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Mathematics

Fractal Geometry: Measuring Dimensions of Self-Similar Sets

Quick fact

A shape like the Sierpinski triangle has a dimension of about 1.585—between 1 and 2—meaning it fills space more than a line but less than a plane. This fractional dimension is its fractal dimension.

Why this is interesting

Have you ever measured a coastline with a ruler, only to find it gets longer the smaller the ruler? That's because natural shapes like coastlines aren't simple lines—they're fractals.