Worley Noise

Previously we discussed two different noise algorithms, Diamond-Square and Perlin noise. Both of these noise algorithms produce similar results and can be used for a variety of things but there are certain places they aren't great. So today we are going to talk about one last noise algorithm that is versatile and produces results very unlike the previous two algorithms. That algorithm is Worley Noise. Also referred to as Cell Noise or Voronoi noise, this algorithm is very useful in generating or simulating stone, water, and cells. So lets get started in talking about this!

Worley noise is one of the more complicated noise function we've covered. Not only that, it is also the slowest of them. It however is more customizable than the other ones. We will see examples of this at the end. First, lets take a look at our constructor.



Here we can see where everything is set up. We have a variable called permutations that is set with unique values from 0 to 255. These numbers are then swapped around to make them in a random order. These are used to determine the location of the "cells" in the final image. In the constructor we call the fill_map method which can be seen below.


The idea of the fill map method is simple. It iterates through each pixel and determines the color it should be. Along with that it also saves the maximum and minimum values that are seen. These can be used for scaling if necessary. In the fill_map method we see smoothed_noise is called so lets look at that.


The smoothed_noise method is where all the calculations are done. All of these are based on distances which will return the grayscale value for that pixel. How this is done can vary though. In the code we see 3 commented out lines. If one is uncommented we can get a completely different looking picture. These are the distance functions and they are what make this algorithm so powerful. By simply changing the distance algorithm a stone texture, water texture, or many other textures can be created. We will see examples of all of these when we actually run the algorithm. Let's take a look at how these distances actually work.


Each distance method is a form of the distance formula ( sqrt( x2 - x1 ) ^ 2 + ( y2 - y1 ) ^ 2 ) ), but they all have their own touches. So now that we have a basic understanding of the algorithm, lets see what it actually outputs. Up first we are going to use euclidean distance.

Euclidean Distance

Here we can see the algorithm output a picture that looks similar to cells. It's very unlike every other noise algorithm we've seen this far. Next, manhattan distance. 

Manhattan Distance

Manhattan distance creates diamond-like shapes. It also creates some very light and very dark areas which can be seen above. Now, chebychev distance.

Chebychev Distance

Chebychev has a similar look to manhattan although instead of diamonds they are more square and very interesting looking. Lastly let's look at quadratic distance. 

Quadratic Distance

Quadratic creates a similar look to euclidean but slightly different. All of these distance function can be modified and more can be added to create many different and unique effects. It's just a matter of playing with them.

As usual I hope you learned something new or found this interesting. For the full source code you can go here. See you next time!