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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.
They can't even quote an article they link to properly ."
Their article: "that is,1, 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on"
Wikipedia: "2, 3, 5, 7, 11, 13. .
Cool. I've looking at automatically generating stuff for games recently. Obviously, this works for authentic-looking backgrounds, but my friends and I were working on a project that involved automating critter generation using classic predator-prey models. One big worry was the farming-to-death of critters that are part of an ecosystem. This idea might be useful for much more nicely randomized or randomized-seeming mob population/spawning.
No OS on the planet can protect itself from a user with the admin password. - Yvan256
How about: Designer discovers new way to use special properties of primes to create more realistic tiled background images.
C'mon, the results are actually pretty cool.
You missed the important thing ... designer creates huge frickin' lego army using a small number of images and some pretty smart use of CSS.
An army, but make out of lego. Put lasers on them and see who takes over the world. :-P
Lost at C:>. Found at C.
Yes, some characters do. The Slashdot Janitors have decreed that only 7-bit ASCII can be used on the site and everything else should be presented in as broken a way as possible.
Because obviously, we're geeks so we're all using 30-year-old ADM3A terminals.
Just because you do not understand something does not make it wrong. Birds haven't "evolved" a boom/bust cycle, that's not how that works. It's the standard predator/prey boom/bust cycle. Birds don't spend vast periods of time underground, you know. Curtains are natural, "natural" here taking the meaning of "organic" rather than "patterned.
Please, don't be one of those guys who tries to prove how smart they are by attempting to find fault with the article. It does not make you look as smart as you think. The fact that you hurt your brain trying to comprehend something the rest of us had no trouble understanding actually makes you look pretty dumb.
- None can love freedom heartily, but good men; the rest love not freedom, but license. -- John Milton
Not only did I learn interesting information about the insects I hate the most (and believe me, if I could, I would destroy every last one of the annoying bugs!) but I also learned that you can have multiple images for backgrounds in CSS and have them lay atop one another. (None of the books or software ever seemed to suggest that it was even possible!)
While the idea is pretty ingenious, if I had known you could specify more than one image for backgrounds, I would have figured this one out on my own -- I have been overlaying images and background images inside of DIVs for a while to get some really nice effects. But now, to be able to lay one atop the another in the same block? AWESOME.
And yes, at the article says, inferior browsers cannot handle this -- I tried it on IE8 to see what would happen and... yeah... it hung.
How about: Designer comes up with interesting, relevant use of math that all the Math geeks who have been running the WWW for 20 years didn't think of on their own.
Subtitle: Bitter math nazis harp on his confusion about 1 being a prime.
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
Primes have, by definition, exactly two factors. 1 has only one: 1.
Of course, you could define them differently, and a hundred years ago, 1 indeed was considered a prime. But the definition excluding 1 has turned out to be much more useful (because almost everywhere you use primes you'd have to add "except 1" otherwise), therefore 1 is no longer considered prime.
The Tao of math: The numbers you can count are not the real numbers.
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.
A lot of proofs in recursion / computability theory actually depend on the fact that one is not a prime number. More specifically, they depend on the property of numbers that is called unique factorisation into primes, a very important theorem in mathematics that is a corner stone for many proofs in a variety of mathematical disciplines. If you count 1 as a prime number, this theorem does not hold, with all the consequences that you might suspect it entails.
Just sayin'. 1 is not a prime number.
This is in fact true.
The best reason for leaving one out of the prime number set is because it enables you to state the prime number theorem more succinctly:
Every integer n>1 has a unique factorisation as a product of primes (Prime factorisation)
If one was prime, then the factorisation would not be unique. For example 6=2.3, but if 1 was an allowed prime then 6=1.2.3=1.1.2.3=1.1.1.2.3= .... 1^n .2.3. So it's preferred to leave one out.
There are other reasons, but the prime number theorem is perhaps the best one.
May the Maths Be with you!
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).
The new UI has been getting more buggy every week rather than less buggy. Off site links not working, clicking 'score' to view how things are moderated collapsing the comment, scrolling issues, clicking anywhere on the comment navigating to the parent, weird highlighting when submitting a comment... and that's just off the top of my head and coming from someone who was initially supportive of the changes. All on FF4.0
You somehow simultaneously displayed a lack of understanding for the mechanisms of evolution (mutation and natural selection), and obliviousness to the point of the mathematics being discussed: using prime numbers to reduce periodicty of a given set of cycles.
Also, your third and fourth paragraphs display utter ignorance of biology.
Why are you even here? This article was very well articulated, and more important, useful, unlike your reply.
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