Why do fractal dragons appear... Are they really fractal
dragons?
L-systems, (Wikipedia page)
describe fractal like structres with words (strings of symbols)
describing some fractal process
and rules to transform them.
For each curve, we can give an instruction for the path:
L means turn left, R means turn right, h means cross a horizontal line, v means cross a
vertical line.
The hinged tiling process corresponds to either:
L → L ,
R → R ,
h → hLv,
v → hRv
or
L → L ,
R → R ,
h → hRv ,
v → hLv
Here is a picture to explain the description of this process as an L-system
(Also on
this page.)
Apply operation:
0
This shows that these curves are actually fractal dragon curves,
because they are constructed by the same L-system rule.
These are already well known,
but constructed from a new perspective - hinged tilings.
This opens up the possibility of using different hinged
Truchet tilings,
e.g., hexagons - not done this yet!