Agent-Based Models (Part 13)

Azimuth 2024-07-24

Our 6-week Edinburgh meeting for creating category-based software for agent-based models is done, yet my collaborators are still busy improving and expanding this software. I want to say more about how it works. I have a lot of catching up to do!

Today I mainly want to announce that Kris Brown has made a great page explaining our software through a working example:

Conway’s Game of Life.

His explanation uses an idea interesting in its own right: ‘literate programming’, where the code is not merely documented, but worked into a clear explanation of the code in plain English. I would copy it all onto this blog, but that’s not extremely easy—so just go there!

His explanation is a good alternative or supplement to mine. This is how my explanation went:

Part 9: The theory of ‘stochastic C-set rewriting systems’. This is our framework for describing agents using somewhat general but still simple data structures that randomly change state at discrete moments in time.

Part 10: Here I describe a choice of category C suitable for the Game of Life. For this choice, C-sets describe living and dead cells, and the edges connecting them.

Part 11: Here I explain stochastic C-set rewrite rules that describe time evolution in the Game of Life.

Part 12: Here I describe the formalism of ‘attributed C-sets’. In the Game of Life we merely use these a way to assign coordinates to cells: they don’t affect the running of the game, only how we display it. But in other agent-based models they become much more important: for example, some agents might have a ‘weight’ or ‘height’ or other quantitative information attached to them, which may change with time, and these are treated as ‘attributes’.

So, there’s plenty you can read about our approach to the Game of Life.

But as I mentioned before, the Game of Life is a very degenerate example of a stochastic C-set rewriting system, because it’s actually deterministic! What if we want a truly stochastic example?

It’s easy. I’ll talk about that next time.