/
fractals.py
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/
fractals.py
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from turtle import fd, bk, right, left, up, down
import turtle as t
import math
### A library of functions that draw fractals.
### @author Peter Sujan
### Various utility methods
def reset():
old_speed = t.speed()
t.reset()
t.speed(old_speed)
def setFill(fill):
t.fill(fill)
def drawSquare(size, fill):
setFill(fill)
for i in range(4):
fd(size)
right(90)
setFill(False)
def drawTriangle(size, fill):
setFill(fill)
for i in range(3):
fd(size)
right(120)
setFill(False)
def drawPolygon(size, fill, n):
setFill(fill)
for i in range(n):
fd(size)
right(360.0 / n)
setFill(False)
### Functions that draw fractals.
def koch(size, level):
""" One side of the Koch Snowflake.
http://en.wikipedia.org/wiki/Koch_snowflake
"""
if level < 1:
fd(size)
else:
koch(size / 3.0, level - 1)
left(60)
koch(size / 3.0, level - 1)
right(120)
koch(size / 3.0, level - 1)
left(60)
koch(size / 3.0, level - 1)
def fullKoch(size, level):
""" The full Koch Snowflake.
http://en.wikipedia.org/wiki/Koch_snowflake
"""
for i in range(3):
koch(size, level)
right(120)
def cCurve(size, level):
""" The Levy C-Curve fractal.
http://en.wikipedia.org/wiki/C-curve
"""
if level < 1:
fd(size)
else:
left(45)
cCurve(size / 2.0, level - 1)
right(90)
cCurve(size / 2.0, level - 1)
left(45)
def squiral(size, level):
""" A square spiral. """
if level < 1:
fd(size)
else:
fd(size * level)
right(90)
squiral(size, level - 1)
def UMCTriangle(size, angle, level):
""" A 'uniform mass center triangle' fractal """
newAngle = angle / 2.0
obtuse = 180 - angle * 2
if level < 1:
fd(size)
left(180 - angle + newAngle)
fd(size / (2 * math.cos(math.radians(newAngle))))
bk(size / (2 * math.cos(math.radians(newAngle))))
right(newAngle)
fd(size / (2 * math.cos(math.radians(angle))))
left(180 - obtuse + obtuse / 2.0)
fd(size / (2 * math.cos(math.radians(angle))) * math.sin(math.radians(newAngle)) / math.sin(math.radians(180 - newAngle - obtuse / 2.0)))
bk(size / (2 * math.cos(math.radians(angle))) * math.sin(math.radians(newAngle)) / math.sin(math.radians(180 - newAngle - obtuse / 2.0)))
right(obtuse / 2.0)
fd(size / (2 * math.cos(math.radians(angle))))
left(180 - angle + newAngle)
fd(size / (2 * math.cos(math.radians(newAngle))))
bk(size / (2 * math.cos(math.radians(newAngle))))
right(newAngle)
else:
for i in range(3):
UMCTriangle(size, newAngle, level - 1)
fd(size)
fd(size / (2 * math.cos(math.radians(angle))))
fd(size / (2 * math.cos(math.radians(angle))))
def accidentalButCool(size, angle, level):
newAngle = angle / 2.0
obtuse = 180 - angle
if level < 1:
for i in range(3):
fd(size)
left(obtuse)
fd(size / (2 * math.cos(math.radians(newAngle))))
bk(size / (2 * math.cos(math.radians(newAngle))))
right(newAngle)
else:
for i in range(3):
accidentalButCool(size, newAngle, level - 1)
def gosper(size, level, direction):
""" The Gosper Curve.
