Holger K. von Jouanne-Diedrich uses fractal math to create realistic-looking artificial islands:
Here we will turn this principle on its head and use it to actually create realistic-looking landmasses with R. The inspiration for this came from chapter 4 “Infinite Detail” of the book “Math Bytes” by my colleague Professor T. Chartier from Davidson College in North Carolina.
The idea is to start with some very simple form, like a square, and add more detail step-by-step. Concretely, we go through every midpoint of our ever more complex polygon and shift it by a random amount. Because the polygon will be getting more and more intricate we have to adjust the absolute amount by which we shift the respective midpoints.
Click through for the code.