Graph-directed fractal interpolation functions

Deniz, Ali; Özdemir, Yunus

doi:10.3906/mat-1604-39

Cited by 6 publications

(7 citation statements)

References 14 publications

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“…for all p = l, p, l = 1, 2, ..., n, i = 1, 2, ..., N l . In [5] we can find the proof regarding the existence of a graph-directed fractal function:…”

Section: Graph Directed Fractal Interpolation Functionmentioning

confidence: 99%

“…In the case n = 2 the construction of these iterated function systems can be done using the method given in [5].…”

Section: Graph Directed Fractal Interpolation Functionmentioning

confidence: 99%

“…In order to obtain fractal interpolation functions with more flexibility, Wang and Yu [9] used instead of a constant scaling parameter a variable vertical scaling factor. Also the notion of fractal interpolation can be generalized to the graph-directed case introduced by Deniz andÖzdemir in [5]. In this paper we study the case of a stochastic fractal interpolation function with graph-directed fractal function.…”

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confidence: 99%

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Graph-directed random fractal interpolation function

Somogyi

Soós

2021

Stud. Univ. Babes-Bolyai Math.

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"Barnsley introduced in [1] the notion of fractal interpolation function (FIF). He said that a fractal function is a (FIF) if it possess some interpolation properties. It has the advantage that it can be also combined with the classical methods or real data interpolation. Hutchinson and Ruschendorf [7] gave the stochastic version of fractal interpolation function. In order to obtain fractal interpolation functions with more exibility, Wang and Yu [9] used instead of a constant scaling parameter a variable vertical scaling factor. Also the notion of fractal interpolation can be generalized to the graph-directed case introduced by Deniz and Ozdemir in [5]. In this paper we study the case of a stochastic fractal interpolation function with graph-directed fractal function."

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“…for all p = l, p, l = 1, 2, ..., n, i = 1, 2, ..., N l . In [5] we can find the proof regarding the existence of a graph-directed fractal function:…”

Section: Graph Directed Fractal Interpolation Functionmentioning

confidence: 99%

“…In the case n = 2 the construction of these iterated function systems can be done using the method given in [5].…”

Section: Graph Directed Fractal Interpolation Functionmentioning

confidence: 99%

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confidence: 99%

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Graph-directed random fractal interpolation function

Somogyi

Soós

2021

Stud. Univ. Babes-Bolyai Math.

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“…The dimension theory of the interpolation functions was studied in several papers, see for example Bedford [14], Keane, Simon and Solomyak [42] and Ruan, Su and Yao [52]. Here we present a generalised version of fractal interpolation functions G : [0, 1] → R constructed with Markov systems, similar to Deniz and Özdemir [22].…”

Section: Lower Bound For the General Case With One Dimensional Basementioning

confidence: 99%

Dimension of the repeller for a piecewise expanding affine map

Bárány¹,

Rams²,

Simon³

2020

Ann. Acad. Sci. Fenn. Math.

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In this paper, we study the dimension theory of a class of piecewise affine systems in euclidean spaces suggested by Barnsley, with some applications to the fractal image compression. It is a more general version of the class considered in the work of Keane, Simon and Solomyak [42] and can be considered as the continuation of the works [5, 6] by the authors. We also present some applications of our results for generalized Takagi functions and fractal interpolation functions.

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“…In [13], Deniz et al considered graph-directed iterated function system (GDIFS) for finite number of data sets and proved the existence of fractal functions interpolating corresponding data sets with graphs as the attractors of the GDIFS.…”

Section: Introductionmentioning

confidence: 99%

Graph-Directed Coalescence Hidden Variable Fractal Interpolation Functions

Akhtar¹,

Prasad²

2016

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Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on  2 is the graph of the CHFIFs interpolating the corresponding data sets.

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Graph-directed fractal interpolation functions

Cited by 6 publications

References 14 publications

Graph-directed random fractal interpolation function

Graph-directed random fractal interpolation function

Dimension of the repeller for a piecewise expanding affine map

Graph-Directed Coalescence Hidden Variable Fractal Interpolation Functions

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