Applying a slow annealing procedure, we have transformed geometrically simple, faceted polymer single crystals into periodically branched crystals. Interestingly, the period of the branches increased logarithmically with annealing time and depended on crystallization temperature in a similar fashion as the thickness of the lamellar crystal. We tentatively relate the periodic pattern to meta-stable states, differing in crystalline order and thus melting temperature. The degree of meta-stability and its variance depend on lamellar thickness but can also change with the degree of molecular order, causing differences in melting behaviour. Our results propose that periodic variations in thermal stability within a polymer single crystal can be made visible by annealing.