Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Niching methods for genetic algorithms
Niching methods for genetic algorithms
Multi-Objective Methods for Tree Size Control
Genetic Programming and Evolvable Machines
Comparison of tree and graph encodings as function of problem complexity
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Machine Graphics & Vision International Journal
Coevolution of Fitness Predictors
IEEE Transactions on Evolutionary Computation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Human-competitive results produced by genetic programming
Genetic Programming and Evolvable Machines
Grammar-based immune programming
Natural Computing: an international journal
A GPU-based implementation of an enhanced GEP algorithm
Proceedings of the 14th annual conference on Genetic and evolutionary computation
| Hi-index | 0.00 |
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--2. While some analytical techniques have been developed to find a specific solution to problems of this form, we show that it can be readily solved using genetic programming without recourse to deep mathematical insight. We find a previously unknown solution to this problem, suggesting that genetic programming may be an essential tool for finding solutions to arbitrary iterated functions.