  One possible mechanism to explain how animals got their coat patterns was
proposed by Alan Turing. He assumed that two kinds of morphogens diffuse on a
surface and interact with each other, generating a reaction-diffusion
mechanism. We developed a new framework for pattern generation incorporating a
non-diffusing transcription factor in the system. The diffusion factors (one
inhibitor and one activator) acting on cell surface receptors modulate the
activity of a transcription factor. The difference in the local concentration
of diffusion factors is translated into the degree of activation of
transcription factors. The speed of this process determines then pattern
formation velocity, i.e. the elapsed time from an initial noisy situation to a
final developed pattern. If the pattern formation velocity slows down compared
to the growth of the surface, the phenomenon of "growing surface interference"
occurs. We find that this phenomenon might explain the rosette pattern observed
on different types of felids and the pale stripes found between the regular
black stripes of zebras. We also investigate the dynamics between pattern
formation velocity and growth and to what extent a pattern may freeze on
growing domains.