http://en.wikipedia.org/wiki/Gosper_curve
"""
if level < 1:
if direction > 0:
right(60)
fd(size)
left(60)
fd(2 * size)
left(120)
fd(size)
left(60)
fd(size)
right(120)
fd(size)
right(60)
fd(size)
else:
fd(size)
left(60)
fd(size)
left(120)
fd(size)
right(60)
fd(size)
right(120)
fd(2 * size)
right(60)
fd(size)
left(60)
else:
if direction > 0:
right(60)
gosper(size / 2.5, level - 1, -1)
left(60)
gosper(size / 2.5, level - 1, 1)
gosper(size / 2.5, level - 1, 1)
left(120)
gosper(size / 2.5, level - 1, 1)
left(60)
gosper(size / 2.5, level - 1, -1)
right(120)
gosper(size / 2.5, level - 1, -1)
right(60)
gosper(size / 2.5, level - 1, 1)
else:
gosper(size / 2.5, level - 1, -1)
left(60)
gosper(size / 2.5, level - 1, 1)
left(120)
gosper(size / 2.5, level - 1, 1)
right(60)
gosper(size / 2.5, level - 1, -1)
right(120)
gosper(size / 2.5, level - 1, -1)
gosper(size / 2.5, level - 1, -1)
right(60)
gosper(size / 2.5, level - 1, 1)
left(60)
def gosperIsland(size, level):
down()
for i in range(6):
gosperIslandHelper(size, level)
right(120)
def gosperIslandHelper(size, level):
# TODO: finish this later
return 0
def vicsekS(size, level):
""" The saltire form of the Vicsek fractal. """
newSize = size / 3.0
if level < 1:
down()
drawSquare(newSize, True)
up()
fd(2 * newSize)
down()
drawSquare(newSize, True)
up()
bk(2 * newSize)
right(90)
fd(newSize)
left(90)
fd(newSize)
down()
drawSquare(newSize, True)
up()
bk(newSize)
right(90)
fd(newSize)
left(90)
down()
drawSquare(newSize, True)
up()
fd(2 * newSize)
down()
drawSquare(newSize, True)
up()
bk(2 * newSize)
left(90)
fd(2 * newSize)
right(90)
else:
down()
vicsekS(newSize, level - 1)
up()
fd(2 * newSize)
down()
vicsekS(newSize, level - 1)
up()
bk(2 * newSize)
right(90)
fd(newSize)
left(90)
fd(newSize)
down()
vicsekS(newSize, level - 1)
up()
bk(newSize)
right(90)
fd(newSize)
left(90)
down()
vicsekS(newSize, level - 1)
up()
fd(2 * newSize)
down()
vicsekS(newSize, level - 1)
up()
bk(2 * newSize)
left(90)
fd(2 * newSize)
right(90)
def vicsekC(size, level):
""" The cross form of the Vicsek fractal. """
newSize = size / 3.0
if level < 1:
up()
fd(newSize)
down()
drawSquare(newSize, True)
up()
bk(newSize)
right(90)
fd(newSize)
left(90)
down()
drawSquare(newSize, True)
fd(newSize)
drawSquare(newSize, True)
fd(newSize)
drawSquare(newSize, True)
bk(newSize)
right(90)
fd(newSize)
left(90)
drawSquare(newSize, True)
up()
left(90)
fd(2 * newSize)
right(90)
bk(newSize)
else:
up()
fd(newSize)
down()
vicsekC(newSize, level - 1)
up()
bk(newSize)
right(90)
fd(newSize)
left(90)
down()
vicsekC(newSize, level - 1)
fd(newSize)
vicsekC(newSize, level - 1)
fd(newSize)
vicsekC(newSize, level - 1)
bk(newSize)
right(90)
fd(newSize)
left(90)
vicsekC(newSize, level - 1)
up()
left(90)
fd(2 * newSize)
right(90)
bk(newSize)
def dragon(size, level, direction):
""" The Dragon Curve.
