Parallel array grammars as models for the growth of planar patterns

摘要

We review the concept of growth on a discrete planar grid based on eight-neighbor time delays, and show that this process can be regarded as pattern generation by a context-sensitive isometric array grammar. We introduce a concept of growth in an environment by allowing the generation process to be influenced by a background pattern of scalar values, and illustrate how this increases the power of the model. We also demonstrate, in the domain of MR images of MS lesions, how the environment in which a growth process occurs can be recovered from an image.