A variation of the Sierpinski gasket can be formed by splitting a square into four equal pieces, each scaled by 1/2 and then removing the upper right square. The following video illustrates the construction.
The IFS for this version of the Sierpinski Gasket is
$$\begin{array}{l} {f_1}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}} {0.5} & 0 \\ 0 & {0.5} \\ \end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}} 0 \\ {0.5} \\ \end{array}} \right] \\ {f_2}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}} {0.5} & 0 \\ 0 & {0.5} \\ \end{array}} \right]{\bf{x}} \\ {f_3}({\bf{x}}) = \left[ {\begin{array}{*{20}{c}} {0.5} & 0 \\ 0 & {0.5} \\ \end{array}} \right]{\bf{x}} + \left[ {\begin{array}{*{20}{c}} {0.5} \\ 0 \\ \end{array}} \right] \\ \end{array}$$
