Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

A n umerical method for obtaining a crystalline ow starting from a general polygon is presented. A crystalline ow is a polygonal ow and can be regarded as a discrete version of a classical curvature ow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary dierential equations (ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour gure.