Barnsley fern

The Barnsley fern $F$ is the only non-empty compact subset of $\mathbb{R}^{2}$ satisfying the relation

F=\bigcup_{i=1}^{4}T_{i}(F)

where $T_{i}\colon\mathbb{R}^{2}\to\mathbb{R}^{2}$ are the following linear mappings:

	$\displaystyle T_{1}(x,y)$	$\displaystyle=(0.85x+0.04y,-0.04x+0.85y+1.6),$
	$\displaystyle T_{2}(x,y)$	$\displaystyle=(0.2x-0.26y,0.23x+0.22y+1.6),$
	$\displaystyle T_{3}(x,y)$	$\displaystyle=(-0.15x+0.28y,0.26x+0.24y+0.44),$
	$\displaystyle T_{4}(x,y)$	$\displaystyle=(0,0.16y).$

Title	Barnsley fern
Canonical name	BarnsleyFern
Date of creation	2013-03-22 16:05:33
Last modified on	2013-03-22 16:05:33
Owner	paolini (1187)
Last modified by	paolini (1187)
Numerical id	7
Author	paolini (1187)
Entry type	Example
Classification	msc 28A80