usrbinenv python3 turtleexamplesuite tdemofractalcurves py this program draws two fractalcurvedesigns 1 a hilbert curve in a box 2 a combination of kochcurves the curvesturtle class and the fractalcurve methods are taken from the pythoncard example scripts for turtlegraphics example derived from turtle geometry the computer as a medium for exploring mathematics by harold abelson and andrea disessa p 9698 rotate and draw first subcurve with opposite parity to big curve interface to and draw second subcurve with same parity as big curve third subcurve fourth subcurve a final turn is needed to make the turtle end up facing outward from the large square 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 if dir 1 turn outward if dir 1 turn inward p 146 frame 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 example derived from turtle geometry the computer as a medium for exploring mathematics by harold abelson and andrea disessa p 96 98 rotate and draw first subcurve with opposite parity to big curve interface to and draw second subcurve with same parity as big curve third subcurve fourth subcurve a final turn is needed to make the turtle end up facing outward from the large square 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 if dir 1 turn outward if dir 1 turn inward p 146 frame
from turtle import *
from time import sleep, perf_counter as clock

class CurvesTurtle(Pen):
    
    
    
    
    def hilbert(self, size, level, parity):
        if level == 0:
            return
        
        self.left(parity * 90)
        self.hilbert(size, level - 1, -parity)
        
        self.forward(size)
        self.right(parity * 90)
        self.hilbert(size, level - 1, parity)
        
        self.forward(size)
        self.hilbert(size, level - 1, parity)
        
        self.right(parity * 90)
        self.forward(size)
        self.hilbert(size, level - 1, -parity)
        
        
        self.left(parity * 90)

    
    
    
    
    def fractalgon(self, n, rad, lev, dir):
        import math

        
        
        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()

    
    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)

    
    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()