p=0.01 Stem
p=0.85 Main frond
p=0.07 Left
p=0.07 Right
How it works: Four affine transformations are applied randomly with fixed probabilities.
The attractor of this IFS (Iterated Function System) is the fern shape — regardless of starting point.
Discovered by Michael Barnsley (1988), it shows how complex natural forms arise from simple repeated rules.
The main body (p=0.85) compresses and rotates; the two small transforms make the side leaflets;
the rare transform (p=0.01) draws the stem.