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Bounding the Dimension of Points on a Line

Published 1 Dec 2016 in cs.CC and math.CA | (1612.00143v3)

Abstract: We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x, ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower bound on the (classical) Hausdorff dimension of generalized sets of Furstenberg type.

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Authors (2)

  1. Neil Lutz 
  2. D. M. Stull 

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