Prime gradient noise

Abstract Procedural noise functions are fundamental tools in computer graphics used for synthesizing virtual geometry and texture patterns. Ideally, a procedural function should be compact, aperiodic, parameterized, randomly accessible. Traditional lattice such as Perlin noise, however, exhibit periodicity due to the axial correlation induced while hashing vertices gradients. In this paper, we introduce parameterized called prime gradient (PGN) that minimizes discernible enhancing algorithmic efficiency. PGN utilizes gradients, set of random unit vectors constructed from subsets numbers plotted polar coordinate system. To map indices employs Szudzik pairing, bijection F : ℕ 2 → ℕ. Compositions pairing higher dimensions. At core is ability parameterize generation though sequence offsetting which facilitates creation fractal with varying levels heterogeneity ranging homogeneous hybrid multifractals. A comparative spectral analysis proposed other noises including show significantly reduces hence, texture. We demonstrate utility several examples modeling, pattern synthesis, solid texturing.