A pyramid that grows by powers of 2

The features of a new pyramid scheme are presented. It is based on a decomposition of a square grid into overlapping 2 x 2 blocks. The diagonal of the square cell becomes the side of a square at the next higher level. Assume unit length at the bottom level 0 of the pyramid, then the side length of a cell at level n is 2^n^2. The number of the elements at level n + 1 is one half of the level n.