Tuesday, February 14, 2012

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


Ramanan said...

Have you read Basil Moore's Shaking The Invisible Hand - it goes into complexity and economics.

Robert Vienneau said...

I've read some Basil Moore, but not that book. Rochard Goodwin and Barkley Rosser have written books about complex dynamics and economics that I find of interest.