b2o22b2o27b2o3b2o26b2o$bo17bo20bo21bo2bo27b o24bo26bo2bo66bo2bo26bo2bo22bo7bo24bo5bo3bo$bo17bo20bo21bo2bo27bo24bo 26bo2bo66bo2bo26bo2bo22bo7bo24bo5bo3bo$17b2o19b2o23b2o29b2o23b2o98b2o 22b2o27b2o3b2o26b2o$bo14bo23bo24bo30bo21bo2bo26bo66bo5bo23bo2bo22bo2bo 4bo27bo2bo3bo$bo14bo23bo24bo30bo21bo2bo26bo66bo5bo23bo2bo22bo2bo4bo27b o2bo3bo$17b2o19b2o54b2o23b2o98b2o22b2o27b2o3b2o26b2o14$2o14b4o17b4o20b 7o26b2o20b8o20b6o61b14o16b10o19b12o19b18o$16b4o40bo7bo25b2o20b8o$60bo 7bo25b2o$60bo7bo25b2o$61b7o26b2o$89b5o2b5o$88bo5b2o5bo$87bob5o2b5obo$ 88bo5b2o5bo$89b5o2b5o$94b2o$94b2o$94b2o$94b2o$94b2o$37b4o$37b4o$37b4o$ 34b3o4b3o$33bo3b4o3bo$32bob3o4b3obo97b8o59b16o$33bo3b4o3bo$34b3o4b3o$ 37b4o$37b4o$37b4o5$92b6o$92b6o$90b2o6b2o$90b2o6b2o$90b2o6b2o$87b3o2b6o 2b3o$87b3o2b6o2b3o$87b3o2b6o2b3o$84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b3o$ 84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b3o$80b4o3b3o2b6o2b3o3b4o$80b4o3b3o2b 6o2b3o3b4o$78b2o4b3o3b2o6b2o3b3o4b2o$77bo2b4o3b3o2b6o2b3o3b4o2bo$77bo 2b4o3b3o2b6o2b3o3b4o2bo$77bo2b4o3b3o2b6o2b3o3b4o2bo$74b3ob2o4b3o3b2o6b 2o3b3o4b2ob3o$73bo3bo2b4o3b3o2b6o2b3o3b4o2bo3bo$72bob3ob2o4b3o3b2o6b2o 3b3o4b2ob3obo$71bobo3bo2b4o3b3o2b6o2b3o3b4o2bo3bobo$70bobob3ob2o4b3o3b 2o6b2o3b3o4b2ob3obobo$71bobo3bo2b4o3b3o2b6o2b3o3b4o2bo3bobo$72bob3ob2o 4b3o3b2o6b2o3b3o4b2ob3obo$73bo3bo2b4o3b3o2b6o2b3o3b4o2bo3bo$74b3ob2o4b 3o3b2o6b2o3b3o4b2ob3o$77bo2b4o3b3o2b6o2b3o3b4o2bo$77bo2b4o3b3o2b6o2b3o 3b4o2bo$77bo2b4o3b3o2b6o2b3o3b4o2bo$78b2o4b3o3b2o6b2o3b3o4b2o$80b4o3b 3o2b6o2b3o3b4o$80b4o3b3o2b6o2b3o3b4o$84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b 3o$84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b3o$87b3o2b6o2b3o$87b3o2b6o2b3o$87b 3o2b6o2b3o$90b2o6b2o$90b2o6b2o$90b2o6b2o$92b6o$92b6o!
Code: Select all
x = 193, y = 84, rule = B3i4int5ey6k7e_S1e2k3ey4irt5i b2o13bo2bo13b2o21b2o52b2o65b2o$3bo12bo2bo12bo22bo2bo50bo2bo60bo2bo2bo$ 3bo13b2o13bo22bo2bo50bo2bo60bo2bo2bo$b2o16bo13b2o21b2o52b2o$o18bo12bo 2bo19bo2bo53bo60bo2bo2bo$o31bo2bo19bo2bo53bo60bo2bo2bo$b2o30b2o21b2o 52b2o65b2o6$b3o10b8o$o3bo9b8o$b3o10b8o9b7o$14b8o8bo7bo$31b7o4$50b15o 43b6o57b11o$49bo15bo41bo6bo55bo11bo$49bo15bo41bo6bo55bo11bo$49bo15bo 41bo6bo55bo11bo$49bo15bo38b3ob6ob3o52bo11bo$49bo15bo38b3ob6ob3o52bo11b o$49bo15bo36b2o3bo6bo3b2o50bo11bo$49bo15bo36b2o3bo6bo3b2o50bo11bo$50b 15o37b2o3bo6bo3b2o43b7ob11ob7o$102b2o3bo6bo3b2o42bo7bo11bo7bo$102b2o3b o6bo3b2o41bob7ob11ob7obo$97b5o2b3ob6ob3o2b5o35bobo7bo11bo7bobo$96bo5b 2o3bo6bo3b2o5bo35bob7ob11ob7obo$96bo5b2o3bo6bo3b2o5bo36bo7bo11bo7bo$ 94b2ob5o2b3ob6ob3o2b5ob2o35b7ob11ob7o$93bo2bo5b2o3bo6bo3b2o5bo2bo41bo 11bo$93bo2bo5b2o3bo6bo3b2o5bo2bo41bo11bo$93bo2bo5b2o3bo6bo3b2o5bo2bo 41bo11bo$90b3ob2ob5o2b3ob6ob3o2b5ob2ob3o38bo11bo$89bo3bo2bo5b2o3bo6bo 3b2o5bo2bo3bo37bo11bo$88bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo36bo11bo$88bo b3ob2ob5o2b3ob6ob3o2b5ob2ob3obo36bo11bo$86b2obo3bo2bo5b2o3bo6bo3b2o5bo 2bo3bob2o35b11o$85bo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bo$84bob2obo3bo 2bo5b2o3bo6bo3b2o5bo2bo3bob2obo$83bobo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3o bo2bobo$82bobob2obo3bo2bo5b2o3bo6bo3b2o5bo2bo3bob2obobo$81bobobo2bob3o b2ob5o2b3ob6ob3o2b5ob2ob3obo2bobobo$80bobobob2obo3bo2bo5b2o3bo6bo3b2o 5bo2bo3bob2obobobo$81bobobo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bobobo$ 49b16o17bobob2obo3bo2bo5b2o3bo6bo3b2o5bo2bo3bob2obobo$49b16o18bobo2bob 3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bobo$49b16o19bob2obo3bo2bo5b2o3bo6bo3b 2o5bo2bo3bob2obo$49b16o20bo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bo$49b 16o21b2obo3bo2bo5b2o3bo6bo3b2o5bo2bo3bob2o38b4o$49b16o23bob3ob2ob5o2b 3ob6ob3o2b5ob2ob3obo40b4o$49b16o23bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo40b 4o$49b16o24bo3bo2bo5b2o3bo6bo3b2o5bo2bo3bo41b4o$90b3ob2ob5o2b3ob6ob3o 2b5ob2ob3o42b4o$93bo2bo5b2o3bo6bo3b2o5bo2bo45b4o$93bo2bo5b2o3bo6bo3b2o 5bo2bo45b4o$93bo2bo5b2o3bo6bo3b2o5bo2bo45b4o$94b2ob5o2b3ob6ob3o2b5ob2o 46b4o$96bo5b2o3bo6bo3b2o5bo48b4o$96bo5b2o3bo6bo3b2o5bo38b10o4b10o$97b 5o2b3ob6ob3o2b5o39b10o4b10o$102b2o3bo6bo3b2o42b2o10b4o10b2o$102b2o3bo 6bo3b2o42b2o10b4o10b2o$102b2o3bo6bo3b2o40b2o2b10o4b10o2b2o$102b2o3bo6b o3b2o40b2o2b10o4b10o2b2o$102b2o3bo6bo3b2o42b2o10b4o10b2o$104b3ob6ob3o 44b2o10b4o10b2o$104b3ob6ob3o46b10o4b10o$107bo6bo49b10o4b10o$107bo6bo 59b4o$107bo6bo59b4o$108b6o60b4o$174b4o$174b4o$174b4o$174b4o$174b4o$ 174b4o$174b4o!