A computer algorithm for determining the Hausdorff dimension of certain fractals
Author:
Lucy Garnett
Journal:
Math. Comp. 51 (1988), 291300
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 timeconsuming on a computer. However, the dimension can be computed using Newton's method if there exists a selfexpanding 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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 D. Sullivan, Seminar on Conformal and Hyperbolic Geometry, Inst. Hautes Études Sci. Seminar notes, 1982, pp. 192.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809421560
PII:
S 00255718(1988)09421560
Article copyright:
© Copyright 1988 American Mathematical Society
