Linear Richardson plots from non-fractal data sets

Richardson analysis, one of the principal methods of fractal analysis, is performed by measuring the perimeter of a curve with strides of varying length and constructing a log-log plot of perimeter against stride length. Certain simple geometrical forms can produce linear plots that mimic fractal behavior, and two smooth curves have been discovered that produce linear Richardson plots for strides varying by two orders of magnitude or more. The existence of such curves was not suspected before this study. Richardson analyses that suggest fractal geometry of low dimension or over a limited range of stride length should be checked against the source data for independent evidence of self-similarity.