Better Gradient Noise

We present three improvements to Perlin’s gradient noise algorithm. First, a small change in the permutation hash function combined with separate pseudorandom tables yields significantly better axial decorrelation. Second, a modification to the reconstruction kernel approximating a global higher-order differencing operator produces better bandlimitation. Third, the quality of 2D surfaces using solid 3D noise is improved by reconstructing the stencil projected onto a surface normal. These three techniques are mutually orthogonal, generalize to higher dimensions, and are applicable to nearly any gradient noise, including simplex noise. Combining them yields a desirable Fourier spectrum for graphics applications.