1. Texture Synthesis Using Reaction-Diffusion Systems and Genetic Evolution Joseph Zumpella, Andrew Thall, Department of Computer Science, Allegheny College zumpellaj@aol.com, athall@allegheny.edu A genetic algorithm was used with an observer-based fitness function to explore the parameter spaces of reaction-diffusion (RD) systems for the purpose of aesthetic image-texture generation. By combining a biochemically based method of image generation with a biologically based method to create and cull populations of such images, image-evolution can be guided by a user in novel directions. While the genetic signature of each system was severe, restricting the diversity of evolved images, the basic algorithm proved sound and the method holds promise for extending the system to evolve new RD systems rather than simply alter parameters of existing ones. METHODS SUMMARY Reaction-Diffusion Systems Reaction-diffusion was first proposed as a mechanism for biological pattern formation by Turing [4]. Further work with more elaborate chemical systems was by Meinhardt [2]. RD systems were first used in computer graphics for texture synthesis by Turk [5] and by Witkin and Kass [6]. Simulated chemicals have concentrations that vary across a grid of cells; they diffuse across the grid and react with one another until equilibrium is reached or the reaction is halted. The cells are colored according to the concentrations of each chemical. Genetic Selection for RD-systems Genetic algorithms have been used for image generation for many years, beginning with Sims [3] and including recent work by Lewis [1]. Our work explored the parameter space of RD systems, based on Turk’s code for spot- or stripe-generation. Our genotype for the spot RD system consisted of six genes:, where i specified the number of iterations to perform. The ranges over which the genes might vary were tuned by hand to include extreme values bordering chaotic or flat- field images. Cross-over and Mutation Operations The software allows cross-over variation by selecting either two or three images from the tableau of nine in a given generation. Crossover is effected by either averaging or copying of genes between parents. Mutation can be done in two ways: across an entire generation randomly over the entire gene-set; based on mutating a single member of the population using specified genes to create a new 9-image tableau. Interface for User-based Fitness Selection The interface allows a user to select a reaction-diffusion system, generating a set of 9 initial images from either a spot or stripe system, and then perform cross-over or mutation based on selection from among the generated images. RESULTS Examples from Stripe-evolving Systems Examples from Spot-evolving Systems The system was tested by volunteers who were given a brief introduction to the interface and to the cross-over and mutation operators. Evolutionary search is an effective choice for parametric exploration of the space of RD-texture systems, which are characterized by high interdependence between system parameters and by discontinuities in the image- function vis-à-vis stable and serendipitously discovered texture patterns. Improvements to current system: Greater sensitivity in specification of mutations Improvements to the user-interface allowing maintenance of a larger gene-pool and selection over multiple generations. Alternative color-space mapping (HVS spaces rather than RGB) or chemically based pigment models for blending colors based on cell-concentrations Algorithmic and hardware acceleration of the RD computations Promising extensions of this work: Genetic selection creating new reaction-diffusion systems, for evolutionary creation of systems between and beyond the simple three or five chemical models. Anisotropic pattern formation in the genetic variation and evolution of surface displacements, as per Witkin and Kass. Goal-directed image-evolution with human or automatic fitness functions. DISCUSSION [1] Lewis, M. (2001) Creating Continuous Design Spaces for Interactive Genetic Algorithms with Layered, Correlated Pattern Functions. Ph.D. thesis, Ohio State University. [2] Meinhardt, H. (1982) Models of Biological Pattern Formation, Academic Press. [3] Sims, K. (1991) Artificial evolution for computer graphics. In Proceedings of the 18 th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press, SIGGRAPH 91, 319- 328. [4] Turing, A.M. (1952) The chemical basis of morphogenesis. Phil. Trans. Royal Soc. of London Series B: Biological Sciences, 237, 37-72. [5] Turk, G. (1991) Generating textures on arbitrary surfaces using reaction-diffusion. In Proceedings of the 18 th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press, SIGGRAPH 91, 289-298. [6] Witkin, A. and Kass, M. (1991) Reaction-diffusion textures. In Proceedings of the 18 th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press, SIGGRAPH 91, 299- 308. [7] Zumpella, J. (2004) Texture Synthesis Using Reaction-Diffusion Systems and Genetic Evolution. Senior thesis, Allegheny College, Dept. of Computer Science, Tech Report CS04-16, available at http://cs.allegheny.edu/~thall/papers. References SIGGRAPH 2004 Turing’s two-chemical RD system, discretized for a regular grid, is useful for forming spotted patterns [5]. Meinhardt’s five-chemical RD system, is useful for forming striped patterns [5]. In early trials with the grey-scale version of the program, one volunteer had a liking for biological-appearing “bacterial” patterns. Note the brittleness of interesting patterns; in the genetic neighborhood of an interesting pattern, nearby ones often evolve to flat fields or simple repetitive patterns. Images showing new generations of spot (left) and stripe (right) patterns after several cross-over operations.