For an introduction with just a little bit of mathematics, I recommend the book Chaos: Making a New Science by James Gleick.
The Logistic Map
Andy Burbanks's Period Doubling Site at Loughborough, UK
Gallery of Mathematics Site at Loughborough, UK (The parent of the previous site.)
Takashi Kanamaru's Logistic Map Site at Tokyo
Takashi Kanamaru's Bifurcation Diagram for the Logistic Map Site at Tokyo
Takashi Kanamaru's Chaos Site at Tokyo (The parent of the previous sites.)
Bob Devaney's Nonlinear Web Site at Boston
Bob Devaney's Java Applets Site at Boston (The parent of the previous site.)
The Mandelbrot Set
There are almost a million hits when searching for "Mandelbrot Set" on google. Here is one of my favorites amoung them: a YouTube movie of Baroque Manelbrot Zoom.
The Lorenz Equations
Michael Cross's Site at CalTech
Patrick Worfolk's Site at the Geometry Center
Animated Gif of the Lorenz Attractor.