Ebook: Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis

This book 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. The book 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.

Key topics and features:

* Provides an introduction and historical account of the principles of biological pattern formation (morphogenesis)
* Gives an overview of mathematical modeling approaches to morphogenesis, and an introduction to cellular automata and analytic techniques
* A supplementary web-based Java applet---Cellular Automaton Simulator---enables interactive simulation of various cellular automaton applications described in the book; available on the internet at www.biomodeling.info
* Self-contained presentation is accessible to a broad audience; only basic calculus and linear algebra are required
* Careful balance of theory, models, and applications useful to both experimentalists and theoreticians
* Includes suggestions for further research topics

The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling. The book's accessible presentation and interdisciplinary approach make it suitable for graduate and advanced undergraduate courses and seminars in mathematical biology, biomodeling, and biocomputing.

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This book 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. The book 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.

 

Key topics and features:

 

* Provides an introduction and historical account of the principles of biological pattern formation (morphogenesis)
* Gives an overview of mathematical modeling approaches to morphogenesis, and an introduction to cellular automata and analytic techniques
* A supplementary web-based Java applet---Cellular Automaton Simulator---enables interactive simulation of various cellular automaton applications described in the book; available on the internet at www.biomodeling.info
* Self-contained presentation is accessible to a broad audience; only basic calculus and linear algebra are required
* Careful balance of theory, models, and applications useful to both experimentalists and theoreticians
* Includes suggestions for further research topics

 

The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling. The book's accessible presentation and interdisciplinary approach make it suitable for graduate and advanced undergraduate courses and seminars in mathematical biology, biomodeling, and biocomputing.

---

This book 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. The book 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.

 

Key topics and features:

 

* Provides an introduction and historical account of the principles of biological pattern formation (morphogenesis)
* Gives an overview of mathematical modeling approaches to morphogenesis, and an introduction to cellular automata and analytic techniques
* A supplementary web-based Java applet---Cellular Automaton Simulator---enables interactive simulation of various cellular automaton applications described in the book; available on the internet at www.biomodeling.info
* Self-contained presentation is accessible to a broad audience; only basic calculus and linear algebra are required
* Careful balance of theory, models, and applications useful to both experimentalists and theoreticians
* Includes suggestions for further research topics

 

The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling. The book's accessible presentation and interdisciplinary approach make it suitable for graduate and advanced undergraduate courses and seminars in mathematical biology, biomodeling, and biocomputing.

Content:
Front Matter....Pages i-xxv
Front Matter....Pages 1-1
Introduction and Outline....Pages 3-11
On the Origin of Patterns....Pages 13-43
Mathematical Modeling of Biological Pattern Formation....Pages 45-56
Front Matter....Pages 57-57
Cellular Automata....Pages 59-101
Front Matter....Pages 103-103
Random Movement....Pages 105-128
Growth Processes....Pages 129-142
Adhesive Cell Interaction....Pages 143-159
Alignment and Cellular Swarming....Pages 161-172
Pigment Cell Pattern Formation....Pages 173-183
Tissue and Tumor Development....Pages 185-206
Turing Patterns and Excitable Media....Pages 207-256
Discussion and Outlook....Pages 257-278
Back Matter....Pages 279-331

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This book 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. The book 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.

 

Key topics and features:

 

* Provides an introduction and historical account of the principles of biological pattern formation (morphogenesis)
* Gives an overview of mathematical modeling approaches to morphogenesis, and an introduction to cellular automata and analytic techniques
* A supplementary web-based Java applet---Cellular Automaton Simulator---enables interactive simulation of various cellular automaton applications described in the book; available on the internet at www.biomodeling.info
* Self-contained presentation is accessible to a broad audience; only basic calculus and linear algebra are required
* Careful balance of theory, models, and applications useful to both experimentalists and theoreticians
* Includes suggestions for further research topics

 

The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling. The book's accessible presentation and interdisciplinary approach make it suitable for graduate and advanced undergraduate courses and seminars in mathematical biology, biomodeling, and biocomputing.

Content:
Front Matter....Pages i-xxv
Front Matter....Pages 1-1
Introduction and Outline....Pages 3-11
On the Origin of Patterns....Pages 13-43
Mathematical Modeling of Biological Pattern Formation....Pages 45-56
Front Matter....Pages 57-57
Cellular Automata....Pages 59-101
Front Matter....Pages 103-103
Random Movement....Pages 105-128
Growth Processes....Pages 129-142
Adhesive Cell Interaction....Pages 143-159
Alignment and Cellular Swarming....Pages 161-172
Pigment Cell Pattern Formation....Pages 173-183
Tissue and Tumor Development....Pages 185-206
Turing Patterns and Excitable Media....Pages 207-256
Discussion and Outlook....Pages 257-278
Back Matter....Pages 279-331
....