Design Fractal Art On The Supercomputer In Your Pocket

Frax, a new iOS app, leverages the computational oomph in your new iPhone to make dizzying detailed mathematical art.

Fractals are deeply weird: They’re mathematical objects whose infinite “self-similarity” means that you can zoom into them forever and keep seeing the same features over and over again. Famous fractal patterns like the Mandelbrot set tend to get glossed over by the general public as neato screensavers and not much else, but now a new iOS app called Frax is attempting to bridge that gap.


Frax, to its credit, leans right into the “ooh, neat colors!” aspect of fractal math. The twist is that the formidable processing horsepower in current iPhones and iPads allows Frax to display and manipulate these visual patterns in dizzying detail–far beyond the superficial treatment of, say, a screensaver. “The iPhone was the first mobile device to have the horsepower to do realtime graphics like this, so we saw the opportunity to bring the visual excitement of fractals to a new medium, and in a new style,” says Ben Weiss, who created Frax with UI guru Kai Krause and Tom Beddard (a designer we’ve written about before). “As the hardware has improved, the complexity of the app has grown exponentially, as has its performance.” Frax lets you pan, zoom, and animate fractal art–plus play with elaborate 3-D and lighting effects.

Weiss says that he, Krause, and Beddard “intentionally hid all the numerical inputs and math under the hood, but I definitely hope that some will get as hooked on the mathematical side of it, as I did, and develop the interest to start exploring the science and technology behind the app.”

That technology had some interesting user-experience consequences for the app. For one, you can’t infinitely zoom into any fractals in Frax because eventually the iPhone’s 64-bit chip won’t be able to distinguish the position of one pixel from another. “Frax intentionally stops zooming before it hits this wall, to prevent the image from degrading into blocky pixels,” says Weiss, but adds that certain mathematical sets in the app don’t tax the chip as much and “can be zoomed perpetually.” He and Beddard also created a “ceiling” for the zooming effect–pull too far out, and the Frax logo appears to remind you to turn around. “If you were to keep zooming out, the fractal would shrink down to an invisible point and you’d never find it again,” he explains. “All the interesting stuff tends to happen when you zoom in, so that’s what we try to encourage.”

Frax offers a paid upgrade which unlocks hundreds of visual parameters to play with, as well as access to Frax’s own cloud-based render farm (for outputting your mathematical masterpieces at 50-megapixel resolution). Whether you use Frax to meditate, doodle, or play with actual math, the app stands as a surprising reminder of just how supercomputer-like our smartphones have become. If Frax occasionally reminds you to be awed by that fact instead of indifferent or annoyed, it’ll have done you a valuable service.

[Check out Frax]


About the author

John Pavlus is a writer and filmmaker focusing on science, tech, and design topics. His writing has appeared in Wired, New York, Scientific American, Technology Review, BBC Future, and other outlets.