Finding Pattern in Array of Values 1-64

Hello World,

so I've this 1-D Array of about 100k Elements, Ranging in Value from 1 to 64. Plotting various Sections of the Array, the Order of Values does not seem to follow any discernable pattern, but I'd like to know that for sure. Plotting a histogram of the Array, for one, shows a highly non-uniform distribution of Values. Some, it looks like, do not occur at all.

What's the smartest way to go about this, to detect, if there be one, an underlying recursiveness, regularity, pattern, or function, according to which the numbers are arranged, or determine with certainty the absence of any regularity or pattern?

Kind Regards,

Tim

[Adam Danz]

For starters, I'd just plot the vector as

plot(x, 'o-') % assuming x is a vector

Usually human vision is fast and good at detecting patterns. If you've already done this, what does it look like?

[Star Strider]

I would experiment with xcorr, xcov, and their friends (such as findsignal) to see what they reveal:

x = zeros(1,100)+0.1;
x(20:28) = [1:5 4:-1:1];
x(60:68) = -[1:5 4:-1:1];

[r,lags] = xcov(x);

figure
subplot(2,1,1)
plot(x)
grid
subplot(2,1,2)
plot(lags, r)
grid

Here, the two are 40 index units apart, and of opposite signs, and that shows on the plot.

[Adam Danz]

I was thinking along the lines of Star Strider's comment, too. You'd need to test many different window sizes but you may have a good estimate of the best window size by looking at the plotted raw data.