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A Simple Example - The Sierpinski Gasket

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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

% $Revision: 1.1 $ $Date: 1998/09/11 20:05:06 $

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

IteratedFunctionSystemalgorithm.Thefunction startswitht hree pointsthat

define a triangle, and starting at one of these points, chooses one of the

remaining points atrandom.A dot isplacedatthemidpointofthesetwopoints.

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.

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MATLAB COMPILER RELEASE NOTES Guida Utente Pagina 61