Generate a 6 level Sierpinski Triangle in python: graphics.py can be downloaded

Question

Generate a 6 level Sierpinski Triangle in python:

graphics.py can be downloaded at "http://mcsp.wartburg.edu/zelle/python/graphics.py"

Sierpinksy.py:

from graphics import*

def sierpinskiT(points, level, win):
colormap = ['blue', 'red', 'green', 'white', 'yellow', 'violet', 'orange']

p = Polygon(points)
p.setFill(colormap[level % len(colormap)])
p.draw(win)
if level > 0:
# Add recursive calls here

pass

def getMid(pt1, pt2):
return Point((pt1.getX()+pt2.getX())/2.0, (pt1.getY()+pt2.getY())/2.0)

if __name__ == '__main__':
win = GraphWin('st', 500, 500)
win.setCoords(20, -10, 80, 50)
myPoints = [Point(25,0), Point(50, 43.3), Point(75, 0)]
sierpinskiT(myPoints, 4, win)

Explanation / Answer

#!/usr/bin/env python ################################################################################################ # import necessary modules # ------------------------ from numpy import * import turtle ################################################################################################ # Functions defining the drawing actions (used by the function DrawSierpinskiTriangle). # ------------------------------------------------------------------------------------- def Left(turn, point, fwd, angle, turt): turt.left(angle) return [turn, point, fwd, angle, turt] def Right(turn, point, fwd, angle, turt): turt.right(angle) return [turn, point, fwd, angle, turt] def Forward(turn, point, fwd, angle, turt): turt.forward(fwd) return [turn, point, fwd, angle, turt] ################################################################################################ # The drawing function # -------------------- # # level level of Sierpinski triangle (minimum value = 1) # ss screensize (Draws on a screen of size ss x ss. Default value = 400.) #----------------------------------------------------------------------------------------------- def DrawSierpinskiTriangle(level, ss=400): # typical values turn = 0 # initial turn (0 to start horizontally) angle=60.0 # in degrees # Initialize the turtle turtle.hideturtle() turtle.screensize(ss,ss) turtle.penup() turtle.degrees() # The starting point on the canvas fwd0 = float(ss) point=array([-fwd0/2.0, -fwd0/2.0]) # Setting up the Lindenmayer system # Assuming that the triangle will be drawn in the following way: # 1.) Start at a point # 2.) Draw a straight line - the horizontal line (H) # 3.) Bend twice by 60 degrees to the left (--) # 4.) Draw a straight line - the slanted line (X) # 5.) Bend twice by 60 degrees to the left (--) # 6.) Draw a straight line - another slanted line (X) # This produces the triangle in the first level. (so the axiom to begin with is H--X--X) # 7.) For the next level replace each horizontal line using # X->XX # H -> H--X++H++X--H # The lengths will be halved. decode = {'-':Left, '+':Right, 'X':Forward, 'H':Forward} axiom = 'H--X--X' # Start the drawing turtle.goto(point[0], point[1]) turtle.pendown() turtle.hideturtle() turt=turtle.getpen() startposition=turt.clone() # Get the triangle in the Lindenmayer system fwd = fwd0/(2.0**level) path = axiom for i in range(0,level): path=path.replace('X','XX') path=path.replace('H','H--X++H++X--H') # Draw it. for i in path: [turn, point, fwd, angle, turt]=decode[i](turn, point, fwd, angle, turt) ################################################################################################ DrawSierpinskiTriangle(6)

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.