sagenb.org has made worksheets private, this is part of my notebook on cantor dust

cantor-dust-sage.py

#This goes in one cell alone
 
class Carpet:
  '''
  This class contains the generator for Carpet fractals generated by regular polygons.
  It generates the carpet vertices recursively, which is not very efficient, but it
  goes along with the mathematical definition.
  '''
  def __init__(self, x, y, sides, r, contraction):
    '''
    x, y: Top of the carpet
    sides: number of sides
    r: this parameter is related to the length of the first polygon side
    contraction: Factor of the contraction applied on each step.
    '''
    angle = 2*pi/sides
    self.x = x
    self.y = y
    self.r = r
    self.factor = 1 - contraction
    self.contraction = contraction
    self.polar = [(cos(n*angle), sin(n*angle)) for n in range(sides)]
 
  def _children(self, x, y, radius, step=0):
    if step==0:
      yield (x, y)
 
    else:
      newRadius = self.contraction*radius
      deltaR = self.factor*radius
 
      for dX, dY in self.polar:
        for f in self._children(x + deltaR*dX, y + deltaR*dY, newRadius, step - 1):
          yield f
 
 
  def children(self, steps=0):
    return self._children(self.x, self.y, self.r, steps)
 
 
#This piece of code goes in another cell
sides = 5
contraction = .3
r = 500
 
c = Carpet(0, 0, sides, r, contraction)
 
 
#Copy this in another cell
#Beware, with the above configuration, for more than 6 steps the calculation is very lenghty
#Also, not that cantor dust is perfect (it should look sparse)
#but the point size makes it appear clustered
points = list(c.children(steps=4))
list_plot(points)
 
#And finally, one more cell
#This is more appropiated for dust
list_plot(points, pointsize=2)