#!/usr/bin/env python

# 2017-02-12 Simple IFS example
# http://algoristo.com/teaching/
# http://archive.bridgesmathart.org/2016/bridges2016-533.html\

import math
from random import random, choice

ninit = 10000
niter = 10

def rotate(x, y, degrees):
    s = math.sin(math.pi*degrees/180)
    c = math.cos(math.pi*degrees/180)
    return c*x - s*y, c*y + s*x

# Example: Koch snowflake

def k1(x, y):
    return x/3, y/3

def k2(x, y):
    return x/3 + 2.0/3, y/3

def k3(x, y):
    x, y = rotate(x, y, 60)
    return x/3 + 1.0/3, y/3

def k4(x, y):
    x, y = rotate(x, y, -60)
    return x/3 + 0.5, y/3 + math.sqrt(3)/6
    
ifs = [k1, k2, k3, k4]

# Save all stages
datfiles = []
for n in range(niter + 1):
    datfiles.append(open("ifs%i.dat" % n, "w"))

for i in range(1, ninit + 1):
    # Random point
    x = random()
    y = random()

    # Save the initial set
    datfiles[0].write("%f %f\n" % (x, y))
    
    for j in range(1, niter + 1):
        f = choice(ifs)
        x, y = f(x, y)

        datfiles[j].write("%f %f\n" % (x, y))

for dat in datfiles:
    dat.close()