Barnsley fern

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

$$F=\bigcup _{i=1}^4{T}_i(F)$$

where $T_i:{ℝ}^2\to {ℝ}^2$ are the following linear mappings:

$T_1(x,y)$$=(0.85x+0.04y,-0.04x+0.85y+1.6),$

$T_2(x,y)$$=(0.2x-0.26y,0.23x+0.22y+1.6),$

$T_3(x,y)$$=(-0.15x+0.28y,0.26x+0.24y+0.44),$

$T_4(x,y)$$=(0,0.16y).$