Robin Wilson explores the automation of creating Penrose Tile patterns with Blender, and provides a ready to use Python script to achieve the effect.
Penrose tiling is known both for the beautiful patterns it can generate and the peculiar mathematical properties it possesses. It's unusual for two reasons:
1) It's pentagonally symmetric (while most tiling patterns are not)
2) It's non-periodic, that is, it doesn't regularly repeat itself over space.
Because Penrose tiling is non-periodic, it is not possible to construct the patterns in Blender using the array modifier. Instead, I used Blender's scripting tools, and made this video.
If you want to learn how to generate your own Penrose tiling patterns in Blender, you can check out this tutorial.