Difference between revisions of "Barnsley fern"

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Latest revision as of 21:08, 11 October 2019

This page is a solution to the task Barnsley fern in the Rosetta Code, written in Fōrmulæ.

Description (from Rosetta Code)

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

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

Solution

BarnsleyFernCode.png

BarnsleyFernCase01.png