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Hi,

I finally got my escape-time formula working for 3D RIFS - the escape-time method uses the inverse transforms i.e. the expanding ones.
It's a little slow at rendering at the moment as far as a "complete" IFS fractal is concerned but has the advantage over the "normal" chaos game or deterministic methods that zooming in isn't as big an overhead as you don't need to render the whole thing just to see part of it - in fact it doesn't need a z-buffer, it ray traces till it hits something so only some points along the rays and the surface points are calculated.
You can see my frst renders in my scraps at Deviant Art:

http://makinmagic.deviantart.com/gallery/scraps/ (http://makinmagic.deviantart.com/gallery/scraps/)

bye
Dave

Nice work. I want to integrate a Menger Sponge into one of my cube-based Koch-curve-silhouette solids.

David J. Makin wrote:
>
>    It's a little slow at rendering at the moment as far as a
>    "complete" IFS fractal is concerned....
>    ....zooming in isn't as big an overhead as you don't need
>    to render the whole thing just to see part of it....

I like the way the "texture" of your "Menger Sponge Zoom" makes it appear as if it is made the same way that baskets are woven from reeds.  Even the corners of two sides seem to have that "wrapped" looked.

That effect is an artifact of the rendering method - the fractal is made up of tiny overlapping spheres so at the edges you can see them when the detail level is not set sufficiently high to produce a visually continuous surface.
In this case I didn't increase the detail level further (hence reducing the size of the spheres and increasing their concentration) because I also liked the effect and because doing so would have increased the render time.

David,

I started thinking about how to use an escape time approach to convergance IFS fractals, then realized you have already been working on it.

My thinking is that using an escape time algorythm with Apophysis type fractals (also my 3D flames) could break the size/time limitation barrier that's keeping Apo artists out of the Benoit Mandelbrot Fractal Art Contest 2007

It would also help open these fractal flames to distributed computing.

Here are my assumptions.....

• Instead of itterating the whole flame at once, each pixel can be iterated by itself to find it's final color
• Iterating by pixel is zoom independant
• Multi threading would be very efficent
• Huge reduction in memory required
• Speeg gains go up faster as size increases

I'm working out possible algorythms in my head and would like to compare notes if your so inclined.

Hi Don,

All I've done so far is in the (2D IFS) files I previously made available and the test 3D IFS that created the menger sponge.

The two problems with using the escape-time method are:

1. For non-affine fractals the inverse algorithm doesn't produce the same result as the standard (flame) methods.
2. There isn't really a direct comparism to the normal "hits" colouring used in flames.

The advantages are as you said at least for 2D IFS :-) But I found the benefits werren't as great as I expected when I tried the same for 3D IFS.

I can mail you the Ultrafractal formula I've done for 3D IFS if you like - it isn't really suitable for making completely public yet !

bye
Dave

Thanks Dave, I'd love to have a look at it, please email me at doncasteel8587@yahoo.com

I had not thought of using inverse transforms, my thoughts aren't clear enough yet to explain, as soon as I can figure out how to put them into words, I'll post them here.

Don

Hi all,

Here are a couple of papers on 3D fractals that I thought you'd like the links for:

http://graphics.cs.uiuc.edu/~jch/papers/rayifs.pdf

http://graphics.cs.uiuc.edu/~jch/papers/rtqjs.pdf

I should add that my current 3D IFS formula for Ultra Fractal, mmf4.ufm:3D IFS, is a lot better than the one I was working on as mentioned earlier in this thread - however the method I used in the old version of the formula (distance estimation) does allow for the possibility of rendering 3D IFS with non-linear components whereas the method I used in my Ultra Fractal 3D IFS formula can't do that (it's basically as outlined in the "rayifs.pdf" paper). However generally rendering using the distance estimator method for 3D IFS is tricky to get accurate and a lot slower.


bye
Dave