NAME Menger sponge - produce a Menger Sponge (Sierpinski Sponge) as a byte volume AUTHOR Larry Gelberg, Advanced Visual Systems Inc. (larryg@avs.com) SUMMARY Name Menger sponge Type Input Inputs NONE Outputs output - field 3D 3-space 1-vector uniform byte Parameters Name Type Default Choices flip toggle off off on levels islider 1 1 5 DESCRIPTION A Menger Sponge (sometimes known as a Sierpinski Sponge) is a recursively defined volume. It is the 3D analog to a Sierpinski Carpet which is can be poorly defined as a recursive 3x3 grid where the center square of each level of the recursion is missing. A more formal definition can be found in Benoit Mandelbrot's book "The Fractal Geometry of Nature" on page 144. You can see a Sierpinski Carpet if you orthoslice the sponge and look at slice 0 (any direction). PARAMETERS flip (toggle) - this says whether to color the "on" voxels 0 or 255. levels (islider) - this defines the levels of recursion. 1 is a 3x3x3 cube (27 nodes) 2 is a 9x9x9 cube (729 nodes) 3 is a 27x27x27 cube (19,683 nodes) 4 is a 81x81x81 cube (531,441 nodes) 5 is a 243x243x243 cube (14,348,907 nodes and takes a while to compute!) OUTPUTS output - field 3D 3-space 1-vector uniform byte This can be rendered with tracer, or orthosliced EXAMPLE NETWORKS This is stored as menger.net in this directory. Menger sponge | compute shade | tracer | display tracker RELATED MODULES CURDLE (at the IAC) is another example of a module which produces recursively defined "fractal" data sets.