I believe the mandelbrot fractal is merely a single perspective of a 3D structure. That is, all current fractal programs are drawing a 3D structure in merely 2D, a single 2D perspective. But you could produce many many more 2D images by retooling the fractal program to interpret the fractal function as 3D.

Now I know there have been some '3D' fractal programs out there that visualize the mandelbrot set in a three dimensional form. As if the image it produced was a terrain height map, black is high, white is low.

This is not what I mean, this is merely using the same fractal single perspective 2D interpretation like all others as a heightmap. It is showing the outcoming 2D image in 3D, it is not

*interpreting* the fractal as 3D.

Now what exactly do I mean when I say interpret it as 3D?

It is quite simple. When I see recursion getting increasingly smaller, I do not see a 2D image getting recursively smaller. I see it as perspective.

See what I mean?

Imagine if, the recursively smaller portions of the fractal actually did not get recursively smaller. But rather, they were just moving away from you in 3D space. So one swirl, in 3D space, is the same size as it's proceeding swirl, it's just, farther away from you.

This is more than just constructing the fractal into 3D space as shown here

http://www.fractalforums.com/index.php?topic=717.0Which btw is an awesome image, I'm not saying this stuff cause I don't think current fractals are great, I'm just curious to see what this might open up. But as you notice, that 3D fractal still interprets recursively smaller as physically smaller. I want to see what it would look like to interpret recursively smaller as further away in 3D space.

So think of current fractal programs as interpreting the visual image onto X and Y plane, 2D. With iterations as a controller of the detail of that image. I want to see what it would like if the mandelbrot set used the variable of iteration to interpret the placement of voxels along the Z axis.

So sample the mandelbrot set with iteration of 1. Place the sampled points in 3D space varying the position in the X and Y plane based on the output of the evaluation, but all of these voxels retaining a z value of 1. Voxel = point in 3D space

Move to iteration of 2, same as before, position the output of sampled voxels varying the X and Y, but all the voxels with a Z value of 2.

Then to iteration of 3... etc. Basically iterations = Z position.

Has anyone done this?

I come here to find anyone who is familiar enough with the math and possibly knows the basics of an open source fractal program or something to possibly implement this. Because I am not familiar enough with the math or the existing programs to do this in any efficient fashion. But perhaps, some programmer is willing to try a radical new method of visualizing the mandelbrot? Is this a new method? Or has someone else already thought of it and done it?

Now I need some help also possibly figuring out the math. Because I am not sure if just iteration = Z is exactly what I'm thinking.

For example, this is the relation I am looking for between the mandelbrot fractal and the 3D interpretation. The bottom of this image representing the mandelbrot. Like the mandelbrot is at the bottom looking up into a tree that have uniform width branches. So maybe some math needs to be in place to counteract the reduction in size of things to keep it all uniform in size?

Where the big circle in the center of the mandelbrot, is really not a 'big circle'. But rather just the bottom of a tree that has uniform branches from the trunk.

Z=iteration, maybe?

anyone care to help?

I do 3D renderings for my job, so if anyone does manage to help me get this into 3D model format. I could render it in all sorts of ways.