MATLAB Compiler

A Simple Example -- The Sierpinski Gasket

Consider an M-file function called gasket.m:

• function theImage = gasket(numPoints)
  %GASKET An image of a Sierpinski Gasket.
  %   IM = GASKET(NUMPOINTS)
  %
  %   Example:
  %   x = gasket(50000);
  %   imagesc(x);colormap([1 1 1;0 0 0]);
  %   axis equal tight
  
  %   Copyright (c) 1984-98 by The MathWorks, Inc
  %   $ Revision: 1.1 $  $Date: 2002/06/20 22:18:14 $
  
  theImage = zeros(1000,1000);
  
  corners = [866 1;1 500;866 1000];
  startPoint = [866 1];
  theRand = rand(numPoints,1);
  theRand = ceil(theRand*3);
  
  for i=1:numPoints
     startPoint = floor((corners(theRand(i),:)+startPoint)/2);
     theImage(startPoint(1),startPoint(2)) = 1;
  end
  

How the Function Works

This function determines the coordinates of a Sierpinski Gasket using an Iterated Function System algorithm. The function starts with three points that define a triangle, and starting at one of these points, chooses one of the remaining points at random. A dot is placed at the midpoint of these two points. From the new point, a dot is placed at the midpoint between the new point and a point randomly selected from the original points. This process continues and eventually leads to an approximation of a curve.

The curve can be graphed in many ways. Sierpinski's method is

• Start with a triangle and from it remove a triangle that is one-half the height of the original and inverted. This leaves three triangles.
• From each of the remaining three triangles, remove a triangle that is one-fourth the height of these new triangles and inverted. This leaves nine triangles.
• The process continues and at infinity the surface area becomes zero and the length of the curve is infinite.

To achieve a reasonable approximation of the Sierpinski Gasket, set the number of points to 50,000. To invoke the M-file and compute the coordinates, you can use

• x = gasket(50000);
  

To display the figure, you can use

• imagesc(x); colormap([1 1 1;0 0 0]);
  axis equal tight
  

Working with MEX-Files

Compiling the M-File into a MEX-File