The following method, create_carpet, initiates the recursion to a certain recursive level according to a user-defined Parameter mslevel, defined under Global Definitions in the Model Builder. It sets a limit at 5 levels in order to avoid creating an exceedingly large geometry. The method assumes that you have created a 2D Component and that you have declared an integer scalar variable counter.

The method create_carpet in turn calls the main recursive function carpet, listed below, using four input arguments for the recursion level, the center x- and y-coordinates, and the current side length.

The input arguments are defined in the method’s Settings window, as shown below.

The code for the method carpet is shown below.

Note that the number of square geometry objects defined for the level 3 carpet is 512. The number of geometry objects for a level-N carpet is 8N. This means that for the maximum level 5 set by the method create_carpet, the resulting geometry has 32,768 geometry objects.

The methods for the Sierpinski carpet readily generalize to 3D. However, in 3D, you need to be careful not to generate more objects than your computer can handle. The method assumes that you have created a 3D Component and that you have declared an integer scalar variable counter.

The following method, create_sponge, initiates the recursion.

The method sponge, shown below, is called by the above method and recursively creates a Menger sponge.

In this case, the number of geometry objects grows with the level N as 20N and the level-2 sponge shown above has 400 block geometry objects.