Bounds for Iterated Function Systems via Convex Optimization

Intro to IFS

An "Iterated Function System" (IFS) is a mathematical description of a large class of fractal shapes. An IFS consists of a set of "maps" (functions that warp space) that explicitly list the self-similarities of the shape.

For example, the Sierpinski triangle, 4-dragon, and fern below are all typical examples of shapes that can be represented as an IFS.

Sierpinski's fractal triangle 4-fold symmetric fractal Recursive fern fractal

Bounds for IFS

What I present in the program and paper below is a method for computing convex bounding volumes for arbitrary IFS. The method reduces IFS bounding to the well-known problem of convex linear optimization, allowing tight bounding volumes to be produced quickly.

Recursive fern fractal, with bounds


Orion Lawlor, November 15, 2002.
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