Here's a pic of a seashell I picked up at an oceanside tourist shop for 75 cents. No, the design isn't painted on the shell! That's how they grow - it looks either like a common 1-D cellular automata, or like Sierpinski's Triangle. An amazing illustration, IMHO, of CAs in real life.

Like everyone, I was introduced to CAs via Conway's "Life" - a fascinating 2D CA operating on a square grid. I wrote the usual assortment of programs: display, glider-finders, oscillator-finders, etc. Then, I started to get interested in varying the rules of the CA, varying the number of states, and even varying the grid (to triangular or hexagonal). Some of these results and programs will be presented here; none of it is new, but it is all cool.

Here is a text-file link to some life results with alternate rules. Open it with some app that allows you to specify a fixed-width font, or it won't make any sense.

Program for 3-state life

Here's the idea: Instead of each cell being off (zero) or on (one), there is a third state with a cell value of two. The cell value (0, 1, or 2) is added to the neighbor count, and transition rules are defined in a general way so that

cell_new_state = f(neighbor_count, cell_old_state)

A configuration file used by this program allows for any possible transition function.

Here's the program, a Windows 3.1 executable.

Here's a configuration used by the program. Put it in the same directory as the executable, and rename it "life.cfg". After you've tried that, check out these as well:

Config #1 Config #2 Config #3

There is so much that can be done with this program, and I've just scratched the surface. If you come up with an interesting config file, email it to me.

Alternate rule set life-forms

The following are some common life forms for alternate rule sets. The 4 digit number in the title of each picture gives the rule, in the form: <b1><b2><l1><l2>. The number next to each life form is its period if it is an oscillator.

b1,b2: "birth" numbers. An OFF cell having a neighbor count of b1 or b2 will become ON in the next generation.

l1,l2: "life" numbers. An ON cell having a neighbor count of l1 or l2 will remain ON in the next generation, otherwise it turns off.

These numbers do not specify a range. For example, in the picture at left, the "life" numbers are 3 and 5, but not 4. Traditional Conway Life would be denoted with the rule set 2333.

Conway definitely discovered the best 2D square grid 2-state rule set, but some of the alternate ones are OK as well. An outstanding one, not (yet!) pictured here, is 3422 on a hexagonal grid.

The rule set 333h is interpreted: Birth: 3 Life: 3 and higher