"""
Triangle Angle i*Z CONJUGATE I.F.S.
Angle iteration:  w=angle(x-a,y-b): z = i*exp(-i*w)/r+a+i*b
By R. L. BAGULA, Sep 7 2002.
rlbagula@sbcglobal.net

From Paul Bourke site, <paul.bourke@uwa.edu.au>
http://local.wasp.uwa.edu.au/~pbourke/

Translated to Python by leonardo maffi, Sept 11 2006.

Requires:
- Python
- Pygame, http://www.pygame.org/download.shtml
- Psyco optional.
"""

from __future__ import division
import pygame


def lace(screen, nx, ny, npoints=100000):
    from random import randint
    from math import sqrt, sin, cos, hypot, atan2

    pset = screen.set_at
    mx, my = nx/3.5, ny/3.5
    nx2, ny2 = nx/2, ny/2
    s32 = sqrt(3)/2
    colors = (255,0,0), (0,255,0), (0,0,255), (255,255,255)
    x, y = 0.5, 0.75
    for i in xrange(npoints):
        a = randint(0, 3)
        r0 = -hypot(x, y) / 2
        if a == 0:
            w = atan2(x-1, y)
            x = r0*cos(w) + 1
            y = r0*sin(w)
        elif a == 1:
            w = atan2(x+0.5, y - s32)
            x = r0*cos(w) - 0.5
            y = r0*sin(w) + s32
        elif a == 2:
            w = atan2(x+0.5, y+s32)
            x = r0*cos(w) - 0.5
            y = r0*sin(w) - s32
        else:
            w = atan2(x, y)
            x = r0*cos(w)
            y = r0*sin(w)

        if i > 10:
            pset( ( int(nx2 + x*mx), int(ny2 + y*my) ), colors[a])
        if not (i % 6000):
            pygame.display.flip()


try: # Use psyco if possible
    import psyco
    psyco.bind(lace)
except: pass


def pygame_plot(do_plot, nx=640, ny=480, **args):
    pygame.init()
    screen = pygame.display.set_mode((nx, ny))
    pygame.display.set_caption(do_plot.__name__)
    do_plot(screen, nx, ny, **args)
    pygame.display.flip()
    while True:
        e = pygame.event.wait()
        if e.type == pygame.QUIT:
            break

pygame_plot(lace, nx=800, ny=500, npoints=200000)