3D Fractals

Jun 5, 2016 · By Darren Mothersele

misc

Click images below to get the large, high-quality versions.

This is one of my most recent creations…

I created that image above with a program called Mandelbulb 3D. It includes many fractal equations, including the 3D version of the famous Mandelbrot set, the Mandelbulb.

I found it hard at first to get anything interesting out of Mandelbulb, so I went off on an exploration of fractal geometry. I figured I’d be able to get better results if I knew the theory behind what the equations were doing, rather than just randomly combining fractal equations and randomly tweaking parameters.

I started with the Mandelbrot set, like most people who start experimenting with fractals. I quickly moved on to some simple iterated functions. My very first experiments were with some equations I found in an old book “Symmetry in Chaos” by Michael Field and Martin Golubitsky.

I combined this method of plotting the images, with fractal equations, and it mainly went wrong. Some of the wrong images actually looked quite interesting…

Eventually, I accidentally came up with this:

It was actually a black and white render, but I’ve applied some fake colouring. I thought it looked a bit “spacey”, so I sampled colours from a universe photo.

Going back to Mandelbulb, my search for interesting fractal combinations was much more fruitful. Some of my discoveries are below.

In the beginning, I was using fog to emphasise depth. In some cases I think I overdid it…

I think the most “realistic” images have come from using colours sampled from real photos. The hardest part of creating this next image was getting the camera angle right. I think the sampled colours make it look almost like a real forest scene. Natural colours (sampled from real photos) tend to be much more desaturated than the colours picked manually…

This was my first experiment with combining two fractal formulas. Rather than alternating multiple formulas to create a combined geometry, you can visualise the output of two formulas, if you can align them correctly…

This one has a grainy look because I reduced the quality to speed up the rendering process. I thought it looked a bit like a jellyfish, so I added some colours to make it look like it was underwater. Unfortunately, when I increased the quality to create the final render it lost it’s form. So, here’s the grainy version…

This next one might be my favourite so far. Click to see full version. I really like the shading on the “moon” in the background…

Here’s a few more of my fractal experiments…

Darren's Photo

Darren Mothersele

Darren is a software developer who builds simple, creative, and independent technology. Read more »