# Patterns and Entropy

Our next foray into systems theory involves the definitions of patterns and the study of entropy (in the information-theoretical sense). Don’t worry too much about the math, I’m going to be working with a simple intuitive version for the most part, although if you have a background in computers or mathematics there are plenty of neat nooks and crannies to explore.

For a starting point, I will selectively quote Wikipedia’s opening paragraph on patterns (at time of writing):

A pattern, …is a discernible regularity… As such, the elements of a pattern repeat in a predictable manner.

I’ve snipped out the irrelevant bits, so the above definition is relatively meaty and covers the important points. First, a pattern is a discernible regularity. What does that mean? Well, unfortunately not a whole lot really, unless you’re hot on the concept of automata theory and recognizability. But it really doesn’t matter, since your intuitive concept of a pattern neatly covers all of the relevant facts for our purposes.

But what does this have to do with systems theory? Well, consider our reliable example, Conway’s Game of Life. A pattern in Life is a fairly obvious thing: a big long line of living cells is a pattern for example. This brings us to the second part of the above quote: the elements of a pattern repeat. This should be obvious from the example. Of course you can have other patterns in Life; a checkerboard grid is another obvious pattern, and the relatively famous glider is also a pattern.

It seems, on review, that I am doing a poor job of explaining patterns, however I will leave the above for lack of any better ideas at the moment. Just rest comfortable that your intuitive knowledge of what a pattern is should be sufficient.

For the more mathematically inclined, a pattern can be more usefully defined in terms of its information-theoretical entropy (also known as Shannon entropy after its inventor Claude Shannon). Technically anything that is at all non-random (aka predictable) is a pattern, though usually we are interested in patterns of particularly low entropy.

Apologies, this has ended up rather incoherent. Hopefully next post will be better. Reading the links may help, if you’re into that sort of thing.