gistfile1.py

from math import *

# settings

n = 4

radii = [1/2.0 * sqrt((2.0 ** i - 1) / (2.0 ** n - 1)) for i in range(1, n + 1)]

# calculate bezier

a = 2 * pi / n ** 2

x = 8/3.0 * ( cos(a/2) - 1/8.0 * cos(a) - 1/2.0 )
y = ( cos(a) - x ) / tan(a) + sin(a)
dx = x - cos(a)
dy = y - sin(a)
d = sqrt(dx ** 2 + dy ** 2)

# render crazy shapes

class Shape:
  def __init__(self, a, r1, r2):
    self.path = []
    v1, v2, v3, v4 = self.verts(a)
    self.path.append( "L %s" % self.scaled(r2, (v1,)) )
    self.r = [r1, r1, r2]

  def __str__(self):
    path = " ".join(self.path)
    return '<path d="%s" fill="black" />\n' % path

  def extend(self, r1):
    self.r[1] = r1

  def advance(self, a):
    r0, r1, r2 = self.r
    v1, v2, v3, v4 = self.verts(a)
    self.path.append( "C %s" % self.scaled(r2, (v2, v3, v4)) )
    if r1 < r0:
      self.path.insert( 0, "L %s" % self.scaled(r0, (v1,)) )
    if r1 != 0:
      self.path.insert( 0, "C %s" % self.scaled(r1, (v3, v2, v1)) )
    self.r[0] = r1

  def close(self):
    self.path.append("Z")
    self.path.insert(0, "M 0 0")

  def scaled(self, s, va):
    list = []
    for x, y in va:
      list.append( "%s %s" % (s * x, s * y) )
    return " ".join(list)

  def verts(self, a):
    a = pi / 2.0 + pi / 2 ** n - angle
    b = pi / 2.0 - pi / 2 ** n - angle
    v1 = ( cos(a), -sin(a) )
    v2 = ( cos(a) + d * sin(a), -sin(a) + d * cos(a) )
    v3 = ( cos(b) - d * sin(b), -sin(b) - d * cos(b) )
    v4 = ( cos(b), -sin(b) )
    return v1, v2, v3, v4

elements = []
shapes = (n + 1) * [None]

for i in range(1, 2 ** n + 1):
  angle = 2 * pi * i / (2 ** n)
  if not shapes[0]:
    if not shapes[1]:
      shapes[0] = Shape(a, 0, radii[0])
    else:
      shapes[0] = shapes[1]
      shapes[0].extend(0);
  else:
    shapes[0].close()
    elements.append( str(shapes[0]) )
    shapes[0] = None
    for j in range(1, n):
      if not shapes[j]:
        if not shapes[j + 1]:
          shapes[j] = Shape(a, radii[j - 1], radii[j])
        else:
          shapes[j] = shapes[j + 1]
          shapes[j].extend(radii[j - 1])
        break
      shapes[j] = None
  for shape in set(shapes):
    if shape: shape.advance(a)

# ...to a document

print """<?xml version="1.0"?>
<svg xmlns="http://www.w3.org/2000/svg" version="1.2" baseProfile="tiny"
  viewBox="-1 -1 2 2">

  <desc></desc>

  %s
</svg>""" % "  ".join(elements)