Diamond square algorithm

Question

I\'m trying to write the Diamond-Square algorithm in Java to generate a random map but can\'t figure out the implementation...

Anyone with some Java code (or other l

Answer 1

This is an interesting algorithm for generating values. Here is an implementation that I have created based on the explanation give at this page in the references from the wikipedia article. It will create "spherical values" (wrapped at all the edges). There are notes in the comments for how to change it to generate new values on the edges instead of wrapping (though the meaning of average for the edges isn't really correct in these cases).

//size of grid to generate, note this must be a
//value 2^n+1
final int DATA_SIZE = 9;
//an initial seed value for the corners of the data
final double SEED = 1000.0;
double[][] data = new double[DATA_SIZE][DATA_SIZE];
//seed the data
data[0][0] = data[0][DATA_SIZE-1] = data[DATA_SIZE-1][0] = 
  data[DATA_SIZE-1][DATA_SIZE-1] = SEED;

double h = 500.0;//the range (-h -> +h) for the average offset
Random r = new Random();//for the new value in range of h
//side length is distance of a single square side
//or distance of diagonal in diamond
for(int sideLength = DATA_SIZE-1;
    //side length must be >= 2 so we always have
    //a new value (if its 1 we overwrite existing values
    //on the last iteration)
    sideLength >= 2;
    //each iteration we are looking at smaller squares
    //diamonds, and we decrease the variation of the offset
    sideLength /=2, h/= 2.0){
  //half the length of the side of a square
  //or distance from diamond center to one corner
  //(just to make calcs below a little clearer)
  int halfSide = sideLength/2;

  //generate the new square values
  for(int x=0;x<DATA_SIZE-1;x+=sideLength){
    for(int y=0;y<DATA_SIZE-1;y+=sideLength){
      //x, y is upper left corner of square
      //calculate average of existing corners
      double avg = data[x][y] + //top left
      data[x+sideLength][y] +//top right
      data[x][y+sideLength] + //lower left
      data[x+sideLength][y+sideLength];//lower right
      avg /= 4.0;

      //center is average plus random offset
      data[x+halfSide][y+halfSide] = 
    //We calculate random value in range of 2h
    //and then subtract h so the end value is
    //in the range (-h, +h)
    avg + (r.nextDouble()*2*h) - h;
    }
  }

  //generate the diamond values
  //since the diamonds are staggered we only move x
  //by half side
  //NOTE: if the data shouldn't wrap then x < DATA_SIZE
  //to generate the far edge values
  for(int x=0;x<DATA_SIZE-1;x+=halfSide){
    //and y is x offset by half a side, but moved by
    //the full side length
    //NOTE: if the data shouldn't wrap then y < DATA_SIZE
    //to generate the far edge values
    for(int y=(x+halfSide)%sideLength;y<DATA_SIZE-1;y+=sideLength){
      //x, y is center of diamond
      //note we must use mod  and add DATA_SIZE for subtraction 
      //so that we can wrap around the array to find the corners
      double avg = 
        data[(x-halfSide+DATA_SIZE)%DATA_SIZE][y] + //left of center
        data[(x+halfSide)%DATA_SIZE][y] + //right of center
        data[x][(y+halfSide)%DATA_SIZE] + //below center
        data[x][(y-halfSide+DATA_SIZE)%DATA_SIZE]; //above center
      avg /= 4.0;

      //new value = average plus random offset
      //We calculate random value in range of 2h
      //and then subtract h so the end value is
      //in the range (-h, +h)
      avg = avg + (r.nextDouble()*2*h) - h;
      //update value for center of diamond
      data[x][y] = avg;

      //wrap values on the edges, remove
      //this and adjust loop condition above
      //for non-wrapping values.
      if(x == 0)  data[DATA_SIZE-1][y] = avg;
      if(y == 0)  data[x][DATA_SIZE-1] = avg;
    }
  }
}

//print out the data
for(double[] row : data){
  for(double d : row){
    System.out.printf("%8.3f ", d);
  }
  System.out.println();
}

Answer 2

Check out this demo done with Processing:

http://www.intelegance.net/code/diamondsquare.shtml

Also, here's another page with a rough algo written out:

http://www.javaworld.com/javaworld/jw-08-1998/jw-08-step.html?page=2

Finally, a slightly more formal paper:

http://www.student.math.uwaterloo.ca/~pmat370/PROJECTS/2006/Keith_Stanger_Fractal_Landscapes.pdf

Enjoy!

