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

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.

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