The terrain / mountain algorithm does not work as intended

Question

I want to create a landscape with a mountain on it, using a very simple principle, shown by this height map:

0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 1 2 1 0 0 0 0
0 0 0 1 2 3 2 1 0 0 0
0 0 1 2 3 4 3 2 1 0 0
0 0 0 1 2 3 2 1 0 0 0
0 0 0 0 1 2 1 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0

It starts at a random point with height = 4, and then gradually reduces its neighbors.

The recursive idea is simple, I start the point, returning to the top / down / left / right with height - 1(in this example), and only if this has not yet occurred, I set their values.

I implemented it as follows:

private void createMountain(final float[][] heightMapping, final float startHeight) {
    boolean[][] traversed = new boolean[width][depth];
    boolean positive = (startHeight >= 0f);
    int x = random.nextInt(width);
    int z = random.nextInt(depth);
    recursiveUpdate(heightMapping, traversed, x, z, startHeight, positive);
}

private void recursiveUpdate(final float[][] heightMapping, final boolean[][] traversed, final int x, final int z, final float startHeight, final boolean positive) {
    if (x < 0 || x >= width || z < 0 || z >= depth) {
        return;
    }
    if (traversed[x][z]) {
        return;
    }
    if ((positive && startHeight <= 0f) || (!positive && startHeight >= 0f)) {
        heightMapping[x][z] = 0f;
        return;
    }
    traversed[x][z] = true;
    heightMapping[x][z] = startHeight;
    recursiveUpdate(heightMapping, traversed, x, z - 1, calculateNewStartHeight(startHeight, positive), positive);
    recursiveUpdate(heightMapping, traversed, x, z + 1, calculateNewStartHeight(startHeight, positive), positive);
    recursiveUpdate(heightMapping, traversed, x - 1, z, calculateNewStartHeight(startHeight, positive), positive);
    recursiveUpdate(heightMapping, traversed, x + 1, z, calculateNewStartHeight(startHeight, positive), positive);
}

private float calculateNewStartHeight(final float startHeight, final boolean positive) {
    float delta = startHeight / maxDecayFactor;
    return (positive) ? startHeight - delta : startHeight + delta;
}

However, it gives me the following result:

0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.1  
1.9  1.6  1.2  1.0  0.8  0.6  0.5  0.4  0.3  0.3  0.2  0.2  0.1  0.1  0.1  0.1  
2.4  3.0  3.8  4.7  5.9  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.1 

Since the problem is that now it forms a line that was not my goal, instead of gradual smoothing.

How can I implement my desired algorithm?

Answer 1

, DFS, , . .
traversed - , ( ).

:

• , , - DFS BFS. 1 , 2 ..
• - : , if (traversed[x][z]) { return; } - if (heightMapping[x][z] > startHeight) { return; }. , , .

---

BFS - ():

Q <- new Queue() //or even better - priority queue that holds the highest point at the top
Q.push((x,y,height)
visited[width][depth]; //init as all false
while Q.empty() == false:
   curr <- Q.pop()
   if (sanity check for x<0 , y< 0 ,..):
      continue
   if visited[x][y] == true:
      continue
   if height <= 0: //or some epsilon instead of 0 if there are floating point issues
      continue
   heights[x][y] = height
   visited[x][y] = true
   Q.push(x+1,y,calculateNewHeight(...))
   ... //similarly for all directions

Answer 2

.

, , h x, y.

height(x,y) = h
for dist = 1 to h-1
  for x' = x - dist to x + dist
     x_dist = abs(x - x')
     y_dist = dist - x_dist
     height(x', y + y_dist) = h - dist
     height(x', y - y_dist) = h - dist

- , . , , , .