The reaction–diffusion system is one of the most studied nonlinear mechanisms that
generate spatially periodic structures autonomous. On the basis of many mathematical …

There are several theoretical mechanisms that are able to generate spatial patterns
autonomously without any pre-pattern. 1, 2 Among them, the most plausible in the biological …

Skin patterns are the first example of the existence of Turing patterns in living organisms.
Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the …

For many years Turing systems have beenproposed to account for spatial and
spatiotemporal pattern formationin chemistry and biology. We extend the study of Turing …

More than half a century ago, Alan Turing postulated that pigment patterns may arise from a
mechanism that could be mathematically modeled based on the diffusion of two substances …

Current interest in pattern formation can be traced to a seminal paper by Turing, who
demonstrated that a system of reacting and diffusing chemicals, called morphogens, can …

Pigment patterns of organisms have invoked strong interest from not only biologists but also,
scientists in many other fields. Zebrafish is a useful model animal for studying the …

Zebrafish have distinctive black stripes and yellow interstripes that form owing to the
interaction of different pigment cells. We present a two-population agent-based model for the …

Pigment cells in zebrafish− melanophores, iridophores, and xanthophores− originate from
neural crest‐derived stem cells associated with the dorsal root ganglia of the peripheral …

How periodic patterns are generated is an open question. A number of mechanisms have
been proposed–most famously, Turing's reaction-diffusion model. However, many …