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# 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
import wrappers
from random import uniform
class TreesTurtle(wrappers.Turtle):
# TG p. 85
def node(self, length, angle, level):
if level == 0: return
# point along left branch and draw it
self.left(angle)
self.lbranch(length, angle, level - 1)
# draw right branch
self.right(2 * angle)
self.rbranch(length, angle, level - 1)
# make node state-transparent
self.left(angle)
# TG p. 84
def lbranch(self, length, angle, level):
# draw a long stem
self.forward(2 * length)
# do next level
self.node(length, angle, level)
# make lbranch state-transparent
self.back (2 * length)
# TG p. 84
def rbranch(self, length, angle, level):
# draw a short stem
self.forward(length)
# do next level
self.node(length, angle, level)
# make lbranch state-transparent
self.back (length)
# VM p. 292
def tree(self, a, b, n, t, bt, f, l):
if l < 1: return
pos = self.getXY()
self.fd(a)
self.rt(t)
for i in range(n):
pos2 = self.getXY()
self.fd(b)
self.tree(a * f, b * f, n, t, bt, f, l - 1)
#self.bk(b)
self.setXY(pos2)
self.lt(bt)
self.rt((n * bt) - t)
#self.moveTo(pos[0], pos[1])
self.setXY(pos)
#self.bk(a)
# VM p. 306
def randTree(self, a, n, t, bt, f, l):
# to draw multiply branched recursive trees
# with randomized components
if l < 1: return
# save the current position and angle
pos = self.getXY()
heading = self.getHeading()
self.fd(uniform(0.5 * a, 1.5 * a))
self.rt(uniform(0.5 * t, 1.5 * t))
#self.fd(uniform(0.5 * t, 1.5 * t))
for i in range(n):
d = uniform(0.5 * a / 2, 1.5 * a / 2)
# save the position (not the heading)
pos2 = self.getXY()
self.fd(d)
self.randTree(a * f, n, t, bt, f, l - 1)
# restore the position
self.setXY(pos2)
self.lt(uniform(0.5 * bt, 1.5 * bt))
# restore the saved position and heading
self.setXY(pos)
self.setHeading(heading)
def testTree(self, size):
if size < 5: return
self.fd(size)
self.lt(30)
self.testTree(size * .7)
self.rt(60)
self.testTree(size * .7)
self.lt(30)
self.bk(size)
def testRTree(self, size):
if size < 5: return
self.fd(size)
self.lt(30)
self.testRTree(size * ((uniform(1, 5) + 5) / 10))
self.rt(60)
self.testRTree(size * ((uniform(1, 5) + 5) / 10))
self.lt(30)
self.bk(size)
def draw(canvas):
t = TreesTurtle(canvas)
t.cls()
t.left(90)
#t.tree(80, 40, 4, 60, 30, .6, 5)
#t.randTree(50, 3, 60, 30, .6, 4)
#t.randTree(30, 3, 30, 30, .75, 5)
#t.randTree(30, 3, 30, 15, .9, 5)
t.pu()
t.bk(150)
t.pd()
#t.testTree(75)
t.testRTree(50)
#t.lbranch(20, 20, 7)
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