Answer 3

M. Jessup's answer seems to be slightly bugged. Where he had:

      double avg = 
        data[(x-halfSide+DATA_SIZE)%DATA_SIZE][y] + //left of center
        data[(x+halfSide)%DATA_SIZE][y] + //right of center
        data[x][(y+halfSide)%DATA_SIZE] + //below center
        data[x][(y-halfSide+DATA_SIZE)%DATA_SIZE]; //above center

It should instead read:

      double avg = 
        data[(x-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)][y] + //left of center
        data[(x+halfSide)%(DATA_SIZE-1)][y] + //right of center
        data[x][(y+halfSide)%(DATA_SIZE-1)] + //below center
        data[x][(y-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)]; //above center

Otherwise it reads from the wrong locations (which can be uninitialised).

Answer 4

For anyone looking, here is the algorithm provided by M. Jessup wrapped in a class that takes in a seed (to allow reproducing the results), a value for n to specify dimensions (dimensions are 2^n + 1), and exposes the results as a normalised array of floats. It also has the fix for the second part of the algorithm applied.

import java.util.Random;

public class DiamondSquare {

public float[][] data;
public int width;
public int height;

public DiamondSquare(long mseed, int n) {
    //size of grid to generate, note this must be a
    //value 2^n+1
    int DATA_SIZE = (1 << n) + 1;
    width = DATA_SIZE;
    height = DATA_SIZE;
    //an initial seed value for the corners of the data
    final float SEED = 1000.0f;
    data = new float[DATA_SIZE][DATA_SIZE];
    //seed the data
    data[0][0] = data[0][DATA_SIZE-1] = data[DATA_SIZE-1][0] = 
            data[DATA_SIZE-1][DATA_SIZE-1] = SEED;

    float valmin = Float.MAX_VALUE;
    float valmax = Float.MIN_VALUE;

    float h = 500.0f;//the range (-h -> +h) for the average offset
    Random r = new Random(mseed);//for the new value in range of h
    //side length is distance of a single square side
    //or distance of diagonal in diamond
    for(int sideLength = DATA_SIZE-1;
            //side length must be >= 2 so we always have
            //a new value (if its 1 we overwrite existing values
            //on the last iteration)
            sideLength >= 2;
            //each iteration we are looking at smaller squares
            //diamonds, and we decrease the variation of the offset
            sideLength /=2, h/= 2.0){
        //half the length of the side of a square
        //or distance from diamond center to one corner
        //(just to make calcs below a little clearer)
        int halfSide = sideLength/2;

        //generate the new square values
        for(int x=0;x<DATA_SIZE-1;x+=sideLength){
            for(int y=0;y<DATA_SIZE-1;y+=sideLength){
                //x, y is upper left corner of square
                //calculate average of existing corners
                float avg = data[x][y] + //top left
                        data[x+sideLength][y] +//top right
                        data[x][y+sideLength] + //lower left
                        data[x+sideLength][y+sideLength];//lower right
                avg /= 4.0;

                //center is average plus random offset
                data[x+halfSide][y+halfSide] = 
                        //We calculate random value in range of 2h
                        //and then subtract h so the end value is
                        //in the range (-h, +h)
                        avg + (r.nextFloat()*2*h) - h;

                valmax = Math.max(valmax, data[x+halfSide][y+halfSide]);
                valmin = Math.min(valmin, data[x+halfSide][y+halfSide]);
            }
        }

        //generate the diamond values
        //since the diamonds are staggered we only move x
        //by half side
        //NOTE: if the data shouldn't wrap then x < DATA_SIZE
        //to generate the far edge values
        for(int x=0;x<DATA_SIZE-1;x+=halfSide){
            //and y is x offset by half a side, but moved by
            //the full side length
            //NOTE: if the data shouldn't wrap then y < DATA_SIZE
            //to generate the far edge values
            for(int y=(x+halfSide)%sideLength;y<DATA_SIZE-1;y+=sideLength){
                //x, y is center of diamond
                //note we must use mod  and add DATA_SIZE for subtraction 
                //so that we can wrap around the array to find the corners
                float avg = 
                        data[(x-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)][y] + //left of center
                        data[(x+halfSide)%(DATA_SIZE-1)][y] + //right of center
                        data[x][(y+halfSide)%(DATA_SIZE-1)] + //below center
                        data[x][(y-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)]; //above center
                avg /= 4.0;

                //new value = average plus random offset
                //We calculate random value in range of 2h
                //and then subtract h so the end value is
                //in the range (-h, +h)
                avg = avg + (r.nextFloat()*2*h) - h;
                //update value for center of diamond
                data[x][y] = avg;

                valmax = Math.max(valmax, avg);
                valmin = Math.min(valmin, avg);


                //wrap values on the edges, remove
                //this and adjust loop condition above
                //for non-wrapping values.
                if(x == 0)  data[DATA_SIZE-1][y] = avg;
                if(y == 0)  data[x][DATA_SIZE-1] = avg;
            }
        }
    }


    for(int i=0; i<width; i++) {
        for(int j=0; j<height; j++) { 
            data[i][j] = (data[i][j] - valmin) / (valmax - valmin); 
        } 
    }

}
}