Understanding Marvelous Patterns in Complex Systems

This book explores the fascinating and ubiquitous occurrence of spatial patterns and forms, generated in nature by the interplay of chemical and biological reactions with transport processes, as there are diffusion, convection, chemotaxis, or others.  Their role in our perception and in scientific investigations is immanent in the concepts of natural laws. They have the capacity to explain phenomena like self-organization in systems far away from thermodynamic equilibrium or to formulate the influence of nonlinear interactions on complexity. Just take the omnipresent waves, as they propagate in liquids with or without reactivity, act inside biological cells or become apparent in a biomedical context, as in the heart during arrhythmias or in the visual cortex, when a migraine aura is noticed. Such phenomena are prominent topics of future-oriented, and hopefully beneficial research.
Our colleagues and friends contribute to this book in presentations on the origins, mechanisms, and dynamics relevant for their special research endeavors, from earlier to actual, more complex topics. These comprise numerous scientific fields in theory, mathematics, physics and chemistry laboratories, field studies on morphogenesis and the course of biological evolution, or analysis of specific medical data, including epidemiological studies.
On the whole, the book provides a valuable source of information, while also taking the reader on an aesthetic journey through an attractive world full of color and visual adventures.

List of contents

Introduction.- A Phenomenological Overview of Structural Elements and Characteristic Shapes.- Gallery.- Dirichlet Domains: Can They Help to Extract Common Pattern Formation Mechanisms?.- Spirals in Turban Shell.- Rings versus Spirals.- Spiral and Target Patterns in Stingless Bee Combs.- Theory and Specific Methods.- Thermodynamic Principles for Nonequilibrium Chemical Systems.- Fluctuations and Stochastic Theory.- Two-Dimensional Spectrophotometry I - Pioneering Work on Visualization of Chemical Gradients.- Two-Dimensional Spectrophotometry II - Spreading of Reactive Droplets.

About the author

Stefan C. Müller is a physics professor at the University of Magdeburg, Germany. He studied physics at the University of Göttingen. After obtaining there his doctoral degree in 1978, he spent 3 years of postdoctoral research in the USA, first at MIT and then at Stanford University in California. He was a researcher at the Max-Planck-Institute in Dortmund from 1982 to 1994. Following his habilitation at the Göttingen University in 1991, he built up a research group in Magdeburg focussing his work on pattern formation and self-organization in biophysics. He is one of the editors of “Complexity and Synergetics” (Springer, 2018) and, together with Kinko Tsuji, of "Spirals and Vortices" (Springer, 2019). The most recent book written by Kinko Tsuji and himself is "Physics and Music" (Springer, 2021).
Jürgen Parisi is a physics professor at the University of Oldenburg, Germany. He started his studies at the University of Stuttgart, and received the M.S., the doctoral (1982) and the habilitation degrees (1987) from the University of Tübingen. He has worked in the Departments of Science of the Universities of Tübingen, Bayreuth, and Zürich, before transferring his research in 1995 to the Institute of Physics in Oldenburg, where he established a research group for regenerative energy systems and semiconductors. His current research includes nonlinear dynamics and self-organizing structure formation in non-equilibrium dissipative systems. Together with Joachim Peinke, Otto Rössler and Ruedi Stoop he authored „Encounter with Chaos: Self-Organized Hierarchical Complexity in Semiconductor Experiments“ (Springer, 1992) and with Stefan C. Müller „Bottom-Up Self-Organization in Supramolecular Soft Matter“ (Springer, 2015). He was co-editor of the Springer Series „Lecture Notes in Physics“, „Material Science“, and „Synergetics“.

Summary

This book explores the fascinating and ubiquitous occurrence of spatial patterns and forms, generated in nature by the interplay of chemical and biological reactions with transport processes, as there are diffusion, convection, chemotaxis, or others.  Their role in our perception and in scientific investigations is immanent in the concepts of natural laws. They have the capacity to explain phenomena like self-organization in systems far away from thermodynamic equilibrium or to formulate the influence of nonlinear interactions on complexity. Just take the omnipresent waves, as they propagate in liquids with or without reactivity, act inside biological cells or become apparent in a biomedical context, as in the heart during arrhythmias or in the visual cortex, when a migraine aura is noticed. Such phenomena are prominent topics of future-oriented, and hopefully beneficial research.
Our colleagues and friends contribute to this book in presentations on the origins, mechanisms, and dynamics relevant for their special research endeavors, from earlier to actual, more complex topics. These comprise numerous scientific fields in theory, mathematics, physics and chemistry laboratories, field studies on morphogenesis and the course of biological evolution, or analysis of specific medical data, including epidemiological studies.
On the whole, the book provides a valuable source of information, while also taking the reader on an aesthetic journey through an attractive world full of color and “visual adventures.”

Product details

• Assisted by: Stefan C Müller (Editor), Stefan C. Müller (Editor), Parisi (Editor), Jürgen Parisi (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Release: 07.03.2026
• EAN: 9783032087522
• ISBN: 978-3-0-3208752-2
• Illustrations: Approx. 220 p.
• Subjects: Natural sciences, medicine, IT, technology > Technology > General, dictionaries; Angewandte Mathematik, Kybernetik und Systemtheorie, self-organization, Applications of Mathematics, Complex systems, Mathematical and Computational Engineering Applications, Biological systems, Applied Dynamical Systems, Non-equilibrium Systems, Chemical Oscillations and Waves