Plotting the bargraph.bin file
Worlds leading expert on Langtons AntLCEE Tutorial index one two three
Thermo-dynamic wave equation.
- It is a good idea to first check if the LCEE engine is online, click here and make sure you get a response with a build date and version number, if there is no response or you see an error, please be patient as the site may be down while undergoing maintenance.
- Assuming LCEE is live, open a bash terminal, navigate to a clean working directory and type the following into the terminal.
- # wget http://www.buzwordsalad.com/mfile/www_bar.m
- # wget http://www.buzwordsalad.com/mfile/www_bar1.m
which will download two octave m files, now fire up octave by typing the following into the terminal.
- # octave
When the Octave terminal is ready to go, execute the first m file by typing
www_bar
This will begin the 32 frames of 16,777,216 iterations (536,870,912 Iterations) which will take about ten seconds, after which you will see six graphs pop up on the screen.
Figures 1,2 and 3 (along the top) are the 2d plots and their 3d equivalent surface plots can be seen just below them, figures 11,22 and 33 respectively).
To see an evolving sequence of figure 11, click here and a complete animated plot here
Replace the system call in www_bar.m with the following,
- system ("wget 'http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 8050 -g 00003000 -f 0001' -O bargraph.bin");
Save the changes and execute 'www_bar' (ignoring any errors for the moment since we are only plotting one frame and to calculate the derivitive you need at least two frames.
If you have not seen the 'Langtons ant wave equation video' on you tube, please visit here then fast forward the video to 3 minutes in and PAUSE it. Close down Figure 11 and compare Figure 1 with the video which looks like this.
The cumulative plot on the RHS of the video is the same plot from figure 1 you just plotted, (12288 iterations).
The far left binary plot in the video is the familiar langtons ant, just to the right of this, is the occupancy surface plot (how often the ant has visited refects how high or bright the shading is) the specific shading of the occupancy surface plot is referenced along the x axis of the cumulative plot. Therefore the height of figure 1 reflects the total number of lattice squares (y axis) that have received a specific number of visits (x axis) , thus the peak of the cumulative plot shows that more squares in the lattice have gone from zero visits to one visit (the ant is exploring new squares for the first time) and the lowest point of the cumulative plot represents only a single square in the lattice has the most occupancies
Close the video and open up the 'www_bar1.m' file into your editor, (this file is the same as 'www_bar.m' but has the differential frames removed, this helps us continue without the annoying errors that www_bar.m would complain about, we will return to www_bar1.m towards the end of this section
now run the m-file by typing
www_bar1
Which will produce the same cumulative plot but without any errors this time, also a very tatty looking 'probability amplitude plot' named Figure 2 should also have appeared, these two plots are the cumulative and differential plots. Now change the system call to the following.
- system ('wget "http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 0000 -g 00800000 -f 0001" -O bargraph.bin');
This will instruct the server to start 128 frames of 65536 ( 8,388,608 )Iterations of langtons ant producing the following plot.
This is the sweet spot of Langtons ant, the number of iterations is 0.5*E^3 where E=lattice length 256 and 800000=0.5*E^3 which is what you put in the system call. Figure1 is the Cumulative occupancy count and Figure2 is the 1st order differential of Figure1 and represents the Probability amplitude and you can see that the most likely transition state the ant will do is any square that has been visited 128 times. The most unlikely squares the ant will visit are those with very high counts (>200) and counts less than 50.
Now we are going to half the number of iterations, so change the system call to this.
- system ('wget "http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 0000 -g 00400000 -f 0001" -O bargraph.bin');
Giving us 64 frames of 65536 (4,194,304) iterations, half the amount of the previous plot. Now run the 'www_bar1.m' to produce the following plot.
This has the same shape as the previous plot but the whole thing has been translated 50 steps to the right, now the most likeley kind of square the ant will visit is a square that has had about 50 visits, in quantum mechanical terms this means 50 photon events and thus the ant is more likely to interact with these squares than any other kind, (if you follow the Threshold Model for the photon then these squares would represent the most likely place on the lattice to find a photon event where the lattice represents a black body surface and the ant represents a small window into the interior where photons can escape to be viewed, these photons will have a kinetic energy mapped such that 0=ultra violet and N=longwave radio waves, the resolution is only limited by the occupancy magnitude count [ limited to 256 at present]
Now change just the the frame rate in the system call from 1 to 2
- system ('wget "http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 0000 -g 00400000 -f 0002" -O bargraph.bin');
This will now double the number of iterations giving us a grand total of 8,388,608 but done in two stages which can be seen in the plot below. click here to see a video of this evolving over time, total iteration count 335,544,320
This is both plots together, now set the graphing rate back to 800000, leave the frame rate at 2 so the system call looks like this.
- system ('wget "http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 0000 -g 00800000 -f 0002" -O bargraph.bin');
Now run the mfile again to get the following plot.
The psudo 'cos' wave in Figure2 above (see also this image and this image which were taken from this video ) is simply an inversion of the preferred number of counts any given square has accumulated, it is interesting to see semi-sinusoidal plots emerging from an algorithm deemed to be chaotic. Perhaps GOD does not play dice after all, but plays Langtons Ant!
Since the ant preffered squares with a central value of 128 over the first 8 million iterations, it will have marked out on the lattice a large number of left hand turns, hence an equally large number of black squares will have been flipped to white reaching a saturation point which is reflected in the Sum Over All Paths Integral which is key to the future behaviour of the ant, now as the ant enters the second 8 million iterations the ant will now be biased towards those squares which have not been visited yet, thus the center value of 128 is now the least likely to be visited but instead the very high count and very low count squares are most likely, this is what gives rise to the apparent sinusoidal plots. Now double the graphing rate and leave the frame rate 2 so the system call looks like this.
- system ('wget "http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 0000 -g 01000000 -f 0002" -O bargraph.bin');
Now run the mfile again to get the following plot.
It is clear from these two plots that as time goes by, the probability of finding the ant on a square with an occupancy count of 0 or 255 is dropping away in magnitude and the occupancy count prefered by the ant is spreading outwards until in the long term steady state (see middle top Figue in first graph top of page), the ant has has equal preference to any square with an probability amplitude of +/- 2*E.
Now last but not least, edit the www_bar.m file and change the number of frames from 0020 to 0002 so the system call now looks like this
- system ('wget "http://buzwordsalad.com/lcee/bargraph.sh?-d 2 -xy 0000 -g 01000000 -f 0002" -O bargraph.bin');
Now run the 'www_bar.m' mfile you just edited which should produce a plot that looks like this (ignoring the plots 11,22 and 33 which will produce errors)
We are already familiar with cumulative plots (Figure1), they look flattened out due to the large number of iterations between frames, the Amplitude plots (Figure2) are the first order differential of the graphing rate, if we now subtract the two cumulative plots (Figure 1) from each other we get the first order differential of the frame rate (Figure3)
Now edit the frame rate from 2 to 3 and run the mfile again, it should now be clear what you are plotting.
There are 2nd and 3rd order z transform plots of these equations which can be found in the mfile section on the home page of buzwordsalad.com
Stage 2 complete
In this section you were given a couple more 'ready baked' octave scripts and just as before you were then shown how to edit and use the 'LCEE online engine' using the 'system call' withing the m-file to plot the 'bargraph.bin' file. In the next section we will explore the 'output_t.bin' which is at the heart of Langtons ant wave equation. Keep the editor, octave and bash terminal open and head over to section three