Analogues in Higher Dimensions
There is a three-dimensional analogue of the Vicsek fractal. It is constructed by subdividing each cube into 27 smaller ones, and removing all but the "center cross", the central cube and the six cubes touching the center of each face. Its Hausdorff dimension is ≈ 1.7712.
Similarly to the two-dimensional Vicsek fractal, this figure has zero volume. Each iteration removes retains 7 cubes for every 27, meaning a volume of at iteration n, which approaches zero as n approaches infinity.
There exist an inifinite number of cross sections which yield the two-dimensional Vicsek fractal.
Read more about this topic: Vicsek Fractal
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