Yeah, this is one of Wolfram's "elementary cellular automata". This is "rule 30". It's actually a one-dimensional cellular automata. Only neighbors to the left and right are considered. The Y axis represent time / generations / iterations.

So there are 256 possible rules. Each represented by an 8-bit unsigned integer in ASCII format.

The "scenarios" are statically defined like this:

| 111 | 110 | 101 | 100 | 011 | 010 | 001 | 000 | 

And we can use a binary number like this to map scenario outcomes to create a rule set.

0 	1 	1 	0 	1 	1 	1 	0

Where each bit describes the outcome of the scenario.

So if all neighbors are alive (111) the next generation is dead (0). If the left neighbor is alive but right is not (110) the next generation is alive (1).

I'm improving my software and I think some of the changes I've made can make the simulation more clear and also more aesthetic.

In these images, up arrows are alive cells and down arrows are dead cells. I also included 2 images with the "links" feature enabled that shows the links between alive and dead cells across generations.

Bonus (this just looks cool):

Weird, rule 34 always looks something like this for me...

I guess you could say that. I wrote the software that generated the image. Just a small generative art project I'm working on.