V-variable fractals: Dimension results

Michael Barnsley; John E. Hutchinson; Örjan Stenflo

doi:10.1515/form.2011.075

V-variable fractals: Dimension results

Michael Barnsley^*, John E. Hutchinson, Örjan Stenflo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

The families of V-variable fractals for V = 1,2,3, ..., together with their natural probability distributions, interpolate between the corresponding families of random homogeneous fractals and of random recursive fractals. We investigate certain random V × V matrices associated with these fractals and use them to compute the almost sure Hausdorff dimension of V-variable fractals satisfying the uniform open set condition.

Original language	English
Pages (from-to)	445-470
Number of pages	26
Journal	Forum Mathematicum
Volume	24
Issue number	3
DOIs	https://doi.org/10.1515/form.2011.075
Publication status	Published - May 2012

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10.1515/form.2011.075

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abstract = "The families of V-variable fractals for V = 1,2,3, ..., together with their natural probability distributions, interpolate between the corresponding families of random homogeneous fractals and of random recursive fractals. We investigate certain random V × V matrices associated with these fractals and use them to compute the almost sure Hausdorff dimension of V-variable fractals satisfying the uniform open set condition.",

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AU - Stenflo, Örjan

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AB - The families of V-variable fractals for V = 1,2,3, ..., together with their natural probability distributions, interpolate between the corresponding families of random homogeneous fractals and of random recursive fractals. We investigate certain random V × V matrices associated with these fractals and use them to compute the almost sure Hausdorff dimension of V-variable fractals satisfying the uniform open set condition.

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V-variable fractals: Dimension results

Abstract

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