nLab fractal dimension




A concept of fractal dimension measures how the amount of detail of a given space changes with scale. For ordinary manifolds this fractal dimension coincides with the usual dimension, taking values in tha natural numbers. For fractal spaces however the fractal dimension may be a non-negative rational number, in fact a real number, hence a fraction, whence the name “fractal”.

There are various precise realizations of the general idea. They include


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