[JadeNB]

As a mathematician but not a statistician or probabilist (so very much not an expert here), this:

> When we look at this it can sometimes seem as if there is a pattern emerging from the behaviour. However, if you feel like you can see such a pattern it is entirely coincidental, since the nodes are completely unaware of each other.

bothered me. It seems to me that the fact that patterns can emerge from non-coördinated behaviour is one of the interesting facts about mathematics. See, for a dodgy example—because there is some coördination—firefly flash-locking; and, for a genuine example that I literally just happened to be reading about this morning, the fascinating Nobel-Prize work discussed at https://johncarlosbaez.wordpress.com/2016/10/07/kosterlitz-t... . (I encourage you to go read the latter if you haven't already; as you will expect if you have read Baez's work, it's exposition at a level just about anyone, including non-mathematicians, can probably understand of scientific Nobel-Prize work, and those don't come along very often.) I guess, though, that to make any rigorous statement that this can occur, and isn't just an illusion, one has to make a rigorous definition of 'pattern', and the implicit definition of something like "externally imposed structure" has just as much claim to being 'correct' as anything I could cook up.

[open_nsfw]

I'm pretty sure each point was rendered independently - i.e. the nodes have no interactions. So unlike flocking, they are are entirely coincidental.

[strainer]

I enjoyed the link thanks. The patterns concerned there develop out of unstable states (random or patterned) by ~preferences of the interconnecting medium. I notice two dimensional mediums were only examined and 3d may provide scope for more complex phenomenon. The apparent patterning which Hoff mentions is entirely coincidental and uncoordinated by any medium/connection between random variates. Collections of random variates are able to present seemingly unlikely relationships or artefacts which can amount to meaningful or stable forms in other contexts - as monkeys at a keyboard chancing on a few pearls of wisdom.

I have spent a while scrutinising the appearance of patterns in test plots for my random number library: http://strainer.github.io/Fdrandom.js/ and learned that they can be expected to occur to some degree. There surely must be some theoretical and philosophical investigations of chaos capacity to chance on order.