Slashdot Mirror
Using Prime Numbers to Generate Backgrounds
bpeh123 pointed out an article about generating organically tiled backgrounds inspired by the life cycle of cicadas. The trick is to overlay multiple background tiles with prime widths thus generating a series that does not repeat for a sufficiently long period. This introduces a seeming irregularity and makes the background appear much more natural.
The point isn't randomness, the point is unwanted harmonics in pseudo-random patterns. These unwanted harmonics cause regular repetitions in the pattern that make it seem predictable and non-random. Prime numbers are the basis by which a simple PRNG (pseudo-random number generator) generates seemingly-random data that doesn't repeat in any predictable manner. By overlapping two or more sequences with prime lengths, the length of the harmonic is maximized. That means the sequence goes longer before repeating itself. Sequences with non-prime lengths short-circuit the cycle.
For instance, overlapping three sequences of length 7, 11, and 13 forms the following pattern:
http://tinyurl.com/3wserj7
At a glance, the pattern looks fairly random and non-repeating; however if you look more closely you see that the vertical bands of color are repeating very regularly within the pattern. But, since their periodicity is prime, the pattern as a whole doesn't appear to repeat itself. Using alpha and larger 2-dimensional tiles you can create even more complex and random-seeming patterns.
The life cycle of cicadas is similar in that the overlapping cycles tend to cause a seemingly-random pattern of years with lots of cicadas and few cicadas, such that the life cycle of their predators is less likely to hit a bunch of good cicada years in a row and seriously harm the population of them.
This is very much not like Perlin noise, because Perlin noise uses octaves (doubles in frequency). Octaves are harmonic with each other by definition. This uses primes, specifically to cause the harmonics to occur as far apart as possible. Using octaves in this way would cause very repetitive-seeming patterns because the maximum size of your pattern would be defined as the size of your largest sequence, and all of the shorter sequences would tile into it in a neat checkerboard.
Perlin noise requires infinite sequences of pseudo-random numbers and would be extremely ill-suited to using short repeating sequences. This is specifically designed to minimize the length of the sequences you use without causing obvious repetitions in the pattern by using sequences of prime length (since your "sequence" is a PNG, if it's too large it takes a long time to load).