This lattice-like pattern is, in fact, a type of fractal for its recursive nature. I discovered this one while attempting to solve a geometric puzzle.
In the image above four modules in 1 can be tiled to form pattern 2. Four module 2 can be used to form the pattern 3. And the process goes on. The number of module used in each level increases four-fold. ie. 1, 4, 16, 64, 256, .... And yet the overall shape is maintained at any level.
The following is another similar fractal. The pictures themselves are self-explanatory.
I have checked with WolframMathworld site but couldn't find anything similar.
