Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.