Perlin noise infinite generation/tiling

perlin-noiserandom

I got the Perlin Noise algorithm from Here working, and I was wondering if there was a way to make the terrain infinite. The problem lies within this function(Java):

float[][] GenerateWhiteNoise(int width, int height, int seed)
    {
        Random random;
        random = new Random(seed);
        float[][] noise = new float[width][height];
     
        for (int i = 0; i < width; i++)
        {
            for (int j = 0; j < height; j++)
            {
                noise[i][j] = (float)random.nextDouble() % 1;
            }
        }
        
        System.out.println("Generated White Noise with seed:"+seed+"; xOffset:"+xOffset+"; yOffset:"+yOffset);
     
        return noise;
    }

Does anyone know how to make the random generator for this function rely on the offset of the current tile of noise(these are stored in two variables, xOffset and yOffset)? Using something like Math.pow(xOffset,yOffset) and setting that as the seed produced choppy, broken results that simply don't work. Does anybody have some insight?

Any help would be appreciated, thanks!

Best Answer

Here's tiling 4D noise implemented in a GLSL shader:

http://shaderfrog.com/app/view/254

It's based on the implementation in this answer https://gamedev.stackexchange.com/questions/23625/how-do-you-generate-tileable-perlin-noise/23639

Related Solutions

Python – Random string generation with upper case letters and digits

Answer in one line:

''.join(random.choice(string.ascii_uppercase + string.digits) for _ in range(N))

or even shorter starting with Python 3.6 using random.choices():

''.join(random.choices(string.ascii_uppercase + string.digits, k=N))

A cryptographically more secure version: see this post

''.join(random.SystemRandom().choice(string.ascii_uppercase + string.digits) for _ in range(N))

In details, with a clean function for further reuse:

>>> import string
>>> import random
>>> def id_generator(size=6, chars=string.ascii_uppercase + string.digits):
...    return ''.join(random.choice(chars) for _ in range(size))
...
>>> id_generator()
'G5G74W'
>>> id_generator(3, "6793YUIO")
'Y3U'

How does it work ?

We import string, a module that contains sequences of common ASCII characters, and random, a module that deals with random generation.

string.ascii_uppercase + string.digits just concatenates the list of characters representing uppercase ASCII chars and digits:

>>> string.ascii_uppercase
'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
>>> string.digits
'0123456789'
>>> string.ascii_uppercase + string.digits
'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789'

Then we use a list comprehension to create a list of 'n' elements:

>>> range(4) # range create a list of 'n' numbers
[0, 1, 2, 3]
>>> ['elem' for _ in range(4)] # we use range to create 4 times 'elem'
['elem', 'elem', 'elem', 'elem']

In the example above, we use [ to create the list, but we don't in the id_generator function so Python doesn't create the list in memory, but generates the elements on the fly, one by one (more about this here).

Instead of asking to create 'n' times the string elem, we will ask Python to create 'n' times a random character, picked from a sequence of characters:

>>> random.choice("abcde")
'a'
>>> random.choice("abcde")
'd'
>>> random.choice("abcde")
'b'

Therefore random.choice(chars) for _ in range(size) really is creating a sequence of size characters. Characters that are randomly picked from chars:

>>> [random.choice('abcde') for _ in range(3)]
['a', 'b', 'b']
>>> [random.choice('abcde') for _ in range(3)]
['e', 'b', 'e']
>>> [random.choice('abcde') for _ in range(3)]
['d', 'a', 'c']

Then we just join them with an empty string so the sequence becomes a string:

>>> ''.join(['a', 'b', 'b'])
'abb'
>>> [random.choice('abcde') for _ in range(3)]
['d', 'c', 'b']
>>> ''.join(random.choice('abcde') for _ in range(3))
'dac'

Perlin Noise generation for terrain

Perlin noise is completely controlled by the different variables you set, i.e. amplitude, frequency and persistance. The amount of octaves has a little change, but not much. In code that I have written in the past I have just played around with the order of magnitude of the frequency and persistance until I have gotten what I needed. I can try to find my old source if needed.

