Biological Pattern Formation

This page contains information and links to publications arising from Edmund Crampin’s doctoral thesis work on Reaction-Diffusion Pattern Formation on Growing Domains.

In this work we formulated the reaction-diffusion model for Turing pattern formation taking place while the underlying domain is growing, showing that for slow domain growth a robust sequence of patterns is generated.


Download a copy of my DPhil Thesis:

EJ Crampin – DPhil thesis 2000

Cite as:

E.J. Crampin
Reaction-diffusion patterns on growing domains
DPhil Thesis (2000)
University of Oxford

Please note that the thesis has been recompiled and so page numbers and formatting may differ from the original submitted thesis.


The following papers describe work arising from the thesis:

E.J. Crampin, Gaffney E.A., Maini P.K. (1999)
Reaction and diffusion on growing domains: Scenarios for robust pattern formation.
Bulletin of Mathematical Biology 61 (6), 1093

E.J. Crampin, Maini P.K. (2001)
Modelling biological pattern formation: The role of domain growth.
Comments on Theoretical Biology 6 (3), 229-249

E.J. Crampin, Maini P.K. (2001)
Reaction-diffusion models for biological pattern formation.
Methods and Applications of Analysis 8 (3), 415-428

E.J. Crampin, Gaffney E.A., Maini P.K. (2002)
Mode doubling and tripling in reaction-diffusion patterns on growing domains: A piecewise linear model.
Journal of Mathematical Biology 44 107-128

E.J. Crampin, Hackborn W.W., Maini P.K. (2002)
Pattern formation in reaction-diffusion models with nonuniform domain growth.
Bulletin of Mathematical Biology 64 (4), 747-769

Maini P.K., E.J. Crampin, Madzvamuse A., Wathen A.J., Thomas R.D.K. (2003)
Implications of domain growth in morphogenesis;
in Mathematical Modelling & Computing in Biology and Medicine, Proceedings 5th ECMTB Conference (V. Cappasso, Ed.), 67-73

Barrass I., E.J. Crampin, Maini P.K. (2006)
Mode transitions in a model reaction-diffusion system driven by domain growth and noise.
Bulletin of Mathematical Biology 68 (5), 981-995