There's a program that I first started using back in 1991, Fractint
<http://www.fractint.org/ftp/release.20.0/dos/frain200.zip> , that has
a section on L-Systems, and I recall several different Penrose
variations in the list of stored L-System parameters. It's a DOS
program, but you can run it at the command prompt (Start>Run> Cmd). The
program also generates Mandelbrot & similar fractals, and the Lorenz,
Gingerbread & other dot cluster types. There's an option for generating
sounds while the image is calculated.
--- In cnfractal_music@yahoogroups.com, "Robert Walker"
<yahoogroups@...> wrote:
>
> 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
>
> [Non-text portions of this message have been removed]
>



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