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# random?

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How can you check if something is "really" random? Is this grayscale pattern really random or not?

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That pattern is not random.

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Definitely not. It has patterns all over it.

Although I have not studied it, I think that a Poisson distribution is random (or it''s a criteria to determine the randomness of a distribution --- I''m not sure).

You can''t say for sure if a distribution has been randomly generated or not, but you can find a probability.

Cédric

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Although I agree that the picture has patterns on it, I don''t believe it possible to say without doubt that it was not produced by a random process. If you flipped a coin 10 times, and each result alternated between heads and tails, you''d think there was a pattern there, and there clearly is. However, that doesn''t mean that the coin is necessarily biassed in any way.

I don''t know a lot about randomness, so I can''t really answer your original question , but I''d suggest that you could evaluate a probability that data has come from a particular distribution.

Perhaps converting it to a png has brought out some patterns in it? I don''t know anything about png compression, so again, I''m just guessing. Do you have a bitmap version of it?

Miles

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The Art of Computer Programming, Volume II, Chapter 3
has everything you wanted to know about random numbers

Kami no Itte ga ore ni zettai naru!

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quote:
Original post by Miles Clapham
Perhaps converting it to a png has brought out some patterns in it? I don''t know anything about png compression, so again, I''m just guessing. Do you have a bitmap version of it?

IIRC, PNG is basically high-color GIF. It''s lossless.

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nothing is random.. its just you can''t predict sometimes how something acts, or, in this case, looks.. so it looks like some random noise to me, but it isn''t.. nothing is.. there is just stuff terrible difficult to determine, and stuff, that has too much different other things that can affect it..

"take a look around" - limp bizkit

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The image is generated with the following formula:

where x = x-co of pixel, y = y-co of pixel, a = number of pixel counting from left to right, top to bottom, and for the color: 0 = black, 128 = grey, 255 = white, 256 = black again, and so on

then the color of a pixel becomes: int(a*cos(x^y)) with ^ being XOR, not power. So probably the fact that it's a mathematical function makes it not random?

[edited by - Lode on September 1, 2002 8:57:15 AM]

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Young man,

You will have noticed that you can easily transform this thing to the form f(i), whereas x, y and a in the original form have to be expressed as functions of i, x(i), y(i), a(i).

It should not be too difficult, as a itself ( as I understood it) is a reasonable candidate to equal the parameter i (this would make a(i)=i).

Now cou have created a simple random number generator, and a predictable one, and even one that can evaluate any i-th random number in constant time, because it will never depend on any of its predecessors. But this should be exactly its achilles'' ankle, its weak point, its "oh It turned out to be a lousy random number generator" reason. Almost all good random number generators are built in a way so that the numbers are calculated from their predecessors, yours isn''t.

Whether the numbers it generates are random, depends on what''s needed. Judged by my eyes, the pattern looks EXACTLY like the patterns generated by very good random. But as soon as you build it into a greater algorithm, strange side effects may occur, bacause, for example...

* all the numbers are prime,
* none of them are,
* only 15% of them are even
* the 27 never occurs
* it''s always odd,odd,even,even,even,even,odd,odd,...
* or this pattern never occurs
* every prime is followed by 3
* the distibution isn''t flat, although the intermediate is correct (this happens very often)

and so on.

There''s a set of criteriae to test RNGs, as well as ways to build such that fulfill all of them, or that fulfill only a set that is relevant for your app, but are faster, can be found in a lot of books about algorithms, including of course the aforementioned Art of Computer Programming.

But I would start searching the web before, as there should be a lot of info available for those how at least know how to program simple things, which you seem to be one of :-)

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a number of tests you can do to check the image.
1) runs test - to see a valid number of runs.
2) chi-squared test- to see the probability ratio.
3) fequency test- to check the frequency of numbers appearing.

there are more, but most random number collections can pass these. random numbers too have patterns, just that the patterns occur randomly.
such as a random sequence of 1,2 and 3 will eventually have patterns of 12,23,13 but the sequence can still be random if the frequency distribution is rectangular.

Its my duty, to please that booty ! - John Shaft

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