content: """create chaosgame-like fractals
  Copyright (C) 2005 Carl Friedrich Bolz
  
  adapted by @arshajii for Hercules
  """
  
  import math
  import random
  import sys
  import time
  
  DEFAULT_THICKNESS = 1.0
  DEFAULT_WIDTH = 2048 #256
  DEFAULT_HEIGHT = 2048 #256
  DEFAULT_ITERATIONS = 1000000 #5000
  DEFAULT_RNG_SEED = 1234
  
  
  class GVector(object):
      x: float
      y: float
      z: float
  
      def __init__(self, x=0, y=0, z=0):
          self.x = x
          self.y = y
          self.z = z
  
      def Mag(self):
          return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
  
      def dist(self, other):
          return math.sqrt((self.x - other.x) ** 2
                           + (self.y - other.y) ** 2
                           + (self.z - other.z) ** 2)
  
      def __add__(self, other):
          if not isinstance(other, GVector):
              raise ValueError("Can't add GVector to " + str(type(other)))
          v = GVector(self.x + other.x, self.y + other.y, self.z + other.z)
          return v
  
      def __sub__(self, other):
          return self + other * -1
  
      def __mul__(self, other):
          v = GVector(self.x * other, self.y * other, self.z * other)
          return v
      #__rmul__ = __mul__
  
      def linear_combination(self, other, l1, l2=None):
          if l2 is None:
              l2 = 1 - l1
          v = GVector(self.x * l1 + other.x * l2,
                      self.y * l1 + other.y * l2,
                      self.z * l1 + other.z * l2)
          return v
  
      #def __str__(self):
      #    return "<%f, %f, %f>" % (self.x, self.y, self.z)
  
      #def __repr__(self):
      #    return "GVector(%f, %f, %f)" % (self.x, self.y, self.z)
  
  
  class Spline(object):
      """Class for representing B-Splines and NURBS of arbitrary degree"""
      knots: List[int]
      degree: int
      points: List[GVector]
  
      def __init__(self, points, degree, knots):
          """Creates a Spline.
          points is a list of GVector, degree is the degree of the Spline.
          """
          if len(points) > len(knots) - degree + 1:
              raise ValueError("too many control points")
          elif len(points) < len(knots) - degree + 1:
              raise ValueError("not enough control points")
          last = knots[0]
          for cur in knots[1:]:
              if cur < last:
                  raise ValueError("knots not strictly increasing")
              last = cur
          self.knots = knots
          self.points = points
          self.degree = degree
  
      def GetDomain(self):
          """Returns the domain of the B-Spline"""
          return (self.knots[self.degree - 1],
                  self.knots[len(self.knots) - self.degree])
  
      def __call__(self, u):
          """Calculates a point of the B-Spline using de Boors Algorithm"""
          dom = self.GetDomain()
          if u < dom[0] or u > dom[1]:
              raise ValueError("Function value not in domain")
          if u == dom[0]:
              return self.points[0]
          if u == dom[1]:
              return self.points[-1]
          I = self.GetIndex(u)
          d = [self.points[I - self.degree + 1 + ii]
               for ii in range(self.degree + 1)]
          U = self.knots
          for ik in range(1, self.degree + 1):
              for ii in range(I - self.degree + ik + 1, I + 2):
                  ua = U[ii + self.degree - ik]
                  ub = U[ii - 1]
                  co1 = (ua - u) / (ua - ub)
                  co2 = (u - ub) / (ua - ub)
                  index = ii - I + self.degree - ik - 1
                  d[index] = d[index].linear_combination(d[index + 1], co1, co2)
          return d[0]
  
      def GetIndex(self, u):
          dom = self.GetDomain()
          for ii in range(self.degree - 1, len(self.knots) - self.degree):
              if u >= self.knots[ii] and u < self.knots[ii + 1]:
                  I = ii
                  break
          else:
              I = dom[1] - 1
          return I
  
      def __len__(self):
          return len(self.points)
  
      #def __repr__(self):
      #    return "Spline(%r, %r, %r)" % (self.points, self.degree, self.knots)
  
  
  def write_ppm(im, filename):
      magic = 'P6\n'
      maxval = 255
      w = len(im)
      h = len(im[0])
  
