Playing With Fractals

Figure 1: An Enlargement Of A Piece Of The Mandelbrot Set

A number of years ago, I loaned Heinz-Otto Peitgen and Peter H. Richter's 1986 book, The Beauty of Fractals: Images of Complex Dynamical Systems to a relative. This is a coffee-table book that, apparently, was issued as a companion piece to a digital art exhibition. This book was returned to me at Christmas.

So, for fun, I've been writing a fractal-drawing program. I'm not sure what the point of this is, besides reviewing certain aspects of Java programming. I don't plan on distributing my program, even if I did include some help capabilities, icons for various windows, and such like. I deliberately have not looked at any programs that may be out there on Windows, Icon, Mouse, Pointer (WIMP) platforms. I eventually did look at a free app for a touch interface. This app cued me to think about assigning colors on a logarithmic scale, with lighter shades being near the Mandelbrot set boundary.

In software development, a difficulty is often how to define what you want to do. And one can always think of additional capabilities. In my case, at some point I included capabilities to save and load the current state, to print the current canvas, and to provide user-control over the number of iterations and various colorings. I struggled with how to define coloring algorithms. I'm curious about how one might implement Sigel discs, that is, regions of convergence for limit points and cycles within a Julia set. A history capability would also be nice.

Anyways, I haven't been reading all that much economics while taking this excursion into recreational mathematics.

Figure 1: A Julia Set