# 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 BarnsleyFern 2013-03-22 16:05:33 2013-03-22 16:05:33 paolini (1187) paolini (1187) 7 paolini (1187) Example msc 28A80