Optimize Conway's Game of Life
First of all, this should be obvious, but when you have performance issues in code that involves a tight inner loop, you want to simplify that loop as much as you can.  If you can save one cycle in the loop by spending a dozen or a hundred cycles somewhere else, do it, because every cycle in the loop gets multiplied by 5000&sup2;.

Also, what you really want to minimize in the inner loop are memory accesses.  Accessing local variables is fast, since they're typically cached and the JVM knows that their values cannot change unless the code in the method itself changes them.  In comparison, pulling a random element from a large array is relatively slow, since it requires a full RAM access, as is, typically, accessing a member variable or calling an uncached method.

I've done something like this before,* so, rather than listing every improvement I might make to your code, let me start by sketching how I might rewrite your core update loop:

// assume these arrays are (height + 2) by (width + 2)
boolean[][] oldBuffer = universeDoubleBuffer[flipFlopIndex],
            newBuffer = universeDoubleBuffer[newFlipFlopIndex];

for (int y = 1; y &lt;= height; y++) {
    int environment
        = (oldBuffer[y-1][0] ? 32 : 0) + (oldBuffer[y-1][1] ?  4 : 0)
        + (oldBuffer[y  ][0] ? 16 : 0) + (oldBuffer[y  ][1] ?  2 : 0)
        + (oldBuffer[y+1][0] ?  8 : 0) + (oldBuffer[y+1][1] ?  1 : 0);

    for (int x = 1; x &lt;= width; x++) {
        environment = ((environment % 64) * 8)
            + (oldBuffer[y-1][x+1] ? 4 : 0)
            + (oldBuffer[y  ][x+1] ? 2 : 0)
            + (oldBuffer[y+1][x+1] ? 1 : 0);

        newBuffer[y][x] = lookupTable[ environment ];
    }
}


A few things to note about this code:


There is no countLiveNeightbors() method; in fact, the code does not explicitly count live neighbors at all.  Instead, the pattern of the nine cells including and surrounding the cell at (x, y) is maintained in the variable environment, which is used as an index to a 512-element lookup table.

For example, if the surroundings of the current cell look like this (# = live cell, _ = dead cell):

# # _
_ # #
# _ _


then the value of the environment variable will be:

(1 * 256) + (1 * 32) + (0 * 4) +
(0 * 128) + (1 * 16) + (1 * 2) +
(1 *  64) + (0 *  8) + (0 * 1) = 370


Of course, you'll have to set up this lookup table before using it, but that is something you can do outside the core loop (e.g. in your constructor), so it's not performance-critical.

(In fact, while I haven't benchmarked this, I'd at least consider making lookupTable a local variable and rebuilding it every time the update method is called, as the extra cost of rebuilding the table might be balanced out by extra optimization opportunities available to the compiler / JVM if it knows that no other code can modify the table.  You may want to test it both ways and see which one is faster.)

One additional advantage of such a lookup table based implementation is that, by changing the lookup table, it can simulate any two-state cellular automaton using the Moore neighborhood, not just Conway's Game of Life specifically.
By reusing the parts of the environment pattern that are shared between adjacent cells, the code only needs to do three reads from the oldBuffer array per cell, as opposed to nine in your version.  Uncached array access is expensive, so this is likely to provide a significant speedup.  (Also, like your code, mine also makes sure to access the buffers as close to sequentially as possible, iterating first by rows and then by columns.  This is also important for CPU cache locality.)
The code above doesn't update the cells at the edges of the array, which means it doesn't have to worry about (literal) edge cases such as array indices being out of bounds.  (Hopefully, the compiler / JVM may notice this too, and may omit some of its internal array bounds checks.)

If you want your grid to be surrounded by dead cells, you can just initially mark these border cells as dead and leave them untouched in your update method.  Alternatively, if, say, you want the grid to wrap around, you can update the edge cells in a separate loop (which can be less efficient, since it only runs for a tiny fraction of all the cells).


Actually, there are a few ways in which the code I suggested above could be optimized further.  For example, an obvious optimization is to get rid of the two-dimensional array accesses in the inner loop, since they require two array lookups each.

There are (at least) two ways you could do this:


a) In the outer loop, save the previous, current, and next rows of oldBuffer in local variables, like this:

boolean[] prevRow = oldBuffer[y-1],
          currRow = oldBuffer[y],
          nextRow = oldBuffer[y+1];

b) Make the buffers themselves one-dimensional arrays, and adjust the indexing so that, instead of buffer[y][x], you use buffer[ y * (width+2) + x ].  You can precalculate the offset y * (width+2), and possibly also (y &pm; 1) * (width+2), in the outer loop to save a bit of arithmetic, or you could rely on the compiler / JVM to do this for you.  Again, you could try it both ways and see if there's any difference.


