On random numbers…
While hacking a small program today, I encountered something that I hadn’t seen in a while, so I thought I’d blog it:
My random number generator failed me!
I was implementing a little test program to generate some random terrain. The idea was pretty simple: initialize a square array to be all zero height. Set your position to be the middle of the array, then iterate by dropping a block in the current square, then moving to a randomly chosen neighbor. Keep doing this until you place as many blocks asu like (if you wander off the edge, I wrapped around to the other side), and you are mostly done (well, you can do some post processing/erosion/filtering).
When I ran my program, it generated some nice looking islands, but as I kept iterating more and more, it kept making the existing peaks higher and higher, but never wandered away from where it began, leaving many gaps with no blocks at all. This isn’t supposed to happen in random walks: in the limit, the random walk should visit each square on the infinite grid (!) infinitely often (at least for grids of dimension two or less).
A moment’s clear thought suggeseted what the problem was. I was picking one of the four directions to go in the least complicated way imaginable:
dir = lrand48() & 3 ;
In other words, I extracted just the lowest bits of the lrand48() call, and used them as an index into the four directions. But it dawned on me that the low order bits of the lrand48() all aren’t really all that random. It’s not really hard to see why in retrospect: lrand48() and the like use a linear congruential generator, and they have notoriously bad performance in their low bits. Had I used the higher bits, I probably would never have noticed, but instead I just shifted to using the Mersenne Twister code that I had lying around. And, it works much better, the blocks nicely stack up over the entire 5122 array, into pleasing piles.
Here’s one of my new test scenes: