The **Sierpinski Family Machine** presents the Sierpinski Triangle and its relatives. There are three defined transformations. Change the IFS types of these transformations and move the positions of their fixed points marked by white circles.

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The Sierpinski Family Applet

The machine is designed to construct fractal images using the chaos game method. There are three defined transformations which build an IFS (Iterated Functions System). Each transformation shrinks a given figure by the factor 0.5 and it posesses a fixed point, which isn't changed by the transformation.

Eight different transformation types with the named properties are available. They rotate or do mirror effects to virtual figures as shown in the typelist at the bottom of the page. With the predefined properties you'll get the well known Sierpinski Triangle. For each of the three transformations you may select one of the 8 transformation types and you may move the three fixed points (shown as white circles) by dragging them. Doing so, you'll see millions of different fractal images which I call the Sierpinski Familiy Fractals.

This is only a small selection of what you are able to do with my program **Dotfrak**, described on the first IFS page. Here is the Javascript source code chaosgame.js to download (watch the HTML source code on the page, too). You'll find more interactive machines in the sections **Iterations I and II**.

All selectable IFS types are shown with their results on a figure "F" (shrinked 50%)

© 2007 Ulrich Schwebinghaus