Getting Started with Turing Systems
If you want to find out more about Turing systems, this is the place to start. Here I have gathered some popular level material that I have written myself (unfortunately available only in Finnish) complemented by material for an exercise that I have prepared earlier for a graduate level course, some recommended literature and external links.
Popular articles
- My article "Matemaatikko selätti seepran raidat" published in the Finnish Tiede magazine aimed at the general public provides a popular level description of the challenges of computational biology in context of Turing systems. [Näytä tämä artikkeli]
- My article "Matemaatikko luonnonilmiöiden jäljillä" published in the Finnish Arkhimedes magazine aimed at professionals working in natural sciences provides a popular level introduction to the Turing systems. [Lataa tämä artikkeli]
Popular presentations
- My Lectio Praecursoria titled "Kuvionmuodostus biologisissa systeemeissä" that I presented in the public defense on my dissertation on 27th of November 2004 provides a descriptive popular level introduction to the field of pattern formation, biological systems and Turing patterns. [Lataa tämä esitelmä]
Exercise material
- In this exercise I have prepared for graduate students, you first carry out an mathematical analysis of the Brusselator Turing model by following step by step instructions and then confirm your calculations by completing and running a numerical simulation program (in C). [Download instructions] [Download code]
Recommended literature
- My doctoral thesis acts as good starting point for three reasons: 1) It is the newest one of few monographs concentrating on Turing systems and ties together the present knowledge, 2) The adopted perspective is holistic (not specific to biology, chemistry or mathematics as many other), 3) Presentation style is pedagogical and gradually advancing so one can easily start from the beginning and decide when to stop. [View the thesis]
- Philip Ball has written an excellent book "The self-made tapestry: Pattern formation in nature" (Oxford University Press, Oxford, 2001). The content is written in mostly on popular level, but the book beautifully avoids all the pitfalls of an over-simplifying coffee table book and exhaustively introduces all the details of different natural systems exhibiting pattern formation phenomena. [Amazon]
- James D. Murray has written the two bibles of mathematical biology, namely "Mathematical Biology" (Springer-Verlag, Berlin, 1993) and "Mathematical Biology II: Spatial models and biomedical applications" (Springer-Verlag, Berlin, 2003). These books provide a graduate level introduction to mathematical biology. The Turing system specific content is limited to less than a hundred pages, but the basics are explained and positioned to the field extremely well. [Amazon] [Amazon]
- MIT professor Steven Strogatz's book "Nonlinear Dynamics and Chaos" (Perseus, USA, 1994) is a show-off of his outstanding pedagogical skills. This book does not mention Turing systems, but nonlinear dynamics and its mathematical methods that are described in this book with help of numerous examples and exercises provide the foundation for the study of Turing systems. [Amazon]
- Turing pattern formation is closely related to non-equilibirium physics, which is a field not for the faint of heart. Should you want to dive into the secrets of non-equilibrium physics, you should start from the 260-paged monster article "Pattern Formation Outside of Equilibrium" by M. C. Cross and P. C. Hohenberg (1993) or the Nobel Prize work summarizing book "Self-Organisation in Non-Equilibrium Chemical Systems" by G. Nicolis and I. Prigogine (1977). [View online] [Amazon]