Biological patterns generated during development and regeneration often scale with organism size. Some organisms e.g. flatworms can regenerate a re-scaled body plan from tissue fragments of varying sizes. Inspired by these examples, we introduce a generalization of Turing patterns that is both self-organized and self-scaling. We couple a Turing instability to the reaction kinetics of diffusing expander molecules. Our model identifies minimal requirements for robust, self-scaling pattern formation and captures essential features of body plan regeneration in flatworms as observed in experiments.