Michael Barnsleyborn 1946
Iterated function system
British mathematician known for iterated function systems and the Barnsley fern, where a few affine transformations grow a lifelike leaf.
Barnsley Fern
Four affine maps, chosen at random, iterate a point. The attractor is a fern: self-similar fronds from a handful of matrices.
About this pattern
Michael Barnsley, 1988
Barnsley’s IFS: four affine maps, applied at random (1% stem, 85% leaflet, 7% left leaflet, 7% right). The attractor is a fern because the maps are the fern’s own self-similarities, the same trick nature uses in fronds and blood vessels. Motion plays the chaos game in order: points land, the frond densifies, then the sequence recedes.
Behind the mathematics