A computer algorithm for determining the Hausdorff dimension of certain fractals
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- by Lucy Garnett PDF
- Math. Comp. 51 (1988), 291-300 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 51 (1988), 291-300
- MSC: Primary 58F11; Secondary 30D05
- DOI: https://doi.org/10.1090/S0025-5718-1988-0942156-0
- MathSciNet review: 942156