Into the Portal: Directable Fractal Self-Similarity

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.