_16_sierpinski_arrowhead Namespace Reference

Draws a Sierpinski arrowhead curve. More...

Functions
def	Sierpinski_arrowhead_curve (order, length)
	Creates a Sierpinski Arrowhead curve, by recursively breaking an initial line, starting at a given point, into three new segments. More...
def	draw (c, points, contour=False)
	Draw lines, given in points, on canvas c. More...
def	main (argv=None)
	Main program. More...

Detailed Description

Draws a Sierpinski arrowhead curve.

Usage: _16_sierpinski_arrowhead [number_of_divisions]

Author

Paulo Roma Cavalcanti

Since

22/01/2017

See also

http://paulbourke.net/fractals/gasket/

https://en.wikipedia.org/wiki/Sierpinski_triangle

http://ecademy.agnesscott.edu/~lriddle/ifs/siertri/siertri.htm

http://www.oftenpaper.net/sierpinski.htm

https://code.activestate.com/recipes/580614-sierpinski-gasket/

Function Documentation

draw()

def _16_sierpinski_arrowhead.draw	(		c,
			points,
			contour = False
	)

Draw lines, given in points, on canvas c.

Referenced by main().

main()

def _16_sierpinski_arrowhead.main

(

argv = None

)

Main program.

References draw(), _08b_clock_bezier.resize, and Sierpinski_arrowhead_curve().

Sierpinski_arrowhead_curve()

def _16_sierpinski_arrowhead.Sierpinski_arrowhead_curve	(		order,
			length
	)

Creates a Sierpinski Arrowhead curve, by recursively breaking an initial line, starting at a given point, into three new segments.

• There will be:
  • \(3^{n}\) red triangles or
  • \(4^{n}\) if the fourth triangle is drawn.
• The number of white triangles is a Geometric Progression, starting at 1 and with ratio 3, given by:
  • P(0) = 0
  • P(n) = 3 * P(n-1) + 1
  • P(n) = \(\frac{(3^n-1)}{2}.\)

Parameters

order	recursion depth.
length	initial segment size.

Referenced by main().