Int. J. Dev. Biol. 53: 673 - 681 (2009)
doi: 10.1387/ijdb.072484vv
© UBC Press

Pattern formation mechanisms in reaction-diffusion systems

Vladimir K. Vanag and Irving R. Epstein*

Department of Chemistry and Volen Center for Complex Systems, Brandeis University, Waltham, MA, USA

ABSTRACT In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about pattern formation, with possible insights into biologically relevant phenomena. We present experimental examples and discuss several mechanisms by which such spatiotemporal structure may arise, classifying the mechanisms according to the type of instability that results in pattern formation. In some systems, the pattern that emerges depends not only on the chemical and physical parameters but also on the initial state of the system. Interactions between instabilities can result in particularly complex patterns.

Keywords:

pattern formation, reaction-diffusion, chemical kinetics, Turing pattern, wave instability

*Corresponding author e-mail: epstein@brandeis.edu