Cellular Automata

A few days back I stumbled on this:

This image was generated via simulation. Here is how it happens: row by row, starting at the top, the next row will be entirely defined by the previous row, according to a rule. In the image we see rule 30 in action, it’s defined as:

00011110

What is this? Well, this is a byte of value 30. This byte also defines if a point will be black (or “alive”) or white (or “dead”) based on the state of the point right above it (previous row) and the states of the two flanking points of that previous row point.

The initial state of the simulation, in this case, was a black cell (has a value of 1) right in the middle of row zero (top row). If we are on a space with 100 columns, the middle one for the starting state is col 50. Starting our simulation, the new row at column zero has a value of zero: cell at top left of this point does not exist at index -1 so we have zero, cell at the top has a value of zero, and top right cell is zero again, so back to the our Rule 30 table the 000 value transaltes as 0 for this new cell. In the same way, the cell at new row & column 50 has a value of 1 (from 010 at rule defs).

What makes this fascinating is that by following the simple rule row by row, the simulation creates what seems is pure chaos as we see on the patterns that emerge in the middle/bottom section of Rule 30’s simulation image. In other words, the complex image that requires a lot of information to store can be represented in its entirety by knowing the base rule and iterating over it. This informational asymmetry exhibited by celular automata was even subject of research into the field of cryptography in the 80’s and 90’s, but seems it had gone nowhere (yet) as the scientific paper world have not heard about crypto-cell-automata in the past two decades.

Also, this pattern of simple rules yelding complex structures resembles living organisms. Structures like the brain and eyes are overwhelmingly complex, yet the number of genes responsible for building them are comparatively limited. “Cellular automata” wasn’t named only after the cells of the matrix that holds the simulation, after all :3

A new kind of science

Cellular automata are described by Stephen Wolfram in his book “A New Kind of Science”, where he explains the simple aspect of the technology and underlying discussion about their computing power, in a way that is almost philosophical.

Of course there is more to it than what says this barebones blog post (cited book has over 1K pages). So I should cover more of it in the next!

More information:

https://plato.stanford.edu/entries/cellular-automata/ https://en.wikipedia.org/wiki/Rule_30