This chapter examines the complex nature of pattern formation in excitable systems. Many physical, chemical, and biological systems are considered excitable, in which two “components” interact in such a way as to alter each other's state through (nonlinear) processes of inhibition or amplification. Starting from a homogeneous rest state, many systems of this type can spontaneously generate persistent spatiotemporal patterns when subjected to some perturbation. After providing an overview of excitable systems, the chapter discusses the hodgepodge machine and its numerical implementation in the Python code. It then describes four spatial patterns generated by the hodgepodge machine, namely: waves, spirals, spaghettis, and cells. It also explains the spontaneous formation of spatiotemporal patterns. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.
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