Biological patterns generated during development and regeneration often scale
with organism size. Some organisms, e.g., flatworms, can regenerate a rescaled
body plan from tissue fragments of varying sizes. Inspired by these examples,
we introduce a generalization of Turing patterns that is self-organized and
self-scaling. A feedback loop involving diffusing expander molecules regulates
the reaction rates of a Turing system, thereby adjusting pattern length scales
proportional to system size. Our model captures essential features of body plan
regeneration in flatworms as observed in experiments.Comment: 5 pages, 3 color figure
