Barnsley fern

Barnsley fern is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A Barnsley fern is a fractal named after British mathematician Michael Barnsley and can be created using an iterated function system (IFS).

The task: create this fractal fern, using the following transformations:

• ƒ1 (chosen 1% of the time)

   xn + 1 = 0
   yn + 1 = 0.16 yn

• ƒ2 (chosen 85% of the time)

   xn + 1 = 0.85 xn + 0.04 yn
   yn + 1 = −0.04 xn + 0.85 yn + 1.6

• ƒ3 (chosen 7% of the time)

   xn + 1 = 0.2 xn − 0.26 yn
   yn + 1 = 0.23 xn + 0.22 yn + 1.6

• ƒ4 (chosen 7% of the time)

   xn + 1 = −0.15 xn + 0.28 yn
   yn + 1 = 0.26 xn + 0.24 yn + 0.44.

Starting position: x = 0, y = 0