Penrose tiles are sets of polygonal tiles that can be assembled into non-periodic tessellations of the plane. There are three major variations of Penrose tiles; I’ve concentrated on the P3, or rhombus tiles. The set is composed of two rhombi, the thin and fat variations. This figure shows two fat rhombi and one thin:

I decided to fill each tile with a design that gives rise to a series of pursuit curves. By drawing many similar shapes inside, each slightly smaller than the last, the corners will lie on four graceful curves that model the path of an object pursuing another object. Here is a series of 150 quadrilaterals inside the fat tile:

Given that motif, it’s then simply (!) a matter of placing over 150 tiles into a rectangular space:

and filling each tile, taking care to aligning the curves to force aperiodicity. Voila!