Soler's Fractal Gallery: Three-dimensional fractals

These fractals are three-dimensional because, although they are two-dimensional pictures on the screen, they depict three-dimensional virtual objects that exist somewhere in mathematical space, in the same way as a perfect cube exists as a mathematical object. Making three-dimensional fractals is like photographing a sculpture, whereas making two-dimensional fractals is like photographing a painting. With the three-dimensional fractals you can change the angle of view, alter the direction of lighting, move in closer, rotate the object and even penetrate the surface (ouch!).

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 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.

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 new movie showing a Juliabulb rotating front to back.