Birthday of Wacław Sierpiński (1882)

Wacław Sierpiński gave his name to some of the most beautiful fractals in mathematics. The Sierpiński triangle: remove the middle triangle from an equilateral triangle, repeat for each remaining triangle, forever. The result has Hausdorff dimension log(3)/log(2) ≈ 1.585 — more than a line but less than a surface. Remarkably, it appears in Pascal's triangle: shade all odd numbers and the Sierpiński triangle emerges. It also appears in the Towers of Hanoi graph and in certain cellular automata. The same pattern arising from completely unrelated starting points is mathematics at its most mysterious.