Calculating the Dimension of a Crumpled Paper Ball

A flat sheet of paper is two-dimensional. A solid ball is three-dimensional. But what is the dimension of a crumpled piece of paper? It fills 3D space, but it's mostly empty air. This object is a real-world fractal, and its dimension is typically between 2 and 3.

We can estimate this dimension using the scaling law M ∝ RD, where M is the mass of the paper, R is its radius, and D is the fractal dimension we want to find.

How to Perform the Experiment

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Data Analysis Lab

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Point #Radius (R)Mass / Area (M)Action

Analysis & Visualization