Fractal-based algorithmic design of Chinese ice-ray lattices

Rian, Iasef Md

doi:10.1016/j.foar.2021.10.010

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…The second goal of this study is to discover some properties of the new Sierpinski circle model. The result of this study also has a wide social value, especially in consideration of how Sierpinski models, or fractal geometry as a whole, have been widely adopted in material science, computer modelling, chemistry, physics, and architecture [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Study of Sierpinski Fractals Based on Regular Polygons and Circles

Tang,

Yu,

Yan

2024

JAMC

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This paper studied the properties of Sierpinski fractals based on regular polygons and circles. Dilation is adopted as the basic principle to generate "perfect Sierpinski polygons" and "perfect Sierpinski circles"-defined as having neither overlap nor detachment among sub-shapes. The ideal contraction ratios for some regular polygons to become perfect Sierpinski polygons are calculated using trigonometry. A general formula is further derived by making a connection between perfect Sierpinski polygons and Sierpinski circles. A brief exploration is conducted of the Sierpinski circle model, from which some interesting properties are revealed, like the segregation of shapes. Based on these properties, a general formula to calculate the radius of the nth layer of sub-circles within one stage of iteration is derived. Lastly, the connection between the two Sierpinski models is discussed based on the limitations and implications of this study. Future researchers are recommended to dive deeper into the properties of Sierpinski travel and its relationship with other Sierpinski models.

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Section: Introductionmentioning

confidence: 99%

A Study of Sierpinski Fractals Based on Regular Polygons and Circles

Tang,

Yu,

Yan

2024

JAMC

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“…Currently, there is a lot of literature applying fractal theory to modern design. A Laubsted explored the mathematical logic behind fractal geometry and fractal art [3]. JZ Zhang et al used fractal geometric methods to analyze traditional furniture shapes and decorative arts, and concluded a design method applicable to furniture shapes in practice [4].…”

Section: Introductionmentioning

confidence: 99%

The Revitalization Design of Regional Ethnic Cultural Capital in a Sustainable Perspective: The Case of Traditional Chinese Garment Yunjian

et al. 2022

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The formation of the globalization pattern of regional ethnic culture brings new opportunities for the sustainable development of cultural capital. In order to solve the problem of mismatch between the high development demand of regional ethnic costumes and their traditional design methods, this study proposes an innovative design method for regional ethnic traditional costumes, taking the Yunjian, a cloud-shaped sash-like shoulder garment as an example. Firstly, we deeply explored the historical and cultural connotation of the Yunjian through fieldwork and literature research. Then we sorted out and refined its elements, colors and structural features. We classified the patterns according to the composition forms and clarified the path of pattern creation based on fractal theory. We combined the representative elements of Yunjian with the fractal algorithm and proposed the design model of Yunjian fractal pattern. Finally we verified the feasibility of the proposed design method through design practice. The results show that the Yunjian garment created by the method of this paper can better reflect the characteristics of fashion art and ethnic culture.

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Design of Random and Deterministic Fractal Surfaces from Voronoi Cells

Rodríguez-Cuadrado,

San Martín

2024

Computer-Aided Design

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Fractal-based algorithmic design of Chinese ice-ray lattices

Cited by 6 publications

References 15 publications

A Study of Sierpinski Fractals Based on Regular Polygons and Circles

A Study of Sierpinski Fractals Based on Regular Polygons and Circles

The Revitalization Design of Regional Ethnic Cultural Capital in a Sustainable Perspective: The Case of Traditional Chinese Garment Yunjian

Design of Random and Deterministic Fractal Surfaces from Voronoi Cells

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