Abstract
We explore Penrose’s tiling using kites and darts in search for hidden beauty. We focus on the iterative subdivision
process that can be used to create Penrose tilings by subdividing half kites and half darts into smaller half kites and
half darts. By selectively coloring the half darts and half kites, based only on their relative position in the subdivision
process, we create 15 unexpected and distinctive patterns hidden within Penrose tiling. These patterns tend to have
the appearance of a weaving. Alternately, by selectively discarding tiles as we recursively subdivide, we can obtain
fractal patterns that appear lacelike. We finish by filling the negative spaces in the fractal patterns with pursuit curves.