Also, for cellular automata like the Game of Life, where only a small fraction of the cells typically change in each time step, there are much faster algorithms available than even the generic table lookup method described above.


As a first step, ChrisW's suggestion of caching the live neighbor count is likely to be faster whenever the environment of each cell changes relatively infrequently.
An even greater speedup may be obtained by storing a list of active cells, i.e. cells that changed or had at least one of their neighbors change state during the previous update step, and only iterating through those cells on the next update.  (Since the total number of active cells is bounded above by the size of the grid, you can use a simple array as a circular buffer to efficiently store this list.)

Effectively combining active cell lists with double buffering can be somewhat tricky.  An alternative solution is to use a single buffer, but divide your update method into two phases:


In the first phase, you iterate through the list, calculate the new state for each active cell, and store it in the list.
In the second phase, you iterate through the list again and update the grid buffer to match the new states calculated in the first phase.


(That said, using both activity lists and double buffering does have one advantage: it allows you to treat cells that oscillate with a period of two, which are quite common in the Game of Life, as inactive.  This does require you to maintain separate active cell lists for each buffer.)
Finally, if you want a really fast algorithm for simulating Conway's Game of Life, look up Hashlife.  It's literally orders of magnitude faster than any "naïve" simulation algorithm, especially for sparse and highly repetitive patterns like many constructed ones.


*) Please don't take that code as an example of good coding style.  It is pretty fast, though.



Addendum: Here's a basic implementation of the activity list method, using a single buffer, and with the Conway's Game of Life rules hardcoded.

It uses a byte-packed cell state buffer, where the lowest bit of the byte indicates whether the cell is currently in the activity list, the second bit stores the actual state of the cell, and the following (four) bits store the number of surrounding live cells (to avoid having to recalculate it whenever the cell is examined):

// assume that buffer is a (height) by (width) byte array, and that
// xQueue and yQueue are (height * width) int arrays, of which the
// first (activeCells) elements contain the current active cell coords

// loop over active cells, and find those whose state will change
int changedCells = 0;
for (int i = 0; i &lt; activeCells; i++) {
    int x = xQueue[i], y = yQueue[i];
    byte packedState = buffer[y][x];  // = 4*neighbors + 2*state + active
    boolean wasAlive = (oldState &amp; 2 == 2);

    // quickly check if cell will live under the Game of Life rules
    // (10-11 = alive, 2 neighbors; 12-13 = dead, 3 neighbors; 14-15 = alive, 3 neighbors)
    boolean isAlive = (10 &lt;= packedState &amp;&amp; packedState &lt;= 15);

    // add cell to queue if it died or was born
    // we know that changedCells &lt;= i, so it's safe to reuse the same queue space
    if (wasAlive != isAlive) {
        xQueue[changedCells] = x;
        yQueue[changedCells] = y;
        changedCells++;
        // assume active bit is already 1, so no need to change
    }
    else {
        buffer[y][x] = packedState - (byte)1;  // unset active bit
    }
}

// carry out deferred state updates
activeCells = changedCells;
for (int i = 0; i &lt; changedCells; i++) {
    int x = xQueue[i], y = yQueue[i];
    boolean wasAlive = (buffer[y][x] &amp; 2 == 2);
    byte delta = (byte)(wasAlive ? -4 : +4);  // change in neighbor count * 4

    // update neighbor counts of adjacent cells, and mark them as active
    int yMin = (y &gt; 0 ? y-1 : 0), yMax = (y &lt; height-1 ? y+1 : height-1);
    int xMin = (x &gt; 0 ? x-1 : 0), xMax = (x &lt; width-1 ? x+1 : width-1);
    for (int ny = yMin; ny &lt;= yMax; ny++) {
        for (int nx = xMin; nx &lt;= xMax; nx++) {
            byte newState = buffer[ny][nx] + delta;
            // if this cell is not yet active, add it to the queue for next time step
            if (newState &amp; 1 == 0) {
                xQueue[activeCells] = nx;
                yQueue[activeCells] = ny;
                activeCells++;
                newState += (byte)1;
            }
            buffer[ny][nx] = newState;
        }
    }
    // the middle cell only needs to adjusted by +/-2
    buffer[y][x] -= (byte)(delta / 2);
}


Before the first pass, all cells should be initialized to have the correct neighbor counts, have the active bit set and be added to the active cell queue.  I've omitted this part of the code, since it's not performance-critical.

Note that this method does not use any padding cells along the edges of the state array.  Alternatively, we could add the padding and permanently set the active bit for those cells, but not include them in the queue, allowing the min/max coords calculations to be simplified.  I suspect this would not make much difference, but there's no way to be sure without trying it.