PerlinNoise.h

#pragma once

class PerlinNoise
{
public:

  // Constructor
    PerlinNoise();
    PerlinNoise(double _persistence, double _frequency, double _amplitude, int _octaves, int _randomseed);

  // Get Height
    double GetHeight(double x, double y) const;

  // Get
  double Persistence() const { return persistence; }
  double Frequency()   const { return frequency;   }
  double Amplitude()   const { return amplitude;   }
  int    Octaves()     const { return octaves;     }
  int    RandomSeed()  const { return randomseed;  }

  // Set
  void Set(double _persistence, double _frequency, double _amplitude, int _octaves, int _randomseed);

  void SetPersistence(double _persistence) { persistence = _persistence; }
  void SetFrequency(  double _frequency)   { frequency = _frequency;     }
  void SetAmplitude(  double _amplitude)   { amplitude = _amplitude;     }
  void SetOctaves(    int    _octaves)     { octaves = _octaves;         }
  void SetRandomSeed( int    _randomseed)  { randomseed = _randomseed;   }

private:

    double Total(double i, double j) const;
    double GetValue(double x, double y) const;
    double Interpolate(double x, double y, double a) const;
    double Noise(int x, int y) const;

    double persistence, frequency, amplitude;
    int octaves, randomseed;
};

PerlinNoise.cpp

#include "PerlinNoise.h"

PerlinNoise::PerlinNoise()
{
  persistence = 0;
  frequency = 0;
  amplitude  = 0;
  octaves = 0;
  randomseed = 0;
}

PerlinNoise::PerlinNoise(double _persistence, double _frequency, double _amplitude, int _octaves, int _randomseed)
{
  persistence = _persistence;
  frequency = _frequency;
  amplitude  = _amplitude;
  octaves = _octaves;
  randomseed = 2 + _randomseed * _randomseed;
}

void PerlinNoise::Set(double _persistence, double _frequency, double _amplitude, int _octaves, int _randomseed)
{
  persistence = _persistence;
  frequency = _frequency;
  amplitude  = _amplitude;
  octaves = _octaves;
  randomseed = 2 + _randomseed * _randomseed;
}

double PerlinNoise::GetHeight(double x, double y) const
{
  return amplitude * Total(x, y);
}

double PerlinNoise::Total(double i, double j) const
{
    //properties of one octave (changing each loop)
    double t = 0.0f;
    double _amplitude = 1;
    double freq = frequency;

    for(int k = 0; k < octaves; k++) 
    {
        t += GetValue(j * freq + randomseed, i * freq + randomseed) * _amplitude;
        _amplitude *= persistence;
        freq *= 2;
    }

    return t;
}

double PerlinNoise::GetValue(double x, double y) const
{
    int Xint = (int)x;
    int Yint = (int)y;
    double Xfrac = x - Xint;
    double Yfrac = y - Yint;

  //noise values
  double n01 = Noise(Xint-1, Yint-1);
  double n02 = Noise(Xint+1, Yint-1);
  double n03 = Noise(Xint-1, Yint+1);
  double n04 = Noise(Xint+1, Yint+1);
  double n05 = Noise(Xint-1, Yint);
  double n06 = Noise(Xint+1, Yint);
  double n07 = Noise(Xint, Yint-1);
  double n08 = Noise(Xint, Yint+1);
  double n09 = Noise(Xint, Yint);

  double n12 = Noise(Xint+2, Yint-1);
  double n14 = Noise(Xint+2, Yint+1);
  double n16 = Noise(Xint+2, Yint);

  double n23 = Noise(Xint-1, Yint+2);
  double n24 = Noise(Xint+1, Yint+2);
  double n28 = Noise(Xint, Yint+2);

  double n34 = Noise(Xint+2, Yint+2);

    //find the noise values of the four corners
    double x0y0 = 0.0625*(n01+n02+n03+n04) + 0.125*(n05+n06+n07+n08) + 0.25*(n09);  
    double x1y0 = 0.0625*(n07+n12+n08+n14) + 0.125*(n09+n16+n02+n04) + 0.25*(n06);  
    double x0y1 = 0.0625*(n05+n06+n23+n24) + 0.125*(n03+n04+n09+n28) + 0.25*(n08);  
    double x1y1 = 0.0625*(n09+n16+n28+n34) + 0.125*(n08+n14+n06+n24) + 0.25*(n04);  

    //interpolate between those values according to the x and y fractions
    double v1 = Interpolate(x0y0, x1y0, Xfrac); //interpolate in x direction (y)
    double v2 = Interpolate(x0y1, x1y1, Xfrac); //interpolate in x direction (y+1)
    double fin = Interpolate(v1, v2, Yfrac);  //interpolate in y direction

    return fin;
}

double PerlinNoise::Interpolate(double x, double y, double a) const
{
    double negA = 1.0 - a;
  double negASqr = negA * negA;
    double fac1 = 3.0 * (negASqr) - 2.0 * (negASqr * negA);
  double aSqr = a * a;
    double fac2 = 3.0 * aSqr - 2.0 * (aSqr * a);

    return x * fac1 + y * fac2; //add the weighted factors
}

double PerlinNoise::Noise(int x, int y) const
{
    int n = x + y * 57;
    n = (n << 13) ^ n;
  int t = (n * (n * n * 15731 + 789221) + 1376312589) & 0x7fffffff;
    return 1.0 - double(t) * 0.931322574615478515625e-9;/// 1073741824.0);
}