List of fractals by Hausdorff dimension

According to Falconer, one of the essential features of a fractal is that its Hausdorff dimension strictly exceeds its topological dimension. Presented here is a list of fractals ordered by increasing Hausdorff dimension, with the purpose of visualizing what it means for a fractal to have a low or a high dimension.

Built by removing the second quarter at each iteration. Nowhere dense and not a countable set. ${\displaystyle \scriptstyle \varphi ={\frac {1+{\sqrt {5}}}{2}}}$ (golden cut).

${\displaystyle \varphi =(1+{\sqrt {5}})/2}$ (golden ratio).

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