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Into the Portal: Directable Fractal Self-Similarity

Published: 13 July 2024 Publication History

Abstract

We present a novel, directable method for introducing fractal self-similarity into arbitrary shapes. Our method allows a user to directly specify the locations of self-similarities in a Julia set, and is general enough to reproduce other well-known fractals such as the Koch snowflake. Ours is the first algorithm to enable this level of general artistic control while also maintaining the character of the original fractal shape. We introduce the notion of placing “portals” in the iteration space of a dynamical system, bridging the aesthetics of iterated maps with the fine-grained control of iterated function systems (IFS). Our method is effective in both 2D and 3D.

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  1. Into the Portal: Directable Fractal Self-Similarity

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    cover image ACM Conferences
    SIGGRAPH '24: ACM SIGGRAPH 2024 Conference Papers
    July 2024
    1106 pages
    ISBN:9798400705250
    DOI:10.1145/3641519
    This work is licensed under a Creative Commons Attribution-ShareAlike International 4.0 License.

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    Published: 13 July 2024

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    Author Tags

    1. Julia set shape control
    2. Shape Modulus Julia sets
    3. iterated maps

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