for: iOSmacOS

Explore an alternate universe of beautiful fractal shapes.

Press the play button to watch an ever-changing stream of art that has never been seen before and may never be seen again. Or drag, pinch and rotate to gently morph the image yourself. It's like finger-painting with fractals.

Download from the App Store



What are fractals?

First, note that TeraFractal was designed to be fun to play with no matter how little or how much you know about fractals. But fractal math is also very interesting.

Fractals are geometric objects with two important properties. First, they are "self-similar," which means that smaller parts of the fractal look like the larger whole. Second, they have an infinite amount of detail, no matter how far you zoom in. If you were to zoom in on the fractal forever, you would continue to see detailed shapes, each resembling the original whole. When you adjust any component of a fractal, you alter the entire structure at every scale. This is why all of the gestures you perform in TeraFractal affect the whole image, even though you are pushing or pulling or pinching or twisting just one part of the fractal.

Amazingly, every fractal in TeraFractal can be described by just 24 numbers. When you move your fingers on the screen, you are adjusting these parameters.


How does it work?

TeraFractal displays fractal images by "playing" what's known as the Chaos game. Each fractal is defined by a set of transformations that encode location, rotation, scale, and color. TeraFractal randomly chooses one of these transformations and applies it to a starting point, which it plots on-screen. The algorithm then iteratively repeats this process hundreds of thousands of times until the fractal image becomes clear. TeraFractal can perform the entire rendering process more than 20 times per second.

For more information on the mathematics and algorithms behind iterated function systems, see: Devaney, 1992, A First Course in Chaotic Dynamical Systems.




Email questions and great fractals to: robin@matheasel.com



TeraFractal for Mac

TeraFractal is also available for macOS.