Fractals

@radiator0505 These are the simple examples; see also the Koch snowflake. The Mandelbrot set is a bit more sophisticated - complex analysis, differential equations/topology, measure theory. See what wikipedia has for an overview; the basics are within reach of undergraduates. Gleick's book is really good, although he hypes things a bit. I highly recommend The Information by him. You might also like Complexity by Waldrop; same style, and complexity is a sibling to chaos. - Bob