  Boundary-induced pattern formation from a spatially uniform state is
investigated using one-dimensional reaction-diffusion equations. The temporal
oscillation is successively transformed into a spatially periodic 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 generality of the pattern selection process
and algorithm is discussed with possible relevance to biological morphogenesis.
