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Hello! I'm here from Daniel White's article on mandelbulbs, which seems to be getting a lot of traffic lately. I've always appreciated fractals aesthetically, but the furthest I've gone with making them myself was making a simple colorized 2D Mandelbrot. However, these 3D fractals are something else again, and they're enough to inspire me to come here and take a look around. My own focus is in general software development; I'm good at a lot of things but not great at anything, basically. So I'm pretty sure I understand broadly how fractals work, but I could be wrong.

I've seen the massive thread on 3D fractals but haven't gotten around to reading it yet. Am I correct in my understanding that these fractals are generated by doing an inclusion/exclusion test for each 3D point in a given area, and generating a voxel if the point is in the volume? And then you get more detail by decreasing the distance between 3D points and/or increasing the number of iterations for each point.

My idea was to try to write a script for Blender (a 3D modeling program I use) to generate models of the fractals. This would make flybys trivial, and Blender has plenty of support for near material effects, though dynamically increasing zoom levels would be difficult. If you make a cube for each voxel, and then combine the cubes and remove interior faces, you can apply smoothing to create "landscapes" which should theoretically be amenable to inclusion in other 3D projects.

My second, impractical-due-to-cost idea was to make a 3D model of a fractal, and then find a 3D printing service to make a model that I could put on my desk. Painting it might be a bit tricky, though.

My third, impractical-due-to-time idea was to make a roguelike game set on a fractal, where the game gets more difficult as you increase your zoom level. That of course runs into problems like "how should equipment and enemies be fractal" but it's a neat concept to think of.

Yeah, I know scripting languages can be slow. Awhile back I wrote a dumb Perl script to generate 2D Mandelbrot images; at 800x800 with 10 iterations per pixel it took 17 seconds on my computer.

Fortunately, there's a trick you can use with Python (which is the scripting language that Blender uses) to compile it to much faster code without losing the beauty of scripting languages. It's called Cython; basically it's just Python with predeclared types. I have a game project I'm working on that was running slowly during map generation; when I switched the vector class over to Cython I got a 35% speedup of the entire program -- I don't know how much faster the vector class itself got because it stopped showing up in my profiling reports.

For the 3D voxels -- do you try to create a 3D shell, or do you "fill" the interior with voxels? If the former, how do you detect if a given voxel is on the border? By examining the adjacencies? If the latter, how did Daniel White make his "inside the fractal" shots?

EDIT: did a bit more research, I'm guessing you create a 3D shell using something like the marching cubes algorithm. Fine by me; I've used marching squares in the past for 2D...

For my approach, I use the 'shell' approach, yes. To create the inside, I simply reverse the definition of 'inside', so that the inside is the outside and vice versa.

In theory, I suppose one could yes. You would need to find the surface normal. The inside would then be defined as the volume within a certain distance from the surface point, and at the normal's angle.

Greetings, and a belated Welcome to this particular Forum !!!    

That is an interesting experiment using Python script to make your 3-D fractals.