Simplex noise

Simplex Noise is a method for building an n-dimensional noise function , comparable to Perlin Noise , but with less computational effort, especially in higher dimensions.

Ken Perlin developed the algorithm in 2001 in order to circumvent the limits of the classical noise function, especially in higher dimensions.

The advantages of Simplex Noise compared to Perlin Noise:

• less computational complexity and fewer multiplications
• scales in higher dimensions (4D, 5D). With less computational effort, the complexity is for dimensions, instead of that of classic noise ${\displaystyle O(n^{2})}$ ${\displaystyle n}$ ${\displaystyle O(2^{n})}$
• no noticeable directional artifacts (is isotropic)
• well-defined and continuous gradients that can be calculated cheaply
• easy to implement in hardware .

While classic noise interpolates between the values ​​from the surrounding hypergrid endpoints (i.e. north, south, east and west in 2D), simplex noise divides the space into simplizes , i.e. H. n-dimensional triangles that are interpolated between. This reduces the number of data points. While a hypercube has corners in n dimensions , a simplex in n dimensions has only n + 1 corners in dimensions. The triangles are equilateral in 2D, but in higher dimensions the simplices are only approximately regular. ${\displaystyle 2^{n}}$

Simplex Noise is useful for computer graphics applications where noise is typically calculated over 2, 3, 4, or possibly 5 dimensions. -Balls with -Simplex corners are not dimensioned close enough for larger dimensions . This reduces the bearer of the function to zero in large parts of the room. ${\displaystyle n}$ ${\displaystyle n}$

swell

• Short technical article with source code by Stefan Gustavson (PDF)
• Animated "rubber track" as demo Perlins for simplex noise
• Another implementation of simplex noise in C ++ (SimplexNoise1234)

Individual evidence

1. ↑ Ken Perlin: Noise hardware . (PDF) In: Marc Olano (Ed.): SIGGRAPH 2002 Course 36 Notes. Real-time shading languages. 2001 (SIGGRAPH real-time shading course).
2. ↑ Ken Perlin: Making Noise . Retrieved on February 24, 2014 (from a GDCHardcore lecture, December 9, 1999).