Vector-valued fractal interpolation functions and their box dimensions

DOI10.1007/BF01818475zbMath0738.28006MaRDI QIDQ1180543

Peter R. Massopust

Publication date: 27 June 1992

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137415

zbMATH Keywords

Hausdorff dimensioniterated function systembox dimensionself-affinevector-valued fractal interpolation

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Fractals (28A80) Iteration of real functions in one variable (26A18) Hausdorff and packing measures (28A78)

Related Items (19)

LINEAR FRACTAL INTERPOLATION FUNCTION FOR DATA SET WITH RANDOM NOISE ⋮ Concerning the vector-valued fractal interpolation functions on the Sierpiński gasket ⋮ A GENERALIZATION OF FRACTAL INTERPOLATION STOCHASTIC PROCESSES TO HIGHER DIMENSIONS ⋮ Box dimension of \(\alpha\)-fractal function with variable scaling factors in subintervals ⋮ Vector-valued fractal functions: fractal dimension and fractional calculus ⋮ New type of fractal functions for the general data sets ⋮ BOX DIMENSIONS OF α-FRACTAL FUNCTIONS ⋮ Dimensions of new fractal functions and associated measures ⋮ CONSTRUCTION OF NEW AFFINE AND NON-AFFINE FRACTAL INTERPOLATION FUNCTIONS THROUGH THE WEYL–MARCHAUD DERIVATIVE ⋮ FRACTAL DIMENSION VARIATION OF CONTINUOUS FUNCTIONS UNDER CERTAIN OPERATIONS ⋮ Fractal dimension for a class of complex-valued fractal interpolation functions ⋮ A fractal interpolation scheme for a possible sizeable set of data ⋮ On some qualitative analysis for a new class of fractal interpolants ⋮ On the parameter identification problem in the plane and the polar fractal interpolation functions ⋮ Fractal interpolation functions with partial self similarity ⋮ Fractal interpolation functions for random data sets ⋮ Fractal approximation of a function from a countable sample set and associated fractal operator ⋮ Hidden Variable Bivariate Fractal Interpolation Surfaces ⋮ DISTRIBUTION OF LINEAR FRACTAL INTERPOLATION FUNCTION FOR RANDOM DATASET WITH STABLE NOISE

Cites Work

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• The calculus of fractal interpolation functions
• The capacity for a class of fractal functions
• Fractal functions and interpolation
• On the Hausdorff dimension of some fractal sets
• The Lyapunov dimension of a nowhere differentiable attracting torus
• On Weierstrass-like functions and random recurrent sets
• Hidden Variable Fractal Interpolation Functions
• Iterated function systems and the global construction of fractals
• On the Hausdorff Dimension of Some Graphs
• The Hausdorff dimension of self-affine fractals
• On self-affine functions
• The Hausdorff Dimension of the Graphs of Continuous Self-Affine Functions

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