IFStile – Iterated Function Systems – visualize substitution tilings

Last Updated on April 4, 2021

One of the ways to generate fractals is using the Iterated Function System (IFS).

In mathematical terms the system is a finite set of contraction maps w_i for i=1, 2, …, N, each with a contractivity factor s<1, which map a compact metric space onto itself. It’s the basis for fractal image compression techniques.

IFS fractals, as they are known, can be of any number of dimensions, but are often calculated and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence “function system”). The canonical example is the Sierpiński triangle. Substitution tilings are great source of fractal shapes, due to their recursive nature. This method can generate regular-looking fractals as well as non-geometric fractals.

IFSs were conceived in their present form by John E. Hutchinson and popularized by Michael Barnsley’s book Fractals Everywhere.

IFStile is software that generates fractals using the Iterated Function System.


This is freeware software so if you’re hoping to get your hands on the source code, you’re in for a disappointment.

The developer provides a 2.2MB binary tarball for Linux. And there’s binaries for Windows and macOS as well. There’s nothing noteworthy to report when installing the software. Let’s crack on.

Next page: Page 2 – In Operation

Pages in this article:
Page 1 – Introduction / Installation
Page 2 – In Operation
Page 3 – Other Features
Page 4 – Summary

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