| #!/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, 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() |