Nature · Study 040
Barnsley Fern
A fern frond appears point by point as four simple transformations are applied at random. The Barnsley fern, plotted 54,000 dots a second.
What you're looking at
Start with a single point. Pick one of four affine maps at random, with fixed odds, and apply it to get the next point. One map draws the stem, one copies the whole frond slightly smaller and rotated, and two produce the lowest pair of leaflets. Plot every point and the fern emerges from the noise.
The idea behind it
Michael Barnsley published this construction in the 1980s as an example of an iterated function system. Its lesson is about compression: an image with detail at every scale can be stored as a handful of numbers, if the image is made of smaller copies of itself.
Try this
Click or tap to regrow the fern with a slightly different curl.
