This work analyzes the possible performance benefits one could obtain by employing a Self-Similar type of GPU thread map on data-parallel m-simplex domains, which is the geometrical representation of several interaction problems. The main contributions of this work are (1) the proposal of a new block-space map H: mathbb{Z}^{m}mapsto mathbb{Z}^{m} based on a self-similar set of sub-orthotopes, and (2) its analysis in terms of performance and thread space, from which we obtain that mathcal{H}(omega) is time and space efficient for 2-simplices and only time efficient for 3-simplices unless the theoretical model is relaxed to allow concurrent parallel spaces. Experimental tests on a 2-simplex domain support the theoretical results, giving up to 30% of speedup over the standard approach. We also show how the map can utilize GPU tensor cores and further accelerate through fast matrix-multiply-accumulate operations. Finally, we show that extending the map to general m-simplices is a non-trivial optimization problem and depends of the choice of two parameters r, beta, for which we provide some insights in order to obtain a mathcal{H}(omega) map that can be m! times more space efficient than a bounding-box approach.