I would like to create a variety of simple (no self-intersection), independent polygons all with the same area (I will do it multiple times with different areas), but with different perimeter lengths. I guess ideally I would have a factorial design with 10 areas each with 10-20 polygons of varying edge/area ratios (100-200 total polygons). I suppose that the 10 polygons could be generated for 1 area and then a multiplier could be used to increase/decrease the total size of each one for the 10 different area replicates. In reality the shapes don't have to have straight sides, but I figured that would be easier. The polygon doesn't have to be convex, the angles could be highly variable and the shapes irregular, but they don't have to be. The benefit of highly irregular polygons (as opposed to rectangles with different length sides, for example) is the ability to generate polygons with a larger range of perimeter:area ratios.
I am doing this for comparing landscapes with forest harvests of different sizes and shapes (I will eventually apply a function to calculate wildlife abundance for each polygon). Any working solution would do, but solutions using R, Python, and/or GIS (ArcGIS or QGIS) would be preferred. Thanks for any thoughts or suggestions.
