As a mathematician who started out as an art major, I became very excited when the first home computers appeared on the scene in the mid eighties. In 1987 I attended a conference at NYU (I believe it was called “Computer Graphics for the Arts and Sciences”), and marveled at the beautiful fractal pictures created using mathematical methods. On my way home I stopped at Barnes and Noble and bought The Beauty of Fractals by Peitgen and Richter. I was hooked! I bought an IBM PC that had a screen resolution of 320 × 200 and 3 colors. I learned about recursive functions and spent hours drawing stick figures of trees and other fractal figures. Now my PC has a resolution of 1600 × 1280 and 16,777,216 possible colors!
Learning how to create fractal scenery is a wonderful way for students to learn some mathematics and some elementary computer programming. I will introduce some simple “data structures” used in computer science. Much of my inspiration came from the late eighties and early nineties editions of the journal Computer Graphics, a publication of SIGGRAPH (the Special Interest Group on Graphics) of the ACM. The graphics in that journal were produced on large computers using very sophisticated and complicated rendering techniques that can only be accomplished by highly skilled programmers using super computers. They may also require a good knowledge of botany and the laws that govern the birth of inflorescences, or the bending of branches under the force of gravity.