Abstract

This short communication proposes a novel Iterated Function System (IFS) to construct the Jerusalem square fractal, a two-dimensional projection of the Jerusalem cube, characterized by its cross-like self-similar structure. We provide a step-by-step con- struction, a proof of its fractal nature, and Python code for visualization. Properties such as self-similarity, fractal dimension, and connectivity are analyzed with formal proofs. The IFS offers a new perspective on Jerusalem square fractal generation. Results demonstrate the fractal’s intricate geometry, with applications in computer graphics and geometric mod- eling.