Hi there,

While answering the last e-mail, I looked up L-System fractals
in wikipedia, and I just came across this picture of a Penrose tiling as an
L-System:
http://en.wikipedia.org/wiki/Image:Pend05c.gif

It's the same idea as my 3D fractal Penrose. If you did it like that
and just superimposed a few more layers, in the same way
- and if you were to draw the smallest tiles in a very light pen
and use darker pens as the tiles got larger, then zoomed out
until the smallest tiles of all merged to become continuous or
nearly so the result would be a 2D fractal.

To get a more continuous appearance, shade each of the larger
tiles so that it is black at its boundary and shades to white at the
centre, and as before use lighter pens for the smaller tiles
- and superimpose by subtraction from white so that dark grey
+ light grey gives very dark grey - e.g. 90% intensity + 80 %
intensity superimposes as 60% intensity (subtract 10% then 20%).

The result would be a continuous 2D fractal. You could then take that
into 3D by using the intensity as the 3D height.

So that would be a way to make the Penrose tiling into a 3D
fractal landscape. You could superimpose the coloured tiles
over the landscape and you'd notice that the same type of
feature in the landscape has the same pattern of tiles
wrapping over it, so bringing out the larger and larger
scale structures in the Penrose tilings more clearly than in the
usual 2D representation. It might be a fun thing to do. I've got
a Penrose tiling generating program which I wrote which I'm sure
could be modified to do this and may give it a go some day
when I have a bit of time.

Robert

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