#!/usr/bin/env python3
""" turtle-example-suite:

 tdemo_fractalCurves.py

This program draws two fractal-curve-designs:
(1) A hilbert curve (in a box)
(2) A combination of Koch-curves.

The CurvesTurtle class and the fractal-curve-
methods are taken from the PythonCard example
scripts for turtle-graphics.
"""
from turtle import *
from time import sleep, perf_counter as clock

class CurvesTurtle(Pen):
 # example derived from
 # Turtle Geometry: The Computer as a Medium for Exploring Mathematics
 # by Harold Abelson and Andrea diSessa
 # p. 96-98
 def hilbert(self, size, level, parity):
 if level == 0:
 return
 # rotate and draw first subcurve with opposite parity to big curve
 self.left(parity * 90)
 self.hilbert(size, level - 1, -parity)
 # interface to and draw second subcurve with same parity as big curve
 self.forward(size)
 self.right(parity * 90)
 self.hilbert(size, level - 1, parity)
 # third subcurve
 self.forward(size)
 self.hilbert(size, level - 1, parity)
 # fourth subcurve
 self.right(parity * 90)
 self.forward(size)
 self.hilbert(size, level - 1, -parity)
 # a final turn is needed to make the turtle
 # end up facing outward from the large square
 self.left(parity * 90)

 # Visual Modeling with Logo: A Structural Approach to Seeing
 # by James Clayson
 # Koch curve, after Helge von Koch who introduced this geometric figure in 1904
 # p. 146
 def fractalgon(self, n, rad, lev, dir):
 import math

 # if dir = 1 turn outward
 # if dir = -1 turn inward
 edge = 2 * rad * math.sin(math.pi / n)
 self.pu()
 self.fd(rad)
 self.pd()
 self.rt(180 - (90 * (n - 2) / n))
 for i in range(n):
 self.fractal(edge, lev, dir)
 self.rt(360 / n)
 self.lt(180 - (90 * (n - 2) / n))
 self.pu()
 self.bk(rad)
 self.pd()

 # p. 146
 def fractal(self, dist, depth, dir):
 if depth < 1:
 self.fd(dist)
 return
 self.fractal(dist / 3, depth - 1, dir)
 self.lt(60 * dir)
 self.fractal(dist / 3, depth - 1, dir)
 self.rt(120 * dir)
 self.fractal(dist / 3, depth - 1, dir)
 self.lt(60 * dir)
 self.fractal(dist / 3, depth - 1, dir)

def main():
 ft = CurvesTurtle()

 ft.reset()
 ft.speed(0)
 ft.ht()
 ft.getscreen().tracer(1,0)
 ft.pu()

 size = 6
 ft.setpos(-33*size, -32*size)
 ft.pd()

 ta=clock()
 ft.fillcolor("red")
 ft.begin_fill()
 ft.fd(size)

 ft.hilbert(size, 6, 1)

 # frame
 ft.fd(size)
 for i in range(3):
 ft.lt(90)
 ft.fd(size*(64+i%2))
 ft.pu()
 for i in range(2):
 ft.fd(size)
 ft.rt(90)
 ft.pd()
 for i in range(4):
 ft.fd(size*(66+i%2))
 ft.rt(90)
 ft.end_fill()
 tb=clock()
 res = "Hilbert: %.2fsec. " % (tb-ta)

 sleep(3)

 ft.reset()
 ft.speed(0)
 ft.ht()
 ft.getscreen().tracer(1,0)

 ta=clock()
 ft.color("black", "blue")
 ft.begin_fill()
 ft.fractalgon(3, 250, 4, 1)
 ft.end_fill()
 ft.begin_fill()
 ft.color("red")
 ft.fractalgon(3, 200, 4, -1)
 ft.end_fill()
 tb=clock()
 res += "Koch: %.2fsec." % (tb-ta)
 return res

if __name__ == '__main__':
 msg = main()
 print(msg)
 mainloop()