Turing pattern with proportion preservation

Turing pattern with proportion preservation.

Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant. It fails to preserve the proportionality of the pattern, i.e. the ratio of the wavelength to the size, that is often required in biological morphogenesis. To get over this problem, we sh...

Turing pattern outside of the Turing domain

There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution. We consider the case where both solution types may be possible. This leads to a refinement of the Tu...

Turing Pattern Formation without Diffusion

The reaction-diffusion mechanism, presented by AM Turing more than 60 years ago, is currently the most popular theoretical model explaining the biological pattern formation including the skin pattern. This theory suggested an unexpected possibility that the skin pattern is a kind of stationary wave (Turing pattern or reaction-diffusion pattern) made by the combination of reaction and diffusion....

HICAP: Hierarchical Clustering with Pattern Preservation

Chemical Turing Pattern Formation Analyses: Comparison of Theory with Experiment

The development of oneand two-dimensional Turing patterns characteristic of the chlorite-iodide-malonic acid/indicator reaction occurring in an open gel continuously fed unstirred reactor is investigated by means of various weakly nonlinear stability analyses applied to the appropriately scaled governing chlorine dioxide-iodine-malonic acid/indicator reaction-diffusion model system. Then the th...