FRACTAL DIMENSIONS OF SINKHOLES

Sinkhole perimeters are probably fractals (D = 1.209-1.558 for sinkholes with areas larger than 10,000 m2), based on area-perimeter plots of digitized data from karst surfaces developed on six geologic units in the United States. The sites in Florida, Kentucky, Indiana and Missouri were studied using maps with a scale of 1:24,000. Size-number distributions of sinkhole perimeters and areas may also be fractal, although data for small sinkholes is needed for verification. Studies based on small-scale maps are needed to evaluate the number and roughness of small sinkhole populations.