Turing Reaction-Diffusion -- a World in a Grain of Sand
Alyn Rockwood, Irene Gironacci

Hyperseeing: Proceedings of Shape Creation Using Layouts, Programs, & Technology (SCULPT) 2022
Pages 59–64
Short Papers


Turing reaction-diffusion forms the basis for a multi-media, multi-technology approach to capture the mathematical/biological essence of morphogenesis in sculpture. The 2D Kassam algorithm for solving the differential equations defining reaction-diffusion is generalized to 3D. A carefully chosen threshold then generates a compelling isosurface that is polygonalized for 3D printing. Other steps in the process are: 1) Using Fourier filtering to eliminate distracting and poorly reproducible high frequency components, 2) Capping the isosurfaces within the physical printing range while maintaining a solid manifold object for manufacture, 3) Printing the polygon model in plastic and removing support struts, 4) Handcrafting extrapolations to the caps with modeling clay, while preserving tangent plane continuity to the original 3D print, and 5) Finishing aesthetic details by sanding and painting. The resulting sculpture possesses a pleasing visual flow, geometric consistency, tactile appeal, and a nooks and crannies element of discovery. On a deeper level, it evokes awe for Turing's proposed mechanism of biological development and diversity.