I was introduced to symmetric fractals (icons) by the 1992 book, Symmetry In Chaos, by Michael Field and Martin Golubitsky. In it, they mentioned that the beautiful images contained in the book were rendered with extremely powerful (at the time) computers.
In the book’s appendix, there were BASIC programs that one could enter and run on his or her home computer. I remember downloading QBasic and laboriously entering and debugging them. After I got one to work on my Intel 486 PC, I had to let it run overnight, because it took so long to plot enough points to get a decent image. Even then, they weren’t very high-resolution. Here’s a typical result:
So what’s the point of this post? Well, in the nine intervening years between the publication of the first edition of Symmetry in Chaos and today, both computers and software have increased exponentially in power and ease of use. Yesterday, I used Chaoscope to create and tweak the ocatagonal symmetric icon below. It was rendered in 22 seconds on my Lenovo X61 tablet, at any resolution I wished.
I can’t imagine what computers will be capable of doing nine years from now.