Morphogenesis is the biological process during embryonic development which gives rise to a spectrum of spatially differentiated forms. Since his seminal paper “The Chemical Basis of Morphogenesis” in 1952, Alan Turing’s reaction-diffusion theory for morphogenesis has become a foundational model for studying self-organization behavior and pattern formation in biological, chemical, and physical systems. From how the leopard gets its spots to how panic and disease spreads throughout the masses, seemingly chaotic patterns in nature can be effectively studied with reaction-diffusion theory. While the cellular mechanisms that drive pattern formation and give rise to complex hierarchical structural architectures in natural materials such as bamboo are of great abstract and applied interest, relevant computational models remain largely unexplored.

This talk provides:

(1) An introduction to reaction-diffusion theory and agent-based modeling.

(2) A review of biological pattern formation and the role of reaction-diffusion systems for morphogenesis.

(3) An implementation of two cellular models, a cellular automaton (CA) and the cellular Potts model, to simulate Turing patterns under varying inhibitor field values and cell-cell adhesion energy coefficients respectively.