Penrose kite fractal

Written By Paul Bourke
October 2019

Inspired by Kerry Mitchell. First published in "The Pattern Book: Fractals, Art and Nature", pages 304-306. Editor: Clifford Pickover.

One the two tile non-periodic tiles called Penrose tiles consists of a so called "kite" shape and a "dart" shape. The kite shown below can be split into three smaller kites and two half darts.

The lengths and angles of the kite are presented below where phi is golden section defined here as (1+sqrt(5))/2.

This can be repeated recursively, on each level the kites are split into 5 regions. The boundary of these regions is shown below for increasing levels.

The units above can be rotated around the lower left corner to form the following, this is how they were originally presented by Kerry Mitchell.