Dog Ear Carpet Fractal

In order to make my fractal, I removed the points: (1,1), (2,0) and  (2,1). Removing these coordinates resulted in my fractal having an "L"  shape pattern. In the second iteration of this fractal, the "L" shape attaches to the top of an upside down L, forming what look like dog ears. Below are levels 1, 2 and 3 of my fractal carpet.