Matpic
mathematics, in pictures
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Small rules, large behaviour — page 2

Rules short enough to write on one line, producing behaviour nobody can summarise — and the finding that the size of a rule predicts nothing about the difficulty of the questions it raises.
A population that settles at 2/3. A contest over a prize worth 4 that costs 6 to fight for. Left: the growth rate of the share playing Hawk against that share, which is nought at 0, at 2/3 and at 1. Right: the share over time from 5 starting points, all converging on 2/3. Applied

A mixture that is a population

A mixed equilibrium between two choosers is a knife-edge nobody has a reason to stand on. Read the same mixture as a population whose shares grow with how well they do, and it becomes a point every population is carried to — or one every population circles for ever without arriving.

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