# This demo draws the Spiral of Theodorus (see the Wikipedia entry)
# This version fills the triangles with a gradually changing colour.
# It uses the colorchooser dialog from the tkinter module to allow the
# user to specify the starting and ending colours.

import turtle
import math
import tkinter.colorchooser

def main() :
    numSlices = 16
    startColour = tkinter.colorchooser.askcolor(title="Starting Shade")[0]
    startRed = int(startColour[0])
    startGreen = int(startColour[1])
    startBlue = int(startColour[2])
    finishColour = tkinter.colorchooser.askcolor(title="Ending Shade")[0]
    finishRed = int(finishColour[0])
    finishGreen = int(finishColour[1])
    finishBlue = int(finishColour[2])
    redIncr = (startRed - finishRed) / numSlices
    greenIncr = (startGreen - finishGreen) / numSlices
    blueIncr = (startBlue - finishBlue) / numSlices
    turtle.shape("turtle")
    turtle.pensize(1)
    turtle.speed(10)
    turtle.colormode(255)
    turtle.pencolor("blue")
    size = 80
    count = 1
    angle = 0
    turtle.fillcolor((startRed, startGreen, startBlue))
    turtle.begin_fill()
    turtle.forward(size)
    while count < 17 :
        turtle.left(90)
        turtle.forward(size)
        xPos, yPos = turtle.position()
        turtle.home()
        turtle.end_fill()
        angle = angle + math.degrees(math.atan(1 / math.sqrt(count)))
        turtle.left(angle)
        red = finishRed + (numSlices - count) * redIncr
        green = finishGreen + (numSlices - count) * greenIncr
        blue = finishBlue + (numSlices - count) * blueIncr
        turtle.fillcolor((red, green, blue))
        turtle.begin_fill()
        turtle.setposition(xPos, yPos)
        count = count + 1

main()