This pattern has been replaced in the 2018 revision of Extreme Double-knitting with a pattern called Sierpinski L5. Because this is still a good pattern and is no longer included in a book, I have re-released it as a standalone pattern.

The Sierpinski Carpet is a type of fractal — meaning, in simple terms, that it is a shape made up of smaller copies of itself, which are in turn made up of smaller copies, and so on ad infinitum. Fractals can be simplified by only extending them to a certain iteration — and some simplified fractals can be charted for knitting. This fractal is created by starting with a square, then dividing it in 9ths (with a 3x3 grid) and removing the center square. Further iterations are created by subdividing the resulting squares, etc.

My original idea was to build a Level-5 Sierpinski carpet, but at 251 pairs square, it would have created a 45-inch square throw blanket, whereas I was targeting a baby blanket. So I redesigned it so it would have a Level 4 fractal surrounded by Level 3s, surrounded by Level 2s. At about 33 inches square after blocking, this came out just about right.