Simplex Noise in C# for Unity3D - Adapted from James Livingston's MinePackage: http://forum.unity3d.com/threads/minepackage-minecraft-starter-package.69573/

gistfile1.cs

using UnityEngine;
using System.Collections;

public class SimplexNoiseGenerator {
    private int[] A = new int[3];
    private float s, u, v, w;
    private int i, j, k;
    private float onethird = 0.333333333f;
    private float onesixth = 0.166666667f;
    private int[] T;
	
	public SimplexNoiseGenerator() {
        if (T == null) {
            System.Random rand = new System.Random();
            T = new int[8];
            for (int q = 0; q < 8; q++)
                T[q] = rand.Next();
        }
	}
	
	public SimplexNoiseGenerator(string seed) {
		T = new int[8];
		string[] seed_parts = seed.Split(new char[] {' '});
		
		for(int q = 0; q < 8; q++) {
			int b;
			try {
				b = int.Parse(seed_parts[q]);
			} catch {
				b = 0x0;
			}
			T[q] = b;
		}
	}
	
	public SimplexNoiseGenerator(int[] seed) { // {0x16, 0x38, 0x32, 0x2c, 0x0d, 0x13, 0x07, 0x2a}
		T = seed;
	}
	
	public string GetSeed() {
		string seed = "";
		
		for(int q=0; q < 8; q++) {
			seed += T[q].ToString();
			if(q < 7)
				seed += " ";
		}
		
		return seed;
	}
	
	public float coherentNoise(float x, float y, float z, int octaves=1, int multiplier = 25, float amplitude = 0.5f, float lacunarity = 2, float persistence = 0.9f) {
		Vector3 v3 = new Vector3(x,y,z)/multiplier;
		float val = 0;
		for (int n = 0; n < octaves; n++) {
		  val += noise(v3.x,v3.y,v3.z) * amplitude;
		  v3 *= lacunarity;
		  amplitude *= persistence;
		}
		return val;
	}
	
    public int getDensity(Vector3 loc) {
		float val = coherentNoise(loc.x, loc.y, loc.z);
		return (int)Mathf.Lerp(0,255,val);
    }
    
    // Simplex Noise Generator
    public float noise(float x, float y, float z) {
        s = (x + y + z) * onethird;
        i = fastfloor(x + s);
        j = fastfloor(y + s);
        k = fastfloor(z + s);

        s = (i + j + k) * onesixth;
        u = x - i + s;
        v = y - j + s;
        w = z - k + s;

        A[0] = 0; A[1] = 0; A[2] = 0;

        int hi = u >= w ? u >= v ? 0 : 1 : v >= w ? 1 : 2;
        int lo = u < w ? u < v ? 0 : 1 : v < w ? 1 : 2;

        return kay(hi) + kay(3 - hi - lo) + kay(lo) + kay(0);
    }

    float kay(int a) {
        s = (A[0] + A[1] + A[2]) * onesixth;
        float x = u - A[0] + s;
        float y = v - A[1] + s;
        float z = w - A[2] + s;
        float t = 0.6f - x * x - y * y - z * z;
        int h = shuffle(i + A[0], j + A[1], k + A[2]);
        A[a]++;
        if (t < 0) return 0;
        int b5 = h >> 5 & 1;
        int b4 = h >> 4 & 1;
        int b3 = h >> 3 & 1;
        int b2 = h >> 2 & 1;
        int b1 = h & 3;

        float p = b1 == 1 ? x : b1 == 2 ? y : z;
        float q = b1 == 1 ? y : b1 == 2 ? z : x;
        float r = b1 == 1 ? z : b1 == 2 ? x : y;

        p = b5 == b3 ? -p : p;
        q = b5 == b4 ? -q : q;
        r = b5 != (b4 ^ b3) ? -r : r;
        t *= t;
        return 8 * t * t * (p + (b1 == 0 ? q + r : b2 == 0 ? q : r));
    }

    int shuffle(int i, int j, int k) {
        return b(i, j, k, 0) + b(j, k, i, 1) + b(k, i, j, 2) + b(i, j, k, 3) + b(j, k, i, 4) + b(k, i, j, 5) + b(i, j, k, 6) + b(j, k, i, 7);
    }

    int b(int i, int j, int k, int B) {
        return T[b(i, B) << 2 | b(j, B) << 1 | b(k, B)];
    }

    int b(int N, int B) {
        return N >> B & 1;
    }
    
	int fastfloor(float n) {
	    return n > 0 ? (int)n : (int)n - 1;
	}
}

Apologies for the late replies. I didn't see any notifications about these comments until the last one.

To use this in a Unity project do I simply drop this script onto an empty gameObject, or do I need to install any prerequisites?

@Quentin-H At least in Unity 10 years ago, it was a standalone library. I used the coherent noise in a Minecraft clone to experiment with terrain generation.

What is the range of the noise function?

@mackycheese21 From memory I believe -1 to +1. I picked a base plane (e.g. sea level), then used the noise to generate a height map. Within the height range I set different biomes for the transitions (bedrock, lava, stone, dirt, grass/water, mountain/rock, snow).

I'm not sure if I was doing something wrong with the code, however I noticed some really bad repetition for larger values of x y and z.

@AsherBearce That's possible. I haven't used this code for about 10 years -- although I did update my old Minecraft-inspired world generator to show my kids last year and it still worked fine in modern Unity.

My x, y, z values were based on world coordinates with 1 meter as the unit. I never needed more than few thousand blocks in any cardinal direction (I also didn't need altitude). The intensity of noise determined the height at a given location, which then determined the terrain features.

I created a simple app to generate a bitmap image the size of my expected terrain. That let me tweak the octaves, multiplier, amplitude, lacunarity, and persistence with UI sliders until I had a good result. Then I took those values into my app.

I found some other terrain generation screenshots using this code from 10 years ago:

Oh interesting, it must be something silly I'm doing on my end.

@AsherBearce I found some of the older code. Here's an example of how I was calling it:

SimplexNoiseGenerator noise = new SimplexNoiseGenerator();
float n = noise.coherentNoise(blockX,0,blockZ,4,82,2f,0.5f,1.57f);

Then I took that noise value n and used it to create a height. It's a float value from -1.0 to +1.0, so you can multiply it by the midpoint of whatever range of valid height values.

Simplex noise is coherent, so it's smoothly pseudorandom -- hills and valleys are gradual curves rather than chaotic points.

When I made the bitmap version it had 256 values per pixel for intensity.

To simulate sea level where you could dig down or up, the midpoint was 128, so the negative n values reduced midpoint intensity and the positive values increased it. You could adjust the midpoint/underground/aboveground as needed for your terrain/world (e.g. more sky above than underground below, rather than 50/50).

Here is a little noise texture generator I wrote using this code. It generates seamlessly tiling textures.