The Frank-Robinson tiling is an inflation tiling with 4 shapes (“prototiles”) and 4 rules or substitutions that govern how the tiling grows from some initial configuration. You can find the rules in the original paper.
I like the way this tiling looks, so I implemented it in Mathematica. Here is what you get if you start with the “large square” and peform 4 replacement steps:
Instead starting with the vertical rectangle and performing 5 iterations:
I wonder if anyone has used this pattern to tile their bathroom floor.