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Natural ComplexityA Modeling Handbook$
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Paul Charbonneau

Print publication date: 2017

Print ISBN-13: 9780691176840

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691176840.001.0001

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Pattern Formation

Pattern Formation

(p.249) 11 Pattern Formation
Natural Complexity

Paul Charbonneau

Princeton University Press

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.

Keywords:   pattern formation, excitable system, spatiotemporal pattern, hodgepodge machine, Python code, waves, spiral, spaghetti, cells

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