Posted 03 November 2012 - 11:55 PM

You can transform a uniform distribution into something usable for, say, minecraft-style biome generation, but it's much more involved than just summing up distributions. Look into fractional brownian motion, perlin noise, etc...

The graphs on the page you link are probability distribution functions, which map any output number to its probability of being generated (well, actually, since we're looking at a continuous range of values, it's really the probability of generating an output between some A and B). They don't mean anything else and a normal distribution will still have a large variance.

Fractional brownian motion seems to be the closest thing you are looking for. Basically, it will take a sample of uniformily generated random numbers, and output a sample of "smooth" noise, which when mapped to a heightmap, would give a somewhat realistic terrain instead of a completely random mess. It involves summing up octaves of the same uniform sample, with different frequency and amplitude. Is this what you were looking for?

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*