Fractal Space Filling Curves [GA2021 H Verrill page 4/15]
What is a space filling curve?
The Smith Truchet tiling of quarter circles is sort of space filling - it
fills a lot of space.
But
for a mathematical space filling curve, we need a limiting process
to pass from one level of iteration to another, as for example in the
case of the famous
Hilbert curve:
Example: Hilbert curve
Change level of iteration:
There are three types of tile, with replacement rules as follows, the replacement tiles are below the original:
Use the edge option in the above previous picture to more easily see the way the tiles are
replaced with a continuous interpolation possible.
Once you have this basic transformation you can play around with it in lots of ways,
e.g., as in the examples here.
Question:
What is the replacement transformation rule for the quarter circle Smith Truchet tile?
