Solving iterated functions using genetic programming

An iterated function f(x) is a function that when composed with itself, produces a given expression f(f(x))=g(x). Iterated functions are essential constructs in fractal theory and dynamical systems, but few analysis techniques exist for solving them analytically. Here we propose using genetic programming to find analytical solutions to iterated functions of arbitrary form. We demonstrate this technique on the notoriously hard iterated function problem of finding f(x) such that f(f(x))=x2

• Type: Journal
• Year: 2009
• Where: GECCO
• Authors: Michael D. Schmidt, Hod Lipson
• Keywords: GECCO 2009, Genetic Programming, Iterated Function Problem, Iterated Functions, Optimization