Simplex noise is a procedural texture primitive, a type of gradient noise used by visual effects artists to increase the appearance of realism in computer graphics.
Simplex noise is a procedural texture primitive, a type of gradient noise used by visual effects artists to increase the appearance of realism in computer graphics.
It was developed by Ken Perlin to overcome some of the limitations of Perlin noise while having similar properties. It is particularly useful at higher dimensions as computation time scales O(n^2) compared to O(2^n) for conventional noise (where n is the number of dimensions). Minor but noticeable directional artefacts found in Perlin noise have also been corrected in Simplex noise.
Simplex noise gets its name from the "Simplex" that the noise is based upon; a simplex is an n-dimensional equilateral triangle and as such has n+1 corners. In contrast Perlin noise is based upon the Square (or n-dimensional equivalent; square, cube, hypercube) and has 2^n corners.
Fractal noise
Often several octaves of Simplex noises are summed to create fractal noise (other basis noise functions can also be used for fractal noise). Several noises are combined with different frequencies leading to small scale and long scale coherence. The ratios with which these different frequencies are combined is determined by the persistence and can be calculated as follows:
frequency = 2^i
amplitude = persistence^i
where i is the octave number (an integer)
Examples of fractal noise resulting from several octaves of simplex noise
Low Persistence:
High Persistence:
High Persistence (larger scale):
References:
http://en.wikipedia.org/wiki/Simplex_noise
http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
