
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




10 mode 2:ink 0,0:ink 1,18:randomize time
20 scale=38
30 maxpoints=20000: x=0: y=0
40 for z=1 to maxpoints
50 p=rnd*100
60 if p<=1 then nx=0: ny=0.16*y: goto 100
70 if p<=8 then nx=0.2*x-0.26*y: ny=0.23*x+0.22*y+1.6: goto 100
80 if p<=15 then nx=-0.15*x+0.28*y: ny=0.26*x+0.24*y+0.44: goto 100
90 nx=0.85*x+0.04*y: ny=-0.04*x+0.85*y+1.6
100 x=nx: y=ny
110 plot scale*x+320,scale*y
120 next