Mathematics

L-systems, formal grammars, and trees that don’t know they’re trees.

Here is a theorem that sounds too beautiful to be true: if you take a map and lay it on top of the territory it represents, there is always exactly one point on the map that sits directly over the point it represents. The map-point and the territory-point are the same point. Brouwer proved this in 1910 — any continuous function from a compact convex set to itself has at least one fixed point. A point where f(x) = x. A point that the function leaves exactly where it found it. ...