Perlin Noise

Welcome back! Last time we discussed the Diamond-Square algorithm. While that algorithm works great for certain cases, it had its drawbacks that we discussed last post. Instead of fixing those we're gonna just implement a different way to get similar results. That way is Perlin Noise!

So what is Perlin Noise? Well similarly to Diamond-Square, it's a way of generating random height-maps that can be used for a number of things. Games are generally a place they are used commonly to create random terrains. It is very simple to implement and produces much better looking results than Diamond-Square as it does not have the same artifacts. The biggest drawback to Perlin Noise is that it is slightly slower than Diamond Square and it can only generate squares. Both of these can be worked around though so lets dive into the code.



Above we can see the constructor for our Perlin Noise class. We haven't looked at most of the constructors before but this one does more than most. In this one we fill a vector with random values. These random values are dependent on our seed and act as the "gradient" for the rest of the algorithm which will be talked about more later on.



Here we have our perlin method. This is where the majority of our calculations and code is. There is a lot of stuff going on here so I will cover the basics. If you are very interested in each low level idea, Ken Perlin wrote an entire paper about Perlin Noise you can read. So, carrying on. First we take the floor of our values and bitwise and them with 255 ( Read here if you don't know what bitwise operations are ). We then subtract these values from the floor of themselves. Then we see another method we haven't seen yet, fade. Let's look at fade.



Here we can see all of the methods we haven't seen yet. Fade and grad are actually unique in that every implementation of Perlin Noise is supposed to/should use the same equation made by Ken. You can see it is just a simple math equation where we multiply and add some values. So carrying on, we can next see where our gradient values come on. These are chosen based from our x, y, and z, and the subsequent variables that came from them. We then see the grad method actually used. Here a series of bitwise operations change the values. These help insure randomness. They are then linear interpreted ( lerp ) with each other in our lerp method. This is just a stand linear interpolation, nothing fancy. This is done multiple times over every point. So how do we actually use this?



Above is our to_png method. We need some visual representation to output this to to see our results and that is how we do it. So lets run it and see what it looks like.

Wow, look at that! It looks random! And every time we run it it will be random. But wait... What is the commented code? Well with Perlin Noise we can easily modify the produced values to create something... different. Let's uncomment that code and run it and see what happens!

Wow! Look at that! That commented code works well for producing a wood-like texture. Pretty nifty. Playing around more can create different effects but I will let you explore them yourselves. Hope you enjoyed this and learned something new. As usual, see the full code here.