“Into the Portal: Directable Fractal Self-Similarity” – ACM SIGGRAPH HISTORY ARCHIVES

“Into the Portal: Directable Fractal Self-Similarity”

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Title:

    Into the Portal: Directable Fractal Self-Similarity

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Abstract:


    We present a novel method to create self-similar fractals from arbitrary input shapes. Our method introduces “portals” into an iterated map, allowing for user placement of self-similarities and bridging the aesthetics of iterated maps with the fine-grained control of iterated function systems (IFS) in both 2D and 3D.

References:


    [1]
    Michael Barnsley. 2014. Fractals everywhere (2nd ed.). Academic Press.

    [2]
    Michael F Barnsley, Arnaud Jacquin, Francois Malassenet, Laurie Reuter, and Alan D Sloan. 1988. Harnessing chaos for image synthesis. In Proceedings of SIGGRAPH. 131?140.

    [3]
    Stephen Demko, Laurie Hodges, and Bruce Naylor. 1985. Construction of Fractal Objects with Iterated Function Systems. In Proceedings of SIGGRAPH. 271?278.

    [4]
    Adrien Douady, John Hamal Hubbard, and Pierre Lavaurs. 1984. Etude dynamique des polyn?mes complexes. Universit? de Paris-Sud, D?p. de Math?matique Orsay, France.

    [5]
    Nour Fakharany. 2023. Jim Denevan?s Monumental Land Art Debutes in Abu Dhabi. ArchDaily (Nov. 2023).

    [6]
    Robert W Fathauer. 2005. Fractal tilings based on dissections of polyhexes. In Proceedings of Bridges. 427?434.

    [7]
    Pierre Fatou. 1917. Sur les substitutions rationnelles. Comptes Rendus de l?Acad?mie des Sciences de Paris 164 (1917), 806?808.

    [8]
    David Fincher. 1999. Fight Club.

    [9]
    Carolyn Giardina. 2017. ?Guardians of the Galaxy Vol. 2?: A Digital Kurt Russell and Other VFX Tricks Revealed. The Hollywood Reporter (May 2017).

    [10]
    John C Hart, Daniel J Sandin, and Louis H Kauffman. 1989. Ray tracing deterministic 3-D fractals. In Proceedings of SIGGRAPH. 289?296.

    [11]
    Stephen Hawking. 2009. A brief history of time: from big bang to black holes. Random House.

    [12]
    David Hutchins, Olun Riley, Jesse Erickson, Alexey Stomakhin, Ralf Habel, and Michael Kaschalk. 2015. Big Hero 6: into the portal. In SIGGRAPH Talks. 1?1.

    [13]
    Pentti J?rvi. 1997. Not all Julia sets are quasi-self-similar. Proc. Amer. Math. Soc. 125, 3 (1997), 835?838.

    [14]
    Tao Ju, Frank Losasso, Scott Schaefer, and Joe Warren. 2002. Dual contouring of hermite data. In Proceedings of SIGGRAPH. 339?346.

    [15]
    Gaston Julia. 1918. M?moire sur l?it?ration des fonctions rationnelles. J. Math. Pures Appl. 8 (1918), 47?245.

    [16]
    Craig S. Kaplan and David H. Salesin. 2000. Escherization. In Proceedings of SIGGRAPH. 499?510.

    [17]
    Theodore Kim. 2015. Quaternion Julia Set Shape Optimization. In Proceedings of the Eurographics Symposium on Geometry Processing. 167?176.

    [18]
    HV Koch. 1904. Sur une courbe continue sans tangente, obtenue par une construction g?om?trique ?l?mentaire. Arkiv for Matematik, Astronomi och Fysik 1 (1904), 681?704.

    [19]
    Tan Lei. 1990. Similarity between the Mandelbrot set and Julia sets. Communications in mathematical physics 134 (1990), 587?617.

    [20]
    Shih-Syun Lin, Charles C Morace, Chao-Hung Lin, Li-Fong Hsu, and Tong-Yee Lee. 2017. Generation of escher arts with dual perception. IEEE transactions on visualization and computer graphics 24, 2 (2017), 1103?1113.

    [21]
    Kathryn Lindsey and Malik Younsi. 2019. Fekete polynomials and shapes of Julia sets. Trans. Amer. Math. Soc. 371, 12 (2019), 8489?8511.

    [22]
    Kathryn A. Lindsey. 2014. Shapes of polynomial Julia sets. Ergodic Theory and Dynamical Systems 35, 6 (Aug 2014), 1913?1924. https://doi.org/10.1017/etds.2014.8

    [23]
    Benoit B Mandelbrot. 1980. Fractal aspects of the iteration of z? ? z (1-z) for complex ? and z. Annals of the New York Academy of Sciences 357, 1 (1980), 249?259.

    [24]
    Benoit B Mandelbrot. 1982. The fractal geometry of nature. Vol. 1. WH Freeman.

    [25]
    Karl Menger. 1928. Dimensionstheorie: Karl Menger. Springer.

    [26]
    Paul Merrell. 2023. Example-Based Procedural Modeling Using Graph Grammars. ACM Trans. Graph. 42, 4, Article 60 (jul 2023), 16 pages.

    [27]
    Yuichi Nagata and Shinji Imahori. 2023. Creation of Dihedral Escher-like Tilings Based on As-Rigid-As-Possible Deformation. ACM Trans. Graph. (dec 2023).

    [28]
    Alan Norton. 1982. Generation and display of geometric fractals in 3-D. ACM SIGGRAPH Computer Graphics 16, 3 (July 1982), 61?67.

    [29]
    Peichang Ouyang, Kwok Wai Chung, Alain Nicolas, and Krzysztof Gdawiec. 2021. Self-Similar Fractal Drawings Inspired by M. C. Escher?s Print Square Limit. ACM Trans. Graph. 40, 3, Article 31 (jul 2021), 34 pages.

    [30]
    Peichang Ouyang and Robert W Fathauer. 2014. Beautiful math, part 2: aesthetic patterns based on fractal tilings. IEEE Computer Graphics and applications 34, 1 (2014), 68?76.

    [31]
    Peichang Ouyang, Krzysztof Gdawiec, Alain Nicolas, David Bailey, and Kwok Wai Chung. 2022. Interlocking Spiral Drawings Inspired by M. C. Escher?s Print Whirlpools. ACM Trans. Graph. 42, 2, Article 18 (nov 2022), 17 pages.

    [32]
    Ken Perlin. 1985. An image synthesizer. Proceedings of SIGGRAPH 19, 3 (1985), 287?296.

    [33]
    Przemyslaw Prusinkiewicz and Aristid Lindenmayer. 2012. The algorithmic beauty of plants. Springer Science & Business Media.

    [34]
    Jason Sanders and Edward Kandrot. 2010. CUDA by example: an introduction to general-purpose GPU programming. Addison-Wesley Professional.

    [35]
    Alexa Schor and Theodore Kim. 2023. A Shape Modulus for Fractal Geometry Generation. In Proceedings of the Eurographics Symposium on Geometry Processing. 9 pages.

    [36]
    Peter Wonka, Michael Wimmer, Fran?ois Sillion, and William Ribarsky. 2003. Instant Architecture. ACM Trans. Graph. 22, 3 (jul 2003), 669?677.


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