certain kinds of loss of randomness are prevented—sometimes by explicit suspension of trading.

But why is there randomness in markets in the first place?

Practical experience suggests that particularly on short timescales much of the randomness that one sees is purely a consequence of internal dynamics in the market, and has little if anything to do with the nature or value of what is being traded.

So how can one understand what is going on? One needs a basic model for the operation and interaction of a large number of entities in a market. But traditional mathematics, with its emphasis on reducing everything to a small number of continuous numerical functions, has rather little to offer along these lines.

The idea of thinking in terms of programs seems, however, much more promising. Indeed, as a first approximation one can imagine that much as in a cellular automaton entities in a market could follow simple rules based on the behavior of other entities.

To be at all realistic one would have to set up an elaborate network to represent the flow of information between different entities. And one would have to assign fairly complicated rules to each entity—certainly as complicated as the rules in a typical programmed trading system. But from what we have learned in this book it seems likely that this kind of complexity in the underlying structure of the system will not have a crucial effect on its overall behavior.

And so as a minimal idealization one can for example try viewing a market as being like a simple one-dimensional cellular automaton. Each cell then corresponds to a single trading entity, and the color of the cell at a particular step specifies whether that entity chooses to buy or sell at that step. One can imagine all sorts of schemes by which such colors could be updated. But as a very simple idealization of the way that information flows in a market, one can, for example, take each color to be given by a fixed rule that is based on each entity looking at the actions of its neighbors on the previous step.

With traditional intuition one would assume that such a simple model must have extremely simple behavior, and certainly nothing like what is seen in a real market. But as we have discovered in this book,