MTH 455 Homework #8

1. Replicating Pearson's Gray-Scott model experiment.

I have implemented in C++ the numerical solution of
the 2D reaction-diffusion equations for the Gray-Scott model
using the method and conditions described in John Pearson's paper.
Here is the code: pearson.c.pdf.

Now I assume most of you do NOT know C++, but I am hoping
that the important bits will be largely comprehensible to you anyway.

(a) Make as many specific line-to-line correspondences as you can
between the line-numbered version
of the Pearson paper: p1, p2,
and the line-numbered C++ code. For each correspondence
give the line(s) in the paper, the line number(s) in the code, and a brief
note about the correspondence. You will get points for each correspondence
correctly identified and described.

(b) Running the code. In one of the Linux Labs (e.g. the one in Bell Hall), 
or on your own Linux/Intel machine, make a directory to work in by typing
mkdir pearson
in a terminal. (Get a terminal by Penguin -> System Tools -> Terminal.)
Then download the compiled version of the code:
pearson.exe into that directory.
Move into that directory by typing
cd pearson
Make the file runnable by typing
chmod +x pearson.exe
Then you can run it by typing
./pearson.exe
You will be prompted for a file name prefix (best if you
use your own last name with no spaces), parameter values, and the times
you want snapshots at. Enter your own values, as assigned in class,
and let the program run. (Try a short run first, to make sure
everything is working as expected.)
Check that your snapshots are satisfactory by looking at them
with a browser, as described by the program when it ends.
Finally, when you are satisfied with the results of your experiment,
package and mail them to me PRECISELY as follows.
Make a package of all the files you want to send by typing
tar cvf yourname.tar *.html *.png,
or if you don't want to send ALL the html and png files in the directory,
more selectively, something like
tar cvf yourname.tar ringland_expt1.html ringland_expt2.html ringland_expt1*.png ringland_expt2*.png

Then send me the file "yourname.tar" as an attachment
to an email with the Subject line "455 reaction-diffusion experiment".
You could, for example, use UB Webmail from within the Mozilla browser.

All the results of experiments that I've received so far are at
http://orange.math.buffalo.edu//455/pearson_runs_students/ .

If you're interesting in stringing your images together into an
animation, simply run the program "convert", part of the free
software ImageMagick, as follows:
convert -delay 10 my_expt1*.png my_expt1.gif
The delay is the delay between frames in milliseconds, and the
gif file is your animation that you can view in your browser.

2. Conway's 23/3 cellular automaton

(a) Iterate "the toad" by hand on this sheet: pdf.
Do as many iterations as it takes to know the entire future.


(b) Iterate this:  by hand on the part of the sheet
with 11x11 squares. Do as many iterations as it takes to know the entire future.


3. Now let's get philosophical!

(a) Who discovered the Gosper gun? (Hint: Who is buried in Grant's tomb?)

 

(b) Who designed the Gosper gun (Conway, Gosper, someone else, no-one)? Explain.

(c) Did Gosper guns exist in the year 1900? (John Conway was born in 1937.)
Do they exist now? If so, where are they? Do your answers
depend on whether or not we are currently "realizing" one on our computer?
Will Gosper guns exist after the Sun explodes?

(d) Does the Schlogl model have 3 steady states in parts of its parameter space?
Do I have two offices in the Math Building? Are the truths of these two things
of the same kind?