Boundary-induced pattern formation from temporal oscillation: Spatial map analysis

Boundary-induced pattern formation is investigated using spatially one-dimensional, two-component reaction-diffusion equations. Temporal oscillation is successively transformed into a spatial pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern wavelength with the period of oscillation is also obtained The pattern wavelength is proportional to the period of the oscillation when the emergent pattern is periodic. The generality of the pattern selection process and algorithm is discussed with possible relevance to biological morphogenesis