Interactive evolution of equations for procedural models

This paper describes how the evolutionary mechanisms of variation and selection can be used to “evolve” complex equations used by procedural models for computer graphics and animation. An interactive process between the user and the computer allows the user to guide evolving equations by observing results and providing aesthetic information at each step of the process. The computer automatically generates random mutations of equations and combinations between equations to create new generations of results. This repeated interaction between user and computer allows the user to search hyperspaces of posible equations without being required to design the equations by hand or even understand them. Three examples of these techniques have been implemented and are described: procedurally generated pictures and textures, three-dimensional shapes represented by parametric equations, and two-dimensional dynamical systems described by sets of differential equations. It is proposed that these methods have potential as powerful tools for exploring procedural models and achieving flexible complexity with a minimum of user input and knowledge of details.