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#! /usr/bin/python3.8 """ 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()