Understanding Marvelous Patterns in Complex Systems

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“.

• 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.