How do I use gnuplot to create a 3d phase-space plot?

Question

Have a look at this webpage - enclosed but not encrypted

For a three-dimensional phase-space plot, the sequence a, b, c, d, e, f, etc. can be used as space coordinates (a-b, b-c, c-d), (b-c, c-d, d-e), (c-d, d-e, e-f), etc. Patterns in the plot created reveal recurring relations between subsequent sequences. In this phase plot, 50,000 16-bit random numbers would produce an unstructured cloud of dots.

I want to do exactly the same kind of thing. I have a binary file (about 10 MB) and I'd like to create some nice gnuplot style graphs like they have on that web page.

What do I type into gnuplot to make that happen?

Answer 1

1. Create a dump of your binary file in a format suitable for gnuplot. For convenience I used hexdump with a custom output format, which we need to store in a file, e.g. as gnuplot.hdp (in principle the format string can get passed via a command line option, but then we will run into too much nested quotes in the gnuplot script):

   $ cat gnuplot.hdp
   3/1 "%03d " "\n"
   
   $ hexdump -f gnuplot.hdp random.data | head -n 4
   236 027 076
   070 243 055
   047 115 211
   184 206 073
   

2. Plot the data with gnuplot. In the simplest case, we plot bytes 1, 2, 3 and 4, 5, 6 etc. as x, y, z coordinates:

   set parametric
   unset border
   unset xtics
   unset ytics
   unset ztics
   splot "< hexdump -f gnuplot.hdp random.data" using ($1):($2):($3) notitle
   

   A file with random numbers shows -- not surprisingly -- a rather random scatter plot:

   

   But if we use e.g. a badly compressed file, like a simple bitmap, we see a structure (here it's a line):

   

3. If we want to resemble the plot in the cited article a little better, we need 6/1 "%03d " "\n" as hexdump format, so that we get six bytes per line. And we have to extend the splot command in gnuplot:

   splot "< hexdump -f gnuplot.hdp random.data" u ($1-$2):($2-$3):($3-$4) ls 1 not, '' u ($2-$3):($3-$4):($4-$5) ls 1 not, '' u ($3-$4):($4-$5):($5-$6) ls 1 not
   

   gnuplot treats u as an abbreviation for using and not for notitle to keep things short.

   For the bitmap we get now a nice looking object;

   

   the random data looks like that:

   

4. Be aware, that we analyze the data in blocks of 6 bytes, i.e. if only the 6th and 7th byte (or multiples of these) are correlated, the plots won't reveal that.

5. gnuplot should handle a 10MB input file easily, but especially the rotation can get slow -- depending on your computing power.