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Know of how to find patterns in "random" set of data?

 
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This is just a fun, got some time to kill, question, but...I was wondering if anyone had any ideas for how to look for patterns in a computer-generated random set of data. I guess in the simplest sense, it's sort of trying to figure out what was used to create a random collection of data. Any ideas?
 
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There is of course a HUGE body of work on finding patterns in scientific data.
Since we are talking fun project here, I would first look at visualization techniques.

For example, an XY plot where each point has x=previous value,y=this value will show patterns that the eye can pick out with poor random number generators.

Bill
 
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