#!/usr/bin/python
# kohaku0.py - Don Yang (uguu.org)
# Julia set renderer
#
# 11/02/05

import string
import random

# Constants
iteration_count = 26
x_steps = 79
y_steps = 24
aspect_ratio = 1.5

def render_point(z, c):
   """Render a point by exponentiating it repeatedly.  Returns number
   of iterations it takes for the number to diverge, clamped by
   iteration_count."""
   for i in range(iteration_count + 1):
      if abs(z) > 2: return i
      z = z * z + c
   return iteration_count + 1

def iter_char(i):
   """Convert iteration value to character."""
   if i >= 26 or i < 0: return ' '
   return chr(ord('A') + i)

def interesting(x0, x1, y0, y1, c):
   """Check if a particular set of coordinates is interesting by
   checking for high variety of values in sampled points."""
   series = map(lambda p : render_point(p, c),
                [complex(x0, y0),
                 complex(x0, y1),
                 complex(x1, y0),
                 complex(x1, y1),
                 complex((x0 + x1) / 2, (y0 + y1) / 2)])
   average = sum(series) / 5
   stddev = sum(map(lambda x : (x - average) * (x - average), series)) / 5
   if stddev > iteration_count * 4.6: return 1
   return 0

def render_image(x0, x1, xsteps, y0, y1, ysteps, c):
   """Render image."""
   for i in range(ysteps):
      y = (y0 - y1) * float(i) / (ysteps - 1) + y1
      print string.join(
         map(lambda j : iter_char(render_point(
                complex((x1 - x0) * float(j) / (xsteps - 1) + x0, y), c)),
             range(xsteps)), "")

def render_random_image():
   """Generate coordinates repeatedly until an interesting one is found,
   then render image."""
   i = 0
   while not i:
      x0 = random.uniform(-1, 1)
      y0 = random.uniform(-1, 1)
      s = random.uniform(0.1, 1)
      c = complex(random.uniform(-1, 1), random.uniform(-1, 1))
      i = interesting(x0, x0 + s * aspect_ratio, y0, y0 + s, c)
   render_image(x0, x0 + s * aspect_ratio, x_steps, y0, y0 + s, y_steps, c)

random.seed()
render_random_image()