Illustrative
program of the article "X-problem of number 3. Definition
..."
The program can
calculate the value Cr for any mask.
1). Start the demonstration.
Download the program
illustr_prg.zip, unzip, and run illustr_prg.exe.
Press button "Start test" (no. 1 in the
figure). The program will be calculate the value Cr
for mask (2,1). (The mask is located in the upper right
corner).
About 30 seconds on a standard laptop is enough to
find the right Cr = 27. (In figure no. 2).
The criterion of the
program work: changing the numbers in the lower left corner
(in figure no. 3).
How does the
program work?
1). First, the program Monte Carlo plays the number of cells in our one-dimensional
automaton. According
to the formula (in figure no. 1). Remember,
that the limit for this number is 64. (N0 + dN0 <64).
2). Then it Monte Carlo played the number of B cells, according to the
formula (in figure no. 2). (It would be better for this number to be
smaller. When the number of B cells are close to L/2
Automation Machine returns very quickly, and our test will not
be effective). Then, a
given number of cells randomly placed on our line (circle).
3). Next,
see the paper "X-problem of number 3. Definition ..."
The program starts;
calculates matrix Fx(3)(t)
and calculates addendum (if any) to our "resolution" table. The boundary value of t for the array Fx(3) we have as
2000. (The number of C in the figure.
It can be changed (lowered). It
corresponds to about (3/2) * 2000 = 3000 steps of Automaton
Machine. (There is nothing to worry
about our Automaton Machine still not
returningfor this time). All the same, we have ~ 2000 lines taken into
account in the "resolution" tables). If our Machine have returned, the full
results is shown in the program on a dark gray background.
(We
can explain 3 number one standing above the other on each column
of
our table. First number - the number of configurations which
turned out to the numbers 0, 1, 2. Second number - the number
of configurations which turned out to the numbers -0 (= 3), -1
(= 4) -2 (= 5)). And the third
number - is a "merged". (It is clear that both tables
of 0 and -0 - is the same thing. One of it is a full
complement of the other).
You can press
Stop, then click Clear, choose another mask and start a new
test. (After selecting
the proper mask, be sure to
click "Do from mask". It makes the correct offsets to
determine Fx(3)). Which
masks are correct and incorrect, see below.
It is curious
that for the number of cells in a mask
(with the center point) equal to 7 to determine the value Cr
are usually sufficient
a few minutes. But to get the right result
for the 8 points in the mask it is often lacking a few days on
my laptop (with our parameters)!
If you choose the
incorrect mask (or take the wrong offset) then the program
will give warning
"ambiguity" (see in the figure). This means that the "resolution" table formed
ambiguity. Different values of the table
correspond to the same initial values.
The matrices Cv(t)
is given in our program as a "background". For the mask (1,5) it is immediately
visible the violations of IPF in the figure.
