AbstractTwo dimensional images are often used as a basic for calculating shape descriptors of particles. An edge roughness descriptor, the fractal dimension, can be found from a Richardson plot of measured perimeter versus the measuring step length. Data Scatter on these plots is shown to be related to the incipient formation of polygonal harmonics, which are regular polygons formed during a structured walk around the image edge. This relationship was verified using both computer generated fractal images and real particle outlines.