Cellular Automata and Biological Pattern Formation Modelling Characterization, Examples, and Analysis

About this book

Cellular Automata and Biological Pattern Formation Modelling focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models.While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. Cellular Automata and Biological Pattern Formation Modelling is divided into three parts: Part I deals with general principles, theories, and models of pattern formation; Part II examines cellular automaton modeling; and Part III explains various applications. The models and analytic techniques described may be extended to other exciting applications in biology, medicine, and immunology.

Contents

- Introduction and Outline
- On the Origin of Patterns
- Mathematical Modeling of Biological Pattern Formation
- Cellular Automata
- Random Movement
- Growth Processes
- Adhesive Cell Interaction
- Alignment and Cellular Swarming
- Pigment Cell Pattern Formation
- Tissue and Tumor Development
- Turing Patterns and Excitable Media
- Discussion and Outlook

Appendix A. Growth Processes: A Mean-Field Equation
Appendix B. Turing Patterns
Appendix C. Excitable Media: Complete Interaction Rule
Appendix D. Isotropy, Lattices, and Tensors

References
Index

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