A pattern that does not continually re-occur?
I'm not sure I understand what you mean. What kind of pattern are you talking about?
A finite one. A pattern in which you relate one thing to another. It stops there. Basically, can you distinguish that a pattern exists with only 2 symbols?
I'm not being smart, thats just the only way I know how to put it.
Thanks for trying though.
Does that count?
Is a pattern a signal that can be generated using an algorithm?
i dont think a pattern can be established with only two symbols by definition of a pattern.
For example, given two points on a missile trajectory can you predict the third point. You'd have to assume a line but the missile would most likely be on an arc so given a third point gives you enough info to predict the fourth and beyond with ever greater precision.
Now in statistics, they often look for correlations between two variables and that is a kind of pattern.
What about 101001000100001000001...
where the "pattern" is that the number of "0" between two "1"s is one more than previously.
If you want to look at the abstract idea of this kind of thing then look at Kolmogorov Complexity:
Well, you can extend the applicability of a pattern to as many terms as you like, so ... there is no such thing as a finite pattern in the sense it is commonly construed.
On the other hand, regarding periodicity, there has to be some underlying frequency in tabulation as determining the nature of the series in question. Otherwise, there would be no pattern.
If there is something known and recognized as a pattern, it is only so because it is periodical. Even in chaos theory, in deriving a new Xp from a given Xp-1, we follow certain rules as overlapping our initial states.
On another tangent, a truly non-periodical pattern, it would appear, seems demanding of an infinite regress wherein irony is delivered to the persistent. Something like that cannot even conceptually exist in understanding, at least not to my current awareness nor concern.
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