Description

We stream movies, send pictures to friends, and video-chat with distant loved ones, all digitally, and all without a second thought. Empowering this revolution behind the scenes is Information Theory, which provides a mathematical framework to quantify, compress, and transmit information. This picture illustrates an important theorem in Information Theory: the Asymptotic Equipartition Property. It formalizes and generalizes the intuitive notion that if you flip a fair coin many times, you would expect about 50% heads. In the image, each square represents a string of coinflips (with 0=tails and 1=heads), with smaller squares representing longer strings of flips. Like a family tree, each square recursively generates 4 squares below it by appending one of 4 suffixes: 00, 01, 10, or 11. Each square is black, but is made transparent depending on how close to "50% heads" its corresponding string of coinflips is. We see that the vast majority of the tiny squares at the bottom are nearly 50% heads and hence transparent, allowing the underlying Swiss pasture scene to show through.