Fractal surfaces

Massopust, Peter

doi:10.1016/0022-247x(90)90257-g

Cited by 116 publications

(42 citation statements)

References 5 publications

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“…[3] fractal surfaces constructed as attractors of iterated function systems. He considered the case of a triangular domain with coplanar boundary data.…”

Section: Historical Backgroundmentioning

confidence: 99%

“…Furthermore, we compare and contrast several constructions presented in Refs. [3][4][5][6][7][8] by pointing out some of their ambiguities, limitations and restrictions. Particularly, in Section 2, we briefly review the theory of iterated function systems.…”

Section: Clarifications and Interpretationsmentioning

confidence: 99%

“…Then, the corresponding IFS is of the form {R 3 ; w 1ÀN }, where The real numbers a i , b i , c i and…”

Section: Is Defined As Followsmentioning

confidence: 99%

See 2 more Smart Citations

On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

Dillon¹,

Drakopoulos²

2017

Fractal Analysis - Applications in Health Sciences and Social Sciences

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This chapter provides a brief and coarse discussion on the theory of fractal interpolation functions and their recent developments including some of the research made by the authors. It focuses on fractal interpolation as well as on recurrent fractal interpolation in one and two dimensions. The resulting self-affine or self-similar graphs, which usually have non-integral dimension, were generated through a family of (discrete) dynamic systems, the iterated function system, by using affine transformations. Specifically, the fractal interpolation surfaces presented here were constructed over triangular as well as over polygonal lattices with triangular subdomains. A further purpose of this chapter is the exploration of the existent breakthroughs and their application to a flexible and integrated software that constructs and visualises the above-mentioned models. We intent to supply both a panoramic view of interpolating functions and a useful source of links to assist a novice as well as an expert in fractals.

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“…[3] fractal surfaces constructed as attractors of iterated function systems. He considered the case of a triangular domain with coplanar boundary data.…”

Section: Historical Backgroundmentioning

confidence: 99%

Section: Clarifications and Interpretationsmentioning

confidence: 99%

See 1 more Smart Citation

On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

Dillon¹,

Drakopoulos²

2017

Fractal Analysis - Applications in Health Sciences and Social Sciences

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“…In [12], a simple procedural technique for creating a moving fractal tree was proposed; the shape of a tree is first defined using a simple recursive procedure that gives proper scale factors to the branch length, and then is given motions by rotating the branches. Here, fractal interpolation [1,3,10,13,20] is one of the fields greatly related to fractal deformation. Among the studies categorized into fractal interpolation, the studies in [17,18,19] proposed a method that combined IFS and smooth interpolation techniques and achieved fractal deformation.…”

Section: Related Workmentioning

confidence: 99%

Fractal Deformation Using Displacement Vectors Based on Extended Iterated Shuffle Transformation

Fujimoto

Ohno

Muraoka

et al. 2002

The Journal of the Society for Art and Science

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In this paper, we propose a framework of "fractal deformation" using displacement vectors based on "extended Iterated Shuffle Transformation (ext-IST)". An ext-unit-IST is a one-to-one and onto mapping that is extended from a unit-IST, which we have proposed, and is basically defined on a code space. When the mapping is applied on a geometric space, a fractal-like repeated structure, which is referred to as "local resemblance in space/scale directions", is constructed on the relationship between points on the domain and those on the range. By applying the mapping to displacement vectors given on a geometric shape, the shape can be deformed in the fractal-like repeated manner. This fractal deformation is easy to control by changing the displacement vectors intuitively. In addition, a continuous transition between a continuous deformation and a fractal deformation can be realized. We demonstrate how the fractal deformation technique produces attractive results by showing various examples.

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“…For a more general mathematical description of fractal surfaces based on two variable fractal functions, see Massopust. 32 We shall also consider in Sec. 3.10 the general case of fractal spaces, of which fractal surfaces are the particular 2-dimensional achievement.…”

Section: Fractal Surfacesmentioning

confidence: 99%

From Fractal Objects to Fractal Spaces

1993

Fractal Space-Time and Microphysics

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Fractal surfaces

Cited by 116 publications

References 5 publications

On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

Fractal Deformation Using Displacement Vectors Based on Extended Iterated Shuffle Transformation

From Fractal Objects to Fractal Spaces

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