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Mathematics of Computation

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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 $z \to {z^2} + c$ for small real values of c.

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Article copyright: © Copyright 1988 American Mathematical Society