Before using the MATLAB scripts, it is important to explain the
construction of the Sierpinski Carpet and our notation used. The
Sierpinski Carpet, SC , is constructed by eight contraction mappings.
The maps contract the unit square by a factor of 1/3 and translate to
one of the eight points along the boundary. SC is the unique nonempty
compact set satisfying the self-similar identity
For convention, we define the boundary of SC to be the outter unit square containing all of SC.
There are two ways that we refer to cells in any graph approximation of SC. The first is a labeling by cell address,
in which a cell is named by the sequence of contractions maps that map
the unit square to that cell. The length of a cell address depends on
which level graph approximation you are working with. The second method
is a labeling used for the matrices in the MATLAB codes in which we
order each cell by cell address in lexicographic order. The figures
below show a level 2 SC with each cell labeled each way. To avoid
confusion with notation when referring to a cell by its cell address, we
will enclose it in single quotes (making it a string in MATLAB).
