The Art of Space Filling in Penrose Tilings and Fractals

Abstract

Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable MC Escher like image that works esthetically as well as functionally requires resolving incongruencies at a tile's edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical shapes to which he never applied his artistry. These shapes can incorporate designs that form images as appealing as those produced by Escher, and our paper explores this for traditional tessellations, Penrose Tilings, fractals, and fractal/tessellation combinations. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others.