Bounding the dimension of points on a line

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Bounding the dimension of points on a line

Lutz, Neil; Stull, D.M.

Information and computation, December 2020, 2020-12-00, Volume: 275

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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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Lutz, Neil | Stull, D.M.

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