Horizontal segregation of mono-layer granules coordinated by vertical motion.

We experimentally investigate the segregation of a binary mixture of spherical beads confined between two horizontal vertically vibrating plates. The two kinds of beads are of equal diameter and mass but have different restitution coefficients. Segregation occurs in particular ranges of vibration amplitude and frequency. We find that the collisions between beads at an angle to the horizontal plane induce an effective horizontal repulsive force. When one or both bead types bounce up and down in synchronization, the effective repulsive force between the two types of beads is likely to be larger than that found within a single bead type, resulting in the mixture segregating. Non-horizontal collisions also play a role in stabilizing the segregation state by transferring the horizontal kinetic energy back into vertical motion.

Two-stage Turing model for generating pigment patterns on the leopard and the jaguar.

Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we construct a Turing reaction-diffusion model which generates spot patterns initially. Starting from this spotted pattern, we successfully generate patterns of adult leopards and jaguars by tuning parameters of the model in the subsequent phase of patterning.

Turing model for the patterns of lady beetles.

We simulate the patterns on the hard wings of lady beetles using a reaction-diffusion equation based on the Turing model. A part of a spherical surface is used to approximate the geometry of the hard wings. Various patterns common to lady beetles in Taiwan can be produced on this curved surface by adjusting the parameters of the model.