I've loved complex numbers since first learning about them, and my first significant programming experience was writing these types of programs for my TI-89 gra

I've loved complex numbers since first learning about them, and my first significant programming experience was writing these types of programs for my TI-89 graphing calculator in high school in the late 90s. This is a good introduction. Another good equation to play around with is x_next = a x (1 - x), for a from 0 to 4. You'll find that x settles to a single value for low a, eventually bifurcating as you increase a, then bifurcating again. At one point, though, it splits into a cycle of three values, then an erratic distribution. Someone once wrote a paper on how "period three implies chaos".