Two Steps Back Cellular Automata

Inspiration

This CA was inspired by this Tumblr post by Charlie Deck (@bigblueboo on Twitter).

Since there is no name given for this CA, I called it the “Two Steps Back Cellular Automata”.

How it works

This time it is a more simple 1D CA.

Each cell is updated by counting the neighbors 2 cells either side of it and itself (5 cells) and the same 5 cells in the previous generation. This gives you a possible count of active cells between 0 and 10. The count is used into a rule array for the new cell state.

For example, if your rule array is rule[1,0,0,0,0,1,0,1,1,0,1] and the cell has 5 neighbor cells that are alive, then the new cell would be alive too (the rule counts start at 0, so the 6th entry in the rule array is for 5 active neighbors and that entry is 1).

You can convert the 11 digit rule into a binary string. The above is 10000101101 which converts into the decimal number 1069 (not 1441 as in Charlie’s post – looks like he reversed the binary digits before conversion).

Results

There are 2048 possible rules. Not a big amount compared to some CAs, so it was easy to setup a loop and generate all 2048 rules. These are a few of the interesting results starting from a single centered alive cell. I have included a low res and high detail version of each rule.

Rule 313

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 366

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 384

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 494

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 798

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 995

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 1069

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 1072

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 1437

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 1438

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 1623

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 1822

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Rule 2019

Two Steps Back Cellular Automaton

Two Steps Back Cellular Automaton

Extending the neighborhood

Once I went through those 2048 possibilities I extended the neighborhood 1 cell either side. So a total of 14 neighbor cells to check. This bumps the total possible rules up to 32768. I called these ones the “Two Steps Back Extended Cellular Automata”.

Extended Results

Again I kicked off a batch run and waited for the 32,768 results to render. Here are some of the more interesting results.

Rule 6270

Two Steps Back Extended Cellular Automaton

Two Steps Back Extended Cellular Automaton

Rule 10159

Two Steps Back Extended Cellular Automaton

Two Steps Back Extended Cellular Automaton

Rule 21627

Two Steps Back Extended Cellular Automaton

Two Steps Back Extended Cellular Automaton

Rule 28798

Two Steps Back Extended Cellular Automaton

Two Steps Back Extended Cellular Automaton

Rule 30278

Two Steps Back Extended Cellular Automaton

Two Steps Back Extended Cellular Automaton

See this flickr gallery for more samples.

Availability

Two Step Back Cellular Automata and Two Step Back Extended Cellular Automata are now new modes in Visions of Chaos.

Jason.

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