Hinged tiling [GA2021 H Verrill page 5/15]
The iterative process I use to get a mathematically space filling curve from
a Truchet tiling is to use a hinged tiling.
Example Hinged tiling
There are lots of puzzles based around hinged tilings
(or more precisely, to closely related hinged dissections
Wikipedia page).
Lots of different
kind of tilings can be hinged.
My introduction to these was through origami, and work of Barreto, Palmer,
Bateman.
The following origami has a hinged tiling
crease pattern.
The hinged tiling needed on this page is just a hinged tiling of squares.
The following picture actually
cheats to keep the rotations going in the same direction - the
corners where the hinges are has to change at each step.
In this example, the squares stay the same size as they turn, as thought this
was a real physical model, but for the Truchet tiling I will change the size
of the squares.
