Frieze and wallpaper chaotic attractors with a polar spin

Carter, Nathan C.; Grimes, Stephen; Reiter, Clifford A.

doi:10.1016/s0097-8493(98)00097-1

Cited by 12 publications

(4 citation statements)

References 2 publications

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“…We also employ this scheme to color attractors. For more details of the scheme, please refer to [2][3][4][5][11][12][13].…”

Section: Examples and Implementsmentioning

confidence: 99%

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Automatic Generation of Chaotic Attractors with Various Cyclic or Dihedral Symmetries

Wang¹,

Yan²,

Ouyang³

2014

TOCSJ

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Chaotic attractors are created by iterating functions that are equivariant with respect to the cyclic or dihedral groups. An improved color scheme based on the visit frequency of the pixels is proposed to render chaotic attractors. By normalization and scale transformation, aesthetic patterns which simultaneously have several kinds of cyclic or dihedral symmetries are generated. This method can be used to yield a great number of aesthetic patterns automatically.

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“…We also employ this scheme to color attractors. For more details of the scheme, please refer to [2][3][4][5][11][12][13].…”

Section: Examples and Implementsmentioning

confidence: 99%

“…It is surprising that chaotic attractor is compatible with symmetry. Automatic generation of symmetrical patterns has been an active topic of recent study [2][3][4][5][6][7]. There are many methods dedicated to yield patterns with cyclic or dihedral symmetry.…”

Section: Introductionmentioning

confidence: 99%

Automatic Generation of Chaotic Attractors with Various Cyclic or Dihedral Symmetries

Wang¹,

Yan²,

Ouyang³

2014

TOCSJ

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“…"Whirlpools" in style and concept can be described as the nearest relation to our work here. In turn, these artworks inspired many studies devoted to the creation of computer-generated spiral patterns [6,8,11,27,28,35]. However, although spiral tilings are very decorative, there is extremely little mathematical literature on the subject (as against studies of the spiral itself), as first pointed out by Grünbaum and Shephard [13], which might otherwise have been thought studied much more than has happened.…”

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confidence: 99%

“…Fig.5Examples of spiral tilings of: a G 0.2(12,6), b G 0.4(12,6), c G 0.3(15,3), d G 0.3(15,5), e G 0.25(8, 4), f G 0.25(16, 4) symmetry…”

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confidence: 99%

Generation of advanced Escher-like spiral tessellations

et al. 2021

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In this paper, using both hand-drawn and computer-drawn graphics, we establish a method to generate advanced Escher-like spiral tessellations. We first give a way to achieve simple spiral tilings of cyclic symmetry. Then, we introduce several conformal mappings to generate three derived spiral tilings. To obtain Escher-like tessellations on the generated tilings, given pre-designed wallpaper motifs, we specify the tessellations’ implementation details. Finally, we exhibit a rich gallery of the generated Escher-like tessellations. According to the proposed method, one can produce a great variety of exotic Escher-like tessellations that have both good aesthetic value and commercial potential.

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Integer and Fractional Order Chaotic Systems—A Review

Gugapriya

Akilandeswari

2023

Futuristic Communication and Network Technologies

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Frieze and wallpaper chaotic attractors with a polar spin

Cited by 12 publications

References 2 publications

Automatic Generation of Chaotic Attractors with Various Cyclic or Dihedral Symmetries

Automatic Generation of Chaotic Attractors with Various Cyclic or Dihedral Symmetries

Generation of advanced Escher-like spiral tessellations

Integer and Fractional Order Chaotic Systems—A Review

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