Correlation only sees straight-line relationships. Mutual information sees any relationship. Paint up to 500 points below. Both statistics update live, computed the same way as in mutual information calculations in my work for astronomy (Kırmızıbayrak, 2025). Your mission: draw an obvious pattern that scores near zero correlation but high mutual information.
What's happening under the hood: your points are rank-ordered (so each axis becomes uniform), joint densities are estimated with a k-nearest-neighbor search including corrections at the edges, and a copula baseline (the same calculation on shuffled data, averaged over dozens of iterations) is subtracted, leaving only the pure dependence between x and y. The colors are the brush you paint with, inspired by the energy bands astronomers observe in; the math sees only positions. Toggle info heat to recolor every dot by its own term in the MI sum: hotter dots are the points carrying the most information about the pattern.
Good attempts: a circle, an X, a smiley face, a checkerboard, a sine wave. Anything left-right symmetric tends to zero out correlation while mutual information keeps seeing structure, the same reason this method finds signals in astronomical data that classical cross-correlation misses.