Block-space GPU mapping for embedded Sierpiński gasket fractals

Cristobal A Navarro, Raimundo Vega, Benjamin Bustos, Nancy Hitschfeld Kahler
December 2017
DOI arXiv

Abstract

This research examines GPU thread mapping for a Sierpiński gasket fractal embedded in an n×n discrete Euclidean space. The authors propose a block-space mapping function that operates in O(log2 log2(n)) time and uses a thread count proportional to n raised to the Hausdorff dimension (approximately 1.58), achieving parallel space efficiency proportional to O(n^H). Compared to traditional bounding-box approaches, the method delivers sub-exponential improvements in parallel space utilization with speedups reaching approximately 10x for n = 2^16.

Type
Conference paper
Publication
2017 IEEE 19th International Conference on High Performance Computing and Communications (HPCC/SmartCity/DSS)
GPU Computing Thread Mapping Fractals
Cristobal A Navarro
Cristobal A Navarro
Professor at the Universidad Austral de Chile

Professor at the Universidad Austral de Chile

Nancy Hitschfeld Kahler
Nancy Hitschfeld Kahler
+Lab founder | Full Professor Universidad de Chile

Full Professor at the Department of Computer Science, University of Chile. Her main research interests include geometric modeling, geometric meshes, and parallel algorithms (GPU computing), focused in computational science, and engineering applications.