Al Howe

About My Mandelbrot Set Pictures

Many years ago I acquired an excellent program named The Beauty of Fractals Lab. It was for the Macintosh and I had a Mac at the time, so I used it to make many great pictures. Unfortunately that Mac died several years ago, taking the hard drive with it, and the full size images. Also, it is no longer supported.

This part of my webpage showcases many of the pictures, at a reduced size (for the web 10 years ago), yet still fascinating. I have not yet found a comparable program for Windows. The most important feature for me is being able to set up my own color tables.

One of my future goals is to wrote a Mandelbrot Set program that does everything I want it to. That would be great to overcome many of the limitations this program had implemented, such as a limit of 20,000 iterations, and images limited to 1500 pixels on a side. I just need to learn how to interface C++ with Windows. If I am ever able, all these images will be ugdated to immense size.








There are several terms I use when describing the Mandelbrot Set, and they are shown and displayed below. Sorry about the quality of the picture, but it should be easy to see what's going on. (The original was lost on the Mac, and this one was too small so I blew it up 150% and sharpened the edges.) The terms are described below.

Basic Parts

  • Main Set: The full Mandelbrot Set.
  • Floating Sets: The many replicas of the Main Set that appear under magnification. The are slightly warped, but have all the same features plus more.
  • Buds: Any of the circular extensions off the Main Set (or off another bud).

Common Forms

  • Seahorse: Any of the forms that resemble a seahorse - they have a complex head and a single spiral for a tail.
  • Whirlpool (Spiral): Resembling whirlpools, they have a simple body and arms spiraling down the other end.
  • Wave: Basic wavelike forms that are in the valley at the back end of the Main Set. The simplest Whirlpool.
  • Fireworks: Forms halfway between Seahorses and Whirlpools - they don't seem to have any spirals.

Complex Forms

  • Headdresses: Complex designs that appear on the heads of Seahorses and spirals of Whirlpools as you magnify buds on buds or floating sets.
  • Filigree: Very fine, intricate forms appearing in the border areas as you get even closer.
  • Galaxies: Replicas of Julia Sets floating in the filigree. They do not appear to have any floating sets within them, but are formed by the complex interactions of points near the Mandelbrot Set border.