Three-dimensional fractals

In other words, these three-dimensional images give flat views (just as photos do) of a three-dimensional world. Moving from the flat plane to solid shapes means a whole new world to explore and I am excited about it. Of course, drawing the images takes forever (about an hour) and requires more fiddling. Getting good colours is also a problem. Someone has to do it, though.

The three-dimensional objects are drawn using a programming technique called ray tracing. It consists of shining a virtual light beam onto the object and putting a dot of colour on an imaginary screen corresponding to how the light comes back to the virtual camera. For a proper explanation have a look at ray tracing explained. As for the mathematics, this is a three coordinate system called triplex algebra. If you are brave see the maths. Of course, as a user of the program you don't need to worry about any of that. I have made a modest contribution to the maths.

All the fractals here were made using the Visions of Chaos program, which is available at Softology. The program costs $45 but you can use a demonstration version (no file save) indefinitely for free. I highly recommend it. I have written simple instructions for using Visions of Chaos. Although I call all my three-dimensional fractals "mandelbulbs", many of them are actually juliabulbs, ie analogues of Julia sets. Please excuse this lamentable imprecision.

Here is a good explanation of how the mandelbulb was created plus some fine images. Jason Rampe has made an amazing movie of a flight over and into a blue mandelbulb. Here is a movie I made showing a flight into and then out of a juliabulb fractal. Try this movie showing a juliabulb rotating from front to back. I have added large format versions of these movies: flight and rotation. When you view these, make sure you set the resolution to 720p (not the default 360p) and hit the full screen button (the one with the four arrows). New: a rotating mandelbulb in glowing colour. Please hit the two arrow icon (next to the one with 4 arrows) to watch it.