A computer algorithm for determining the Hausdorff dimension of certain fractals

Author:
Lucy Garnett

Journal:
Math. Comp. **51** (1988), 291-300

MSC:
Primary 58F11; Secondary 30D05

MathSciNet review:
942156

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Abstract: A fractal is a set which has nonintegral Hausdorff dimension. Computation of the dimension directly from the definition would be very time-consuming on a computer. However, the dimension can be computed using Newton's method if there exists a self-expanding map on the set. This technique is applied to compute the dimension of the Julia set of the quadratic mapping for small real values of *c*.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0942156-0

Article copyright:
© Copyright 1988
American Mathematical Society