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"""
__version__ = "$Revision: 1.1 $"
__date__ = "$Date: 2004/05/11 01:12:51 $"
"""
# by referring to the Turtle class in this
# module rather than PythonCard.turtle.BitmapTurtle
# directly in scripts, the script can be run in
# a different turtle environment such as LegoTurtle
# by simply changing the import line below
# of course, I haven't written those other
# turtle wrappers, but it never hurts to plan ahead <wink>
# i'm open to suggestions for another way of achieving
# the same result, namely not needing to change myriads
# of turtle scripts in order to run them in a different
# graphics environment (BitmapTurtle, LegoTurtle, etc.)
from PythonCard import turtle
class Turtle(turtle.BitmapTurtle):
pass
# examples derived from
# Visual Modeling with Logo: A Structural Approach to Seeing
# by James Clayson
# and
# Turtle Geometry: The Computer as a Medium for Exploring Mathematics
# by Harold Abelson and Andrea diSessa
class CurvesTurtle(Turtle):
# TG p. 92
def cCurve(self, size, level):
if level == 0:
self.forward(size)
return
self.cCurve(size, level - 1)
self.right(90)
self.cCurve(size, level - 1)
self.left(90)
# TG p. 93
def lDragon(self, size, level):
if level == 0:
self.forward(size)
return
self.lDragon(size, level - 1)
self.left(90)
self.rDragon(size, level - 1)
# TG p. 93
def rDragon(self, size, level):
if level == 0:
self.forward(size)
return
self.lDragon(size, level - 1)
self.right(90)
self.rDragon(size, level - 1)
# 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) # logo uses sin(180 / n); Python uses radians
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)
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