This work studies the problem of GPU thread mapping for a Sierphiski gasket fractal embedded in a discrete Euclidean space of n x n. A block-space map lambda : Z(E)(2) bar right arrow Z(F)(2) is proposed, from Euclidean parallel space E to embedded fractal space F, that maps in O(log(2) log(2) (n)) time and uses no more than O(n(H)) threads with H approximate to 1.58... being the Hausdorff dimension, making it parallel space efficient. When compared to a bounding-box map, lambda(omega) offers a sub-exponential improvement in parallel space and a monotonically increasing speedup once n > n(0). Experimental performance tests show that in practice A(w) can produce performance improvement at any block-size once n > n(0) = 2(8), reaching approximately 10x of speedup for n = 2(16) under typical block configurations.