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 3×3 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 it would have created a 45″ 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.
This pattern was published in the original printing of Extreme Double-knitting but has been supplanted by a new revision, so I have re-released it as a standalone pattern