Abstract: We describe a novel technique for the fast production of large point sets with different spectral properties. In contrast to tile-based methods we use so-called AA Patterns: ornamental point sets obtained from quantization errors. These patterns have a discrete and structured number-theoretic nature, can be produced at very low costs, and possess an inherent structural indexing mechanism equivalent to those used in recursive tiling techniques. This allows us to generate, manipulate and store point sets very efficiently. The technique outperforms existing methods in speed, memory footprint, quality, and flexibility. This is demonstrated by a number of measurements and comparisons to existing point generation algorithms.