A New Deterministic Gasket Fractal Based on Ball Sets

Abstract

In this paper, we propose a new gasket fractal constructed in a deterministic iterated function system (IFS) way by means of interacting ball and square sets in R^2. The gasket consists of the ball sets generated by the IFS, possessing also exact self-similarity. All this leads to a direct deduction of other properties and a clear construction methodology, including a dynamic geometry procedure with an open-source construction protocol. We also develop an extended version of the fractal in R^n. Some resulting configurations consisting of stacked 2D-fractals are plotted. We discuss about potential applications of them in some areas of science, focusing mainly on percolation models. Guidelines for future work are also provided.