new_contents: """Compouting Mandelbrot sets."""
  
  import math
  
  
  def mandel(real, imag):
      """Compute a point inthe Mandelbrot.
  
      The logarithm of number of iterations needed to
      determine whether a complex point is in the
      Mandelbrot set.
  
      Args:
          real: The real coordinate
          imag: The imaginary coordinate
  
      Returns:
          An integer in the range 1-255.
      """
      x = 0
      y = 0
      for i in range(1, 257):
          if x * x + y * y > 4.0:
              break
          xt = real + x * x - y * y
          y = imag * 2.0 * x * y
          x = xt
      return int(math.log(i) * 256 / math.log(256)) - 1
  
  
  def mandelbrot(size_x, size_y):
      """Make a Mandelbrot set image.
  
      Args:
          size_x: Image width
          size_y: Image height
  
      Returns:
          A list of lists of integers in the range 0-255.
      """
      return [[mandel((3.5 * x / size_x) - 2.5,
                      (2.0 * y / size_y) - 1.0)
               for x in range(size_x)]
              for y in range(size_y)]
  
subject: Add Mandelbrot functions