In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying
the foundations of morphogenesis as a self-organized process emerging from …

Vertebrates exhibit a wide range of color patterns, which play critical roles in mediating intra-
and interspecific communication. Because of their diversity and visual accessibility, color …

This paper investigates the pattern dynamics of a harvested predator–prey model with no-
flux boundary conditions. Firstly, we analyze the positive equilibrium types of the local …

Throughout developmental biology and ecology, transport can be driven by nonlocal
interactions. Examples include cells that migrate based on contact with pseudopodia …

Neotropical cichlids demonstrate an enormous diversity of pigment patterns, a
morphological trait that plays an important role in adaptation and speciation. It has been …

Elucidating pattern forming processes is an important problem in the physical, chemical and
biological sciences. Turing's contribution, after being initially neglected, eventually catalysed …

Neuron modelling helps to understand the brain behavior through the interaction between
neurons, but its mechanism remains unclear. In this paper, the spatiotemporal patterns is …

As a classical activator-inhibitor system with diffusion effects, the Gierer–Meinhardt (GM)
model has received a considerable attention in recent years. Discussions on dynamic …

This is a brief account of Turing's ideas on biological pattern and the events that led to their
wider acceptance by biologists as a valid way to investigate developmental pattern, and of …

Highlights•Synthetic biologists engineer spatial patterns in microbial populations.•Different
inputs and processes may be combined to generate different patterns.•This approach …