This work studies the problem of GPU thread mapping for a Sierpinski gasket
fractal embedded in a discrete Euclidean space of n x n. A block-space map
lambda : Z2E -> Z2F is proposed, from Euclidean parallel space E to embedded
fractal space F, that maps in O(log2 log2(n)) time and uses no more than O(nH)
threads with H approx 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 > n0. Experimental performance tests show that in practice
lambda(omega) can produce performance improvement at any block-size once n > n0
= 28, reaching approximately 10× of speedup for n = 216 under typical block
configurations.