Perlin noise basics

Perlin noise is the algorithm used for computing values of a pseudo-random function, smoothly depending on its parameters. It was originally developed in 1982 by Ken Perlin and named after him. Today, it's called classical noise. In 2001, Ken Perlin developed a modification of the algorithm and called it simplex noise. Simplex noise works faster than classical noise, but the results differ a little.

Nowadays both noises are widely used. Often it is not very important which algorithm is used in a given case; that's why we will refer to both of them as just Perlin noise.

For a developer, the Perlin noise function ofNoise( t ) just takes values in the range [0, 1] and depends on the parameter t. The dependence is smooth; that is, a small change in the value of the input parameter t leads to a small change in the output result. But, unlike any other mathematical function such as sin( t ) or exp( t ), Perlin noise is not periodic and is not constantly increasing. It has complex and non-repetitive behavior, which is called pseudo-random behavior. That is, on one hand it is a function that seems random, and on the other hand it is fixed. No matter how many times you compute ofNoise( t ) for the given t, you will obtain exactly the same result.

The main advantage of Perlin noise compared to an ordinary pseudo-random number generator, ofRandom( a, b ), is the controllable smoothness. Indeed, if we will consider float values A0 = ofNoise( t ), A1 = ofNoise( t+0.01 ), and A2 = ofNoise( t+0.1 ) for different values of t, we will find that often A1 is closer to A0 than A2. Hence we can control the resultant smoothness of the graph of ofNoise( t ), built for discrete set of values t, by controlling the step of incrementing these values. Contradictorily, two calls of ofRandom( 0, 1 ) generate two uncorrelated numbers, and there is no way to control their proximity.

Now let's see how to use Perlin noise in openFrameworks projects.