_16_sierpinski_gasket Namespace Reference

Draws a Sierpinski Gasket. More...

Functions
def	Sierpinski (a, b, c, n, fourth=False)
	Creates a Sierpinski Gasket, by recursively partitioning an initial triangle (a,b,c) into three or four new triangles. More...
def	draw (c, points, contour=False)
	Draw triangles, given in points, on canvas c. More...
def	main (argv=None)
	Main program. More...

Detailed Description

Draws a Sierpinski Gasket.

Usage: _16_sierpinski [number_of_divisions]

Author

Paulo Roma Cavalcanti

Since

09/02/2016

See also

http://paulbourke.net/fractals/polyhedral/

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_gasket.draw	(		c,
			points,
			contour = False
	)

Draw triangles, given in points, on canvas c.

Referenced by main().

main()

def _16_sierpinski_gasket.main

(

argv = None

)

Main program.

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

Sierpinski()

def _16_sierpinski_gasket.Sierpinski	(		a,
			b,
			c,
			n,
			fourth = False
	)

Creates a Sierpinski Gasket, by recursively partitioning an initial triangle (a,b,c) into three or four new triangles.

• 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

a	first vertex coordinates.
b	second vertex coordinates.
c	third vertex coordinates.
n	number of subdivisions on each edge (depth of recursion).
fourth	whether to add the fourth triangle.

Referenced by main().