Randomized Sierpinski Gasket Applet -- Green's function

This applet generates a random Sierpinski Gasket and computes its Green's function. The randomization is dependent on parameters alpha and beta (see this paper for detailed explanations). The range of these values can be set in the control pane at the top of the applet. By default, the initial resistance is always fixed at 1.0.

The depth slider located at the bottom of the control pane specifies the depth that the gasket will be drawn at. A depth of 1 is an initial gasket composed of only 3 triangles. Each depth beyond this subdivides all the triangles in the previous step into 3 sub-triangles. The larger the depth, the more accurate approximation of the real gasket is. Note that depth 9 may take minutes to generate.

Once you have set the parameters, click the 'Draw Gasket' button and watch the applet generate a random gasket. You can redraw the gasket without changing any parameters and get a different random gasket every time.

For a balanced non-random gasket, fix alpha at 0.4, and fix beta at 0.5.

The blue circle indicates the location of the maximum of Green's function. Next to it, its (x,z) and (y,z) coordinates are given, with z being the maximal value of Green's function.

This applet uses java www.java.com, which likely requires using firefox and security exceptions.

Java applet that draws a random Sierpinski gasket.