entropy question

[Dingus Waternloo]

my data consists of a point on a grid which moves around through time.
so, you can look at this as a trail through a plane, or a timeseries
of (x,y) coordinates. imagine this as a bug moving around on a table.
is there a way i could measure the "entropy" of this system? is there
an information entropy measure that would be appropriate?

thanks in advance

[kunzmilan]

Entropy is a statistical function, where temperature corresponds to
standard deviation. In your case, it is possible to label different
positions by different symbols, and to read their serie as a text.
Information entropy is applicable.
kunzmilan
[Moderators note: corrected version]

[Dingus Waternloo]

Thank you. Any suggestions for how this may be accomplished with the
following data formats?

I understand how standard deviation could be used for temperature, but
any ideas for which specific equations to use?

1) A list of Cartesian coordinates (2xN array), representing a path

ex:
20,20
21,20
22,20
22,19
23,20
24,19
23,18
22,19

or, 2) As a matrix, with each element representing the number of times
the agent occupied that space

ex:
000000000001111000
000000000001001000
000000000012110000
000111000101000000
000100100101000000
000111121112110000
000000001001000000
000000000110000000

[ksoileau]

On Nov 16, 9:09�am, Dingus Waternloo <timf...@gmail.com> wrote:
> my data consists of a point on a grid which moves around through time.
> so, you can look at this as a trail through a plane, or a timeseries

> of (x,y) coordinates. imagine this as a bug moving around on a table..

> is there a way i could measure the "entropy" of this system? is there
> an information entropy measure that would be appropriate?
>
> thanks in advance

If the movement of the bug is discrete, in the sense that there are N
possible vectors describing the movement, each direction can be coded
with a different letter in an alphabet of N characters. Each path is
then a word made up of a finite sequence of letters from this
alphabet. The entropy of such words is straightforward to compute. One
could make the case that this entropy corresponds to the entropy of
the bug's motion.