Emergent Mind
Fractal Intersections and Products via Algorithmic Dimension
(1612.01659)
Published Dec 6, 2016
in
cs.CC
and
math.MG
Abstract
Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that two prominent, fundamental results about the dimension of Borel or analytic sets also hold for arbitrary sets.
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