4117.sagews

%cython
def sierpinski(n):
   cdef float t
   GG=[]
   LL=[[1,0]]
   for m in xrange(n):
       t=random()
       if t<(1.0/3.0):
           g=[LL[m][0]/2.0,LL[m][1]/2.0]
       elif ((1.0/3.0)<t) & (t<(2.0/3.0)):
           g=[(LL[m][0]+2.0)/2.0,LL[m][1]/2.0]
       else:
           g=[(LL[m][0]+1.0)/2.0,(LL[m][1]+sqrt(3.0))/2.0]
       LL.append(g)
   return LL

S=sierpinski(500000)
point(S, size=1, axes=false)

%cython
def fernleaf(n):
   cdef float t
   GG=[]
   LL=[[0,0]]
   for m in xrange(n):
       t=random()
       if t<(.01):
           g=[0,.16*LL[m][1]]
       elif ((.01)<=t) & (t<(.86)):
           g=[0.85*LL[m][0]+0.04*LL[m][1], -0.04*LL[m][0]+0.85*LL[m][1]+1.6]
       elif (.86<=t) & (t<.93):
           g=[0.2*LL[m][0]-0.26*LL[m][1], 0.23*LL[m][0]+0.22*LL[m][1]+1.6]
       else:
           g=[-0.15*LL[m][0]+0.28*LL[m][1], 0.26*LL[m][0]+0.24*LL[m][1]+0.44]
       LL.append(g)
   return LL

C=fernleaf(100000)

point(C, size=1, color='green', axes=false)