
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




 
\\ Barnsley fern fractal
\\ 6/17/16 aev
pBarnsleyFern(size,lim)={
my(X=List(),Y=X,x=y=xw=yw=0.0,r);
print(" *** Barnsley Fern, size=",size," lim=",lim);
plotinit(0); plotcolor(0,6); \\green
plotscale(0, -3,3, 0,10); plotmove(0, 0,0);
for(i=1, lim,
  r=random(100);
  if(r<=1, xw=0;yw=0.16*y,
    if(r<=8, xw=0.2*x-0.26*y;yw=0.23*x+0.22*y+1.6,
      if(r<=15, xw=-0.15*x+0.28*y;yw=0.26*x+0.24*y+0.44,
        xw=0.85*x+0.04*y;yw=-0.04*x+0.85*y+1.6)));
  x=xw;y=yw; listput(X,x); listput(Y,y);
);\\fend i
plotpoints(0,Vec(X),Vec(Y));
plotdraw([0,-3,-0]);
}
{\\ Executing:
pBarnsleyFern(530,100000);  \\ BarnsleyFern.png
}
 