http://en.wikipedia.org/wiki/Dragon_curve
"""
if level < 1:
down()
right(direction * 45)
fd(size)
left(direction * 90)
fd(size)
right(direction * 45)
else:
down()
right(direction * 45)
dragon(size / math.sqrt(2), level - 1, 1)
left(direction * 90)
dragon(size / math.sqrt(2), level - 1, -1)
right(direction * 45)
def sierpinski(size, level):
""" The Sierpinski Triangle
https://en.wikipedia.org/wiki/Sierpinski_triangle
"""
if level < 1:
left(60)
drawTriangle(size, True)
right(60)
else:
sierpinski(size / 2.0, level - 1)
left(60)
fd(size / 2.0)
right(60)
sierpinski(size / 2.0, level - 1)
left(60)
bk(size / 2.0)
right(60)
fd(size / 2.0)
sierpinski(size / 2.0, level - 1)
bk(size / 2.0)
def sierpinskiArrowhead(size, level, direction):
""" The Sierpinski Arrowhead Curve.
https://en.wikipedia.org/wiki/Sierpi%C5%84ski_arrowhead_curve
"""
if level < 1:
left(60 * direction)
fd(size * direction)
right(60 * direction)
fd(size * direction)
right(60 * direction)
fd(size * direction)
left(60 * direction)
else:
right(120 * direction)
sierpinskiArrowhead(size / 2.0, level - 1, direction * -1)
left(120 * direction)
sierpinskiArrowhead(size / 2.0, level - 1, direction)
left(120 * direction)
sierpinskiArrowhead(size / 2.0, level - 1, direction * -1)
right(120 * direction)
def tSquare(size, level):
""" The T-Square fractal.
http://en.wikipedia.org/wiki/T-Square_%28fractal%29
"""
if level < 1:
drawSquare(size, True)
else:
drawSquare(size, True)
bk(size / 4.0)
left(90)
fd(size / 4.0)
right(90)
tSquare(size / 2.0, level - 1)
up()
fd(size)
down()
tSquare(size / 2.0, level - 1)
right(90)
fd(size)
left(90)
tSquare(size / 2.0, level - 1)
bk(size)
tSquare(size / 2.0, level - 1)
left(90)
up()
fd(size * 3 / 4.0)
down()
right(90)
fd(size / 4.0)
def pythagoras(size, level):
""" The Pythagoras Tree fractal.
http://en.wikipedia.org/wiki/Pythagoras_tree_%28fractal%29
"""
if level < 1:
drawSquare(size, True)
else:
newSize = size / 2.0 * math.sqrt(2)
drawSquare(size, True)
left(135)
fd(newSize)
right(90)
pythagoras(newSize, level - 1)
left(90)
bk(newSize)
right(135)
fd(size)
left(135)
fd(newSize)
right(90)
fd(newSize)
right(90)
pythagoras(newSize, level - 1)
left(90)
bk(newSize)
left(90)
bk(newSize)
right(135)
bk(size)
def hexaflake(size, level, center):
if level < 1:
drawPolygon(size, True, 6)
else:
newSize = size / 3.0
hexaflake(newSize, level - 1, center)
up()
fd(newSize * 2)
down()
hexaflake(newSize, level - 1, center)
up()
bk(newSize * 2)
right(120)
fd(newSize * 2)
down()
left(120)
hexaflake(newSize, level - 1, center)
up()
fd(2 * newSize)
if center:
down()
hexaflake(newSize, level - 1, center)
up()
fd(2 * newSize)
down()
hexaflake(newSize, level - 1, center)
up()
bk(4 * newSize)
right(120)
up()
fd(newSize)
left(60)
fd(newSize)
left(60)
fd(newSize)
down()
hexaflake(newSize, level - 1, center)
up()
fd(2 * newSize)
hexaflake(newSize, level - 1, center)
up()
bk(3 * newSize)
left(120)
fd(newSize)
right(60)
fd(size)
right(60)
def cantorSquare(size, level):
if level < 1:
up()
drawSquare(size, True)
else:
newSize = size / 3.0
up()
cantorSquare(newSize, level - 1)
fd(newSize * 2)
cantorSquare(newSize, level - 1)
right(90)
fd(newSize * 2)
left(90)
cantorSquare(newSize, level - 1)
bk(newSize * 2)
cantorSquare(newSize, level - 1)
right(90)
bk(newSize * 2)
left(90)