#~ Copyright (c) 2014 Jonathan Whitaker

#~ Permission is hereby granted, free of charge, to any person obtaining a copy
#~ of this software and associated documentation files (the "Software"), to deal
#~ in the Software without restriction, including without limitation the rights
#~ to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
#~ copies of the Software, and to permit persons to whom the Software is
#~ furnished to do so, subject to the following conditions:

#~ The above copyright notice and this permission notice shall be included in
#~ all copies or substantial portions of the Software.

#~ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
#~ IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
#~ FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
#~ AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
#~ LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
#~ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
#~ THE SOFTWARE.


# Inspiration drawn from http://math.andrej.com/category/random-art/ . And by 'Inspiration drawn.." I mean it was his 
# cool stuff that sparked this idea, and I may have stolen one or two of his functions (with his permission!). If you're going to 
# make use of this code please make sure the credit goes back to him, and also to me (Jonathan Whitaker, www.gdriv.es/johnowhitaker)

import turtle

#The functions I'll be using
def sin(x):
	return (2.718281828459045**(x*1j)).imag
def cos(x):
	return (2.718281828459045**(x*1j)).real

def Sin(c, phase, freq):
	return (sin(phase + freq * c[0]),sin(phase + freq * c[1]),sin(phase + freq * c[2]))
	
def Cos(c, phase, freq):
	return (sin(phase + freq * c[0]),sin(phase + freq * c[1]),sin(phase + freq * c[2]))
	
def bSin(c, phase, freq):
	freq = freq/10.0
	return (sin(phase + freq * c[0]),sin(phase + freq * c[1]),sin(phase + freq * c[2]))
	
def bCos(c, phase, freq):
	freq = freq/10.0
	return (sin(phase + freq * c[0]),sin(phase + freq * c[1]),sin(phase + freq * c[2]))
	
def Well(c):
	return ((1 - 2 / (1 + c[0]*c[0])** 8), (1 - 2 / (1 + c[1]*c[1])** 8), (1 - 2 / (1 + c[1]*c[1])** 8))
	
def Tent(c):
	return ((1 - 2 * abs(c[0])), (1 - 2 * abs(c[1])), (1 - 2 * abs(c[2])))

def Sum(a, b): #actually average :P
	r1, g1, b1 = a
	r2, g2, b2 = b
	r3, g3, b3 = ((r1+r2)/2.0, (g1+g2)/2.0, (b1+b2)/2.0)
	return [r3, g3, b3]
	
def Product(a, b):
	r, g, b = a[0]*b[0], a[1]*b[1], a[2]*b[2]
	return(r, g, b)
	
def Mod(x,y):
		(r1,g1,b1) = x
		(r2,g2,b2) = y
		try:
			r3 = r1 % r2
			g3 = g1 % g2
			b3 = b1 % b2
			return (r3, g3, b3)
		except:
			return (0,0,0)

def Mix(a, b, c):
	(r1,g1,b1) = a
	(r2,g2,b2) = b
	w1, w2, w3 = (c[0]+1)/2, (c[1]+1)/2, (c[2]+1)/2
	r, g, b = (w1*r1+(1-w1)*r2), (w2*g1+(1-w2)*g2), (w3*b1+(1-w3)*b2)
	return (r, g, b)
	

bob = turtle.Turtle()	
bob.ht()
bob.pensize(2000)
bob.forward(1)
bob.pensize(1)
turtle.tracer(1000)

def draw(function, xstart, ystart, xsize, ysize):
	#xstart, ystart, xsize, ysize = 0, 0, 256, 256
	for y in range(ystart, ystart+ysize, 1):
		bob.penup()
		bob.goto(xstart, y)
		bob.pendown()
		for x in range(xstart, xstart+xsize, 1):
			u = 2 * float((x-xstart)/250.0) - 1.0
			v = 2 * float((y-ystart)/256.0) - 1.0
			X = (u, u, u)
			Y = (v, v, v)
			exec(function)
			r,g,b = (a[0]+1.0)/2,(a[1]+1.0)/2,(a[2]+1.0)/2
			r, g, b = (r-int(r)),(g-int(g)), (b-int(b)) #stop invalid colours
			bob.color(r, g, b)
			bob.forward(1)
		turtle.clear()
	print function
	
draw('a = Well(Mix(Mix(bCos(Sum(X, Product(Y, Y)), 3.02001292317, 2.32109206029), Mix(X, Y, Y), Sum((0.758050721771132, 0.22485439469955082, 0.8909725701161852), X)), Mod(Mix(Y, X, Y), Tent(X)), bCos(Sum(Product((0.0900006170476797, 0.991943272743145, 0.32329566333949544), (0.01520765634544996, 0.4435305107427775, 0.12860730821286004)), Product(Mix(X, X, Y), Mod(X, (0.7671522537642487, 0.40489079867407174, 0.7607519581821848)))), 0.564886284696, 3.59862939928)))', 30, 22, 256, 256)
draw('a = Well(Sum(Well(Mix((0.5191673305223623, 0.16469728452479093, 0.8835335508873503), Y, (0.019148691166625986, 0.1257941003735067, 0.5208588657151579))), Well(Mix(Y, X, Y))))', -286, 22, 256, 256)
draw('a = Product(Product(Sum(Mod((0.46426970212980423, 0.6865556377999732, 0.20342967973875203), (0.8023552568293205, 0.7427859986551726, 0.4764325597419743)), Well(X)), Tent(Tent(X))), Tent(Tent(Mod(X, Y))))', -286, -278, 256, 256)
draw('a = Well(Mix(Mod(Product((0.6708812683648796, 0.3107618525011592, 0.6937389341079395), X), Well(Y)), bSin(Sum(Product(Y, (0.776238672916275, 0.530947648534944, 0.0839970806297533)), Product(bSin(Sum(X, Product((0.7415921100821066, 0.259318723395043, 0.2727435893896609), X)), 1.34300549474, 2.36343320062), Tent(Y))), 2.80540545004, 5.60807613484), Mix(Well(X), Tent(Y), Mod(Y, Y))))', 30, -278, 256, 256)

turtle.exitonclick()