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Task/Sierpinski-triangle-Graphical/Python/sierpinski-triangle-graphical.py

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+#!/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(5)