UC-hunting for different rules

[Rhombic]

Let's take this as a CA-based puzzle, if you wish. For a given rule that doesn't seem hopeless for UC, finding the set of transformations that define universal computation can be an interesting challenge for the solver as well as useful for everyone to see the various ways different reactions can be accomplished in a variety of CA.
Plus it's good practice.

For this rule I already have the pull reaction, which appeared naturally and was too beautifully simple to avoid.

Code: Select all

x = 4, y = 19, rule = B2k3ainr4aew5e/S23-c
bo$b2o$o$2bo$b2o13$2b2o$2b2o!

[_zM]

Add another block without removing the earlier block:

Code: Select all

x = 6, y = 17, rule = B2k3ainr4aew5e/S23-c
bo$b2o$o$2bo$b2o11$4b2o$4b2o!

Delete a block:

Code: Select all

x = 5, y = 17, rule = B2k3ainr4aew5e/S23-c
bo$b2o$o$2bo$b2o11$3b2o$3b2o!

Push by 4:

Code: Select all

x = 14, y = 81, rule = B2k3ainr4aew5e/S23-c
12bo$11b2o$13bo$11bo$11b2o7$7bo$6b2o$8bo$6bo$6b2o11$8bo$7b2o$9bo$7bo$
7b2o8$bo$b2o$o$2bo$b2o7$6bo$6b2o$5bo$7bo$6b2o11$5bo$5b2o$4bo$6bo$5b2o
11$4b2o$4b2o!

Mostly a starting point more than anything else.

[Redstoneboi]

so we have push by 4, and pull by 3.
those are relatively prime, so we can pull/push a block any amount we want.
anyone up to find a fire reaction?

[Rhombic]

so we have push by 4, and pull by 3.
those are relatively prime, so we can pull/push a block any amount we want.
anyone up to find a fire reaction?

I seem to recall there was a script to find linear growths.

[83bismuth38]

anybody need a loaf? maybe? what about this diamond thing? boat? hive? that diamond but alone?

Code: Select all

x = 83, y = 30, rule = B2k3ainr4aew5e/S23-c
5o$2o2bo$3bo10b2o$14b2o9$25b5o11bo$25b2o2bo10bobo$5o23bo10bo3bo3b2o10b
5o17b2o$2o2bo9b2o24bobo4b2o10b2o2bo17b2o$3bo10b2o25bo20bo$47b2o32b2o$
47b2o32b2o7$81b2o$59b5o17b2o$59b2o2bo$62bo18b2o$81b2o!

ayy pull by 1

Code: Select all

x = 32, y = 6, rule = B2k3ainr4aew5e/S23-c
7b5o$7b2o2bo4b5o$10bo5b2o2bo9b2o$5o14bo10b2o$2o2bo$3bo!

pull by... 21.

Code: Select all

x = 41, y = 15, rule = B2k3ainr4aew5e/S23-c
11bo$8b2o2bo$8b5o3$25b5o$3bo13b5o3b2o2bo$2o2bo6bo5b2o2bo6bo10b2o$5o3b
2o2bo7bo18b2o$8b5o3$25b5o$25b2o2bo$28bo!

better boat:

Code: Select all

x = 24, y = 4, rule = B2k3ainr4aew5e/S23-c
5o$2o2bo3b5o9b2o$3bo4b2o2bo9b2o$11bo!

ship:

Code: Select all

x = 35, y = 5, rule = B2k3ainr4aew5e/S23-c
5o14b5o9b2o$2o2bo14b2o2bo9b2o$3bo7b5o6bo$11b2o2bo$14bo!

[Rhombic]

Does this, and the gun, prove UC?

Code: Select all

x = 108, y = 19, rule = B36a/S2-i34t5e
92bobo$93b2o$93bo3$obo$b2o$bo3$42bo32bo29bo$8bo27bo6b2o31b2o28b2o$9bo
27b2o3b2o31b2o28b2o$7b3o26b2o2$13b2o28b2o24bobo4b2o28b2o$13b2o28b2o25b
2o4b2o23bo4b2o$70bo28bobo$100b2o!

[Hdjensofjfnen]

Does this, and the gun, prove UC?

Code: Select all

x = 108, y = 19, rule = B36a/S2-i34t5e
92bobo$93b2o$93bo3$obo$b2o$bo3$42bo32bo29bo$8bo27bo6b2o31b2o28b2o$9bo
27b2o3b2o31b2o28b2o$7b3o26b2o2$13b2o28b2o24bobo4b2o28b2o$13b2o28b2o25b
2o4b2o23bo4b2o$70bo28bobo$100b2o!

p276, probably known, sparky?

Code: Select all

x = 4, y = 5, rule = B36a/S2-i34t5e
bobo$o2bo2$2b2o$3bo!