Polygonal Harmonics of Silhouettes: Shape Analysis

One well documented method for finding the fractal dimension of a silhouette involves approximating the silhouette with polygons which have all but one side equal and the vertices of which fall upon the silhouette edge. These are constructed using a divider stepping method or a computer algorithm which mimics this process. If one does not complete the polygon with an unequal side, as is usually done, but continues the analysis by stepping around the silhouette several times, the dividers start to "walk in their own footsteps" and describe an equilateral polygon in the silhouette. These phenomena, termed polygonal harmonics, are examined and discussed in detail. A rule is developed for harmonic stability and specific cases of the circle, triangle and smooth curves are examined to gain insight into the convergence process.