We investigate the sequence of patterns generated by a reaction–diffusion system on a
growing domain. We derive a general evolution equation to incorporate domain growth in
reaction–diffusion models and consider the case of slow and isotropic domain growth in one
spatial dimension. We use a self-similarity argument to predict a frequency-doubling
sequence of patterns for exponential domain growth and we find numerically that frequency-
doubling is realized for a finite range of exponential growth rate. We consider pattern …