Any non-random patterns in this matrix?

[stevens]

I need to find out if there are any non-random patterns in the following
matrix:

1 1 1 1 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 1 1 0
1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 0 1 1 1 1 1 1 0 1
1 1 1 1 1 1 1 1 0 1 1 1
0 1 1 1 1 0 1 1 1 0 1 1
1 1 1 1 1 1 1 1 0 1 1 1
1 0 1 1 1 1 0 1 1 0 1 1
1 1 1 1 0 1 1 1 1 1 1 0
1 1 0 1 1 1 1 0 1 1 1 1
1 1 1 1 1 0 1 1 1 0 0 1
0 1 1 1 1 1 1 1 1 1 1 1

How would I go about doing this? The patterns do not necessarily have to
be linear sequences, basicly anything non-random is ok.

-Thanks in advance

Steve Schafer

[john baez]

In article <2krma6$c...@bingsuns.cc.binghamton.edu> ste...@bingsuns.cc.binghamton.edu (stevens) writes:

> I need to find out if there are any non-random patterns in the
>following matrix:

One can find a pattern in anything if one looks long enough. It would
sure help us if you gave us a clue as to how this matrix was generated,
why you are trying to find patterns in it, and what sort of patterns you
expect might be in it!!!!!!

[Roberto Sierra]

stevens (ste...@bingsuns.cc.binghamton.edu) wrote:

: I need to find out if there are any non-random patterns in the
: following matrix:

: 1 1 1 1 0 1 1 1 1 1 1 1
: 1 1 1 1 1 1 1 1 0 1 1 0
: 1 1 1 1 1 1 1 1 1 1 1 1
: 1 1 0 0 1 1 1 1 1 1 0 1
: 1 1 1 1 1 1 1 1 0 1 1 1
: 0 1 1 1 1 0 1 1 1 0 1 1
: 1 1 1 1 1 1 1 1 0 1 1 1
: 1 0 1 1 1 1 0 1 1 0 1 1
: 1 1 1 1 0 1 1 1 1 1 1 0
: 1 1 0 1 1 1 1 0 1 1 1 1
: 1 1 1 1 1 0 1 1 1 0 0 1
: 0 1 1 1 1 1 1 1 1 1 1 1

The information in the matrix could be random, or not, depending on
how it was produced. For example, if the program below generated it,
then I would say it's a fairly random matrix:

for (j=0; j<12; ++j) {
for (i=0; i<12; ++i) {
printf( (rand() >= 0.152777)? "1 " :"0 " );
}
printf("\n");
}

If, on the other hand, you took a picture of some ocean waves and
quantized it down to black and white values, then I'd say it's not
terribly random. The matrix itself doesn't show enough about the
system which produced it to determine whether there's a significant
random component to the patterns.

You might rethink the question you are trying to ask and post
to sci.math.statistics, if you receive that group at your site.

That said, the only thing I can say for sure, squinting at the
matrix for a while, is that there are a lot more 1's than 0's,
that ten of the zeros live above the horizontal center-line,
twelve below, ten live to the left of the vertical center-line,
twelve to the right, and there appear to be an awful lot of zeros
almost lined up on the '/' diagonal. That's interesting, but
doesn't answer the more fundamental question about whether these
are caused by the system characteristics, or mere happenstance.

[Spoken as an engineer, not a mathematician]
--
\\|// "Doog" spelled backwards is "good."
- -
o o roberto sierra
J tempered microdesigns
O san francisco, ca
\_/ be...@netcom.com