      #with open(filename, "w", encoding="latin1", newline='') as fp:
      with open(filename, "w") as fp:
          fp.write(magic)
          #fp.write('%i %i\n%i\n' % (w, h, maxval))
          fp.write(f'{w} {h}\n{maxval}\n')
          for j in range(h):
              for i in range(w):
                  val = im[i][j]
                  c = val * 255
                  #fp.write('%c%c%c' % (c, c, c))
                  c = chr(c)
                  fp.write(f'{c}{c}{c}')
  
  
  class Chaosgame(object):
      splines: List[Spline]
      thickness: float
      minx: float
      miny: float
      maxx: float
      maxy: float
      height: float
      width: float
      num_trafos: List[int]
      num_total: int
  
      def __init__(self, splines, thickness=0.1):
          self.splines = splines
          self.thickness = thickness
          self.minx = min([p.x for spl in splines for p in spl.points])
          self.miny = min([p.y for spl in splines for p in spl.points])
          self.maxx = max([p.x for spl in splines for p in spl.points])
          self.maxy = max([p.y for spl in splines for p in spl.points])
          self.height = self.maxy - self.miny
          self.width = self.maxx - self.minx
          self.num_trafos = []
          maxlength = thickness * self.width / self.height
          for spl in splines:
              length = 0.
              curr = spl(0)
              for i in range(1, 1000):
                  last = curr
                  t = 1 / 999 * i
                  curr = spl(t)
                  length += curr.dist(last)
              self.num_trafos.append(max(1, int(length / maxlength * 1.5)))
          self.num_total = sum(self.num_trafos)
  
      def get_random_trafo(self):
          r = random.randrange(int(self.num_total) + 1)
          l = 0
          for i in range(len(self.num_trafos)):
              if r >= l and r < l + self.num_trafos[i]:
                  return i, random.randrange(self.num_trafos[i])
              l += self.num_trafos[i]
          return len(self.num_trafos) - 1, random.randrange(self.num_trafos[-1])
  
      def transform_point(self, point):
          x = (point.x - self.minx) / self.width
          y = (point.y - self.miny) / self.height
          #if trafo is None:
          trafo = self.get_random_trafo()
          start, end = self.splines[trafo[0]].GetDomain()
          length = end - start
          seg_length = length / self.num_trafos[trafo[0]]
          t = start + seg_length * trafo[1] + seg_length * x
          basepoint = self.splines[trafo[0]](t)
          if t + 1 / 50000 > end:
              neighbour = self.splines[trafo[0]](t - 1 / 50000)
              derivative = neighbour - basepoint
          else:
              neighbour = self.splines[trafo[0]](t + 1 / 50000)
              derivative = basepoint - neighbour
          if derivative.Mag() != 0:
              basepoint.x += derivative.y / derivative.Mag() * (y - 0.5) * \
                  self.thickness
              basepoint.y += -derivative.x / derivative.Mag() * (y - 0.5) * \
                  self.thickness
          else:
              print("r", end='')
          self.truncate(basepoint)
          return basepoint
  
      def truncate(self, point):
          if point.x >= self.maxx:
              point.x = self.maxx
          if point.y >= self.maxy:
              point.y = self.maxy
          if point.x < self.minx:
              point.x = self.minx
          if point.y < self.miny:
              point.y = self.miny
  
      def create_image_chaos(self, w, h, iterations, filename, rng_seed):
          # Always use the same sequence of random numbers
          # to get reproducible benchmark
          random.seed(rng_seed)
  
          im = [[1] * h for i in range(w)]
          point = GVector((self.maxx + self.minx) / 2,
                          (self.maxy + self.miny) / 2, 0)
          for _ in range(iterations):
              point = self.transform_point(point)
              x = (point.x - self.minx) / self.width * w
              y = (point.y - self.miny) / self.height * h
              x = int(x)
              y = int(y)
              if x == w:
                  x -= 1
              if y == h:
                  y -= 1
              im[x][h - y - 1] = 0
  
          if filename:
              write_ppm(im, filename)
  
  
  def main():
      splines = [
          Spline([
              GVector(1.597350, 3.304460, 0.000000),
              GVector(1.575810, 4.123260, 0.000000),
              GVector(1.313210, 5.288350, 0.000000),
              GVector(1.618900, 5.329910, 0.000000),
              GVector(2.889940, 5.502700, 0.000000),
              GVector(2.373060, 4.381830, 0.000000),
              GVector(1.662000, 4.360280, 0.000000)],
              3, [0, 0, 0, 1, 1, 1, 2, 2, 2]),
          Spline([
              GVector(2.804500, 4.017350, 0.000000),
              GVector(2.550500, 3.525230, 0.000000),
              GVector(1.979010, 2.620360, 0.000000),
              GVector(1.979010, 2.620360, 0.000000)],
              3, [0, 0, 0, 1, 1, 1]),
          Spline([
              GVector(2.001670, 4.011320, 0.000000),
              GVector(2.335040, 3.312830, 0.000000),
              GVector(2.366800, 3.233460, 0.000000),
              GVector(2.366800, 3.233460, 0.000000)],
              3, [0, 0, 0, 1, 1, 1])
      ]
  
      chaos = Chaosgame(splines, DEFAULT_THICKNESS)
      chaos.create_image_chaos(DEFAULT_WIDTH, DEFAULT_HEIGHT, DEFAULT_ITERATIONS, sys.argv[1], DEFAULT_RNG_SEED)
  
  t0 = time.time()
  main()
  t1 = time.time()
  print(t1 - t0)
  