The Ruffled Crow

Animation, Art, and Other Shiny Things

The Formula

From wiki;

The simplest algorithm for generating a representation of the Mandelbrot set is known as the “escape time” algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.

Fractals have fascinated me for over 20 years. Back in the 80’s I had a fractal drawing program for my C-64 that could take over a day to render a relatively crude fractal image. For every day use, though, four to eight hours wasn’t unusual.

Over a decade ago I picked up a tiny screen saver that adjusts equation parameters and escape colors and redraws the screen continuously. (It can be quite mesmerizing…)

And now, just the other day I ran across this:

The Formula by Tom Beddard at

To create the 3 dimensional Mandelbrot set a tripartate coordinate is used (x,y,z) and, instead of a color to represent escape time, a distance calculation is used.

Even cooler than this is the name of the shape: a Mandelbulb.

The Mandelbrot Set

I don’t understand the math much beyond the most basic equations and I don’t have the software to play with Mr Beddard’s add-ons, so I really appreciate him putting this little film together.

Check out the Gallery; there are some stunning pics in there and, if you have Photoshop CS4 you can download and play with several add-ons found on the Projects page.


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