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Computer rendering of fractal curves and surfaces

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Loren C. CarpenterAuthors Info & Claims

SIGGRAPH '80: Proceedings of the 7th annual conference on Computer graphics and interactive techniques

Page 109

https://doi.org/10.1145/800250.807478

Published: 01 July 1980 Publication History

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Abstract

Fractals are a class of highly irregular shapes that have myriad counterparts in the real world, such as islands, river networks, turbulence, and snowflakes. Classic fractals include Brownian paths, Cantor sets, and plane-filling curves. Nearly all fractal sets are of fractional dimension and all are nowhere differentiable.

Previously published procedures for calculating fractal curves employ shear displacement processes, modified Markov processes, and inverse Fourier transforms. They are either very expensive or very complex and do not easily generalize to surfaces. This paper presents a family of simple methods for generating and displaying a wide class of fractal curves and surfaces. In so doing, it introduces the concept of statistical subdivision in which a geometric entity is split into smaller entities while preserving certain statistical properties.

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Brown C(2024)Fractal-Related Multiscale Geometric Characterisation of TopographiesCharacterisation of Areal Surface Texture10.1007/978-3-031-59310-9_6(151-180)Online publication date: 1-Jun-2024
https://doi.org/10.1007/978-3-031-59310-9_6
Kalateh FKheiry M(2023)A Review of Stochastic Analysis of the Seepage Through Earth Dams with a Focus on the Application of Monte Carlo SimulationArchives of Computational Methods in Engineering10.1007/s11831-023-09972-331:1(47-72)Online publication date: 17-Jul-2023
https://doi.org/10.1007/s11831-023-09972-3
Gowanlock J(2019)Promoting Computer Graphics Research: The Tech Demos of SIGGRAPHAnimation and Advertising10.1007/978-3-030-27939-4_14(267-281)Online publication date: 18-Dec-2019
https://doi.org/10.1007/978-3-030-27939-4_14
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Index Terms

Computer rendering of fractal curves and surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Preliminary papers to be published in Communications of the ACM

Fractals are a class of highly irregular shapes that have myriad counterparts in the real world, such as islands, river networks, turbulence, and snowflakes. Classic fractals include Brownian paths, Cantor sets, and plane-filling curves. Nearly all ...
Computer rendering of fractal curves and surfaces

Fractals are a class of highly irregular shapes that have myriad counterparts in the real world, such as islands, river networks, turbulence, and snowflakes. Classic fractals include Brownian paths, Cantor sets, and plane-filling curves. Nearly all ...
Positive blending Hermite rational cubic spline fractal interpolation surfaces

Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed ...

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Published In

SIGGRAPH '80: Proceedings of the 7th annual conference on Computer graphics and interactive techniques

July 1980

336 pages

ISBN:0897910214

DOI:10.1145/800250

ACM SIGGRAPH Computer Graphics Volume 14, Issue 3
July 1980
327 pages
ISSN:0097-8930
DOI:10.1145/965105
Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1980

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SIGGRAPH '80 Paper Acceptance Rate 52 of 140 submissions, 37%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

View all

Brown C(2024)Fractal-Related Multiscale Geometric Characterisation of TopographiesCharacterisation of Areal Surface Texture10.1007/978-3-031-59310-9_6(151-180)Online publication date: 1-Jun-2024
https://doi.org/10.1007/978-3-031-59310-9_6
Kalateh FKheiry M(2023)A Review of Stochastic Analysis of the Seepage Through Earth Dams with a Focus on the Application of Monte Carlo SimulationArchives of Computational Methods in Engineering10.1007/s11831-023-09972-331:1(47-72)Online publication date: 17-Jul-2023
https://doi.org/10.1007/s11831-023-09972-3
Gowanlock J(2019)Promoting Computer Graphics Research: The Tech Demos of SIGGRAPHAnimation and Advertising10.1007/978-3-030-27939-4_14(267-281)Online publication date: 18-Dec-2019
https://doi.org/10.1007/978-3-030-27939-4_14
Della-Bosca DPatterson DRoberts S(2017)An analysis of game environments as measured by fractal complexityProceedings of the Australasian Computer Science Week Multiconference10.1145/3014812.3014877(1-6)Online publication date: 30-Jan-2017
https://dl.acm.org/doi/10.1145/3014812.3014877
Normant FTricot C(2010)Fractal Simplification of Lines Using Convex HullsGeographical Analysis10.1111/j.1538-4632.1993.tb00284.x25:2(118-129)Online publication date: 3-Sep-2010
https://doi.org/10.1111/j.1538-4632.1993.tb00284.x
Teoh S(2009)RiverLandProceedings of the 5th International Symposium on Advances in Visual Computing: Part I10.1007/978-3-642-10331-5_44(468-479)Online publication date: 26-Nov-2009
https://dl.acm.org/doi/10.1007/978-3-642-10331-5_44
Teoh S(2008)Algorithms for the Automatic Design of Non-formal Urban ParksProceedings of the 4th International Symposium on Advances in Visual Computing, Part II10.1007/978-3-540-89646-3_105(1056-1065)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1007/978-3-540-89646-3_105
Zheng HYe ZLei YLiu X(2007)Fractal properties of interpolatory subdivision schemes and their application in fractal generationChaos, Solitons & Fractals10.1016/j.chaos.2005.10.07532:1(113-123)Online publication date: Apr-2007
https://doi.org/10.1016/j.chaos.2005.10.075
Gervautz MTraxler C(1996)Representation and realistic rendering of natural phenomena with cyclic CSG graphsThe Visual Computer10.1007/BF0178210512:2(62-74)Online publication date: Feb-1996
https://doi.org/10.1007/BF01782105
Jampala S(1992)Fractals: classification, generation and applications[1992] Proceedings of the 35th Midwest Symposium on Circuits and Systems10.1109/MWSCAS.1992.271120(1024-1027)Online publication date: 1992
https://doi.org/10.1109/MWSCAS.1992.271120
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Computer rendering of fractal curves and surfaces

Computer rendering of fractal curves and surfaces

Positive blending Hermite rational cubic spline fractal interpolation surfaces