A Property of Area and Perimeter
We describe an algorithm that creates a fractal pattern within a planar region R by ranplacing within it progressively smaller copies of a subpattern or fill-shape. After placing i copies of the fill-shape, we use the term gasket to describe the unfilled part of R. The size of the next fill-shape is determined by a constant \(\gamma \) times the remaining area of the gasket divided by the total perimeter of the gasket. Experimental evidence is presented indicating that the areas of the fill-shapes obey an inverse power law for large i.
KeywordsAlgorithm Area Perimeter Fractal Power law Space filling
- 2.Ennis, C.: (Always) Room for One More. MAA Math Horizons, February, 2016Google Scholar