[Pyrotex]

Hello, math fans!!!

As you know, I love the Excel application by MS. Herein, I have attached an Excel spreadsheet that contains a 1D Cellular Automaton (CA). There are many possible rules for these critters, and I supply half a dozen sets of rules that can be copied and pasted for your viewing pleasure.

When you open the spreadsheet, you MUST enable macros.

You SHOULD maximize the window to fully fit your screen. If you have a huge screen, you may want to decrease the magnification so the width of the CA is barely smaller than the width of your screen.

Some rules don't generate actors (or Monsters or Gliders) on every run, so click the RUN button 4 or 5 times before giving up.

[Pyrotex]

Dang! The 1.9 Mbyte limit got me. I need 2.9 Mbytes.

TORMOD!!!!!!!!!!!!!

THANK YOU!!!!!!!!!

[Turtle]

Oooooooo!!!! I love one-dimensional cellular automatons!!! If I haven't dematerialized the papers, I may have rule sets for 3-by (there are exactly 256 if I recall) and 5-by one-dimensional cellular automata.

Ooooooo!!! Can't wait to see what ya got Pyro! (I don't have Excel , but I have Quatro Pro and it opens most Excel files. )

[Turtle]

OK A cursory search has turned up some files; I have yet to look for papers.

The code below is a Basic program I wrote for experimenting with 1-dimensional cellular automata. It is short, and fairly well annotated. I never coded a menuing system, rather I would simply change the variables in the code and recompile and run it.

'  3 cell 1 dimensional CA

DEFINT A-Z
CLS
SCREEN 12
'COLOR 0,0

  DIM A(0:639)                  'tested array/ 1 row

'.............. Set a:sets initial cells .................
   A(6)=1:A(8)=1:A(10)=1
   A(26)=1:A(29)=1:A(32)=1:A(35)=1
    A(86)=1:A(90)=1:A(94)=1:A(98)=1
   'A(120)=1:A(125)=1:A(130)=1:A(135)=1:A(140)=1
   A(210)=1:A(216)=1:A(222)=1:A(228)=1:A(234)=1
   A(386)=1:A(390)=1:A(394)=1:A(398)=1
   A(523)=1:A(525)=1:A(530)=1:A(535)=1:A(541)=1
    A(320)=1

'........................... initialize 1st row
  CLS
   FOR I = 0 TO 639
    IF A(I) = 1 THEN PSET (I,0),1 else pset (I,0),0
   NEXT I

'..........................  main loop
   10 locate 1,5
      print "F10 = End"

  FOR J = 0 TO 479                     'increments rows
     DIM B(0:639,1:2)
    FOR K = 0 TO 637                   'increments columns
                  Q=K
                  R=K+1
                  S=K+2
       TEST$=BIN$(A(Q))+BIN$(A(R))+BIN$(A(S))
        SELECT CASE TEST$
         CASE "000"      '1
          B(R,1) = 0                               'this entry turns on a cell;change the value after
          'equal sign between 1 & 0 to change rules set; net 2^8 rule sets
                                      B(R,2) = 1          'this entry colors it
         CASE "100"      '2
          B(R,1) = 1
                                      B(R,2) = 2
         CASE "010"      '3
          B(R,1) = 0
                                      B(R,2) = 3
         CASE "001"      '4
          B(R,1) = 1
                                      B(R,2) = 4
         CASE "110"      '5
          B(R,1) = 0
                                      B(R,2) = 5
         CASE "101"      '6
          B(R,1) = 0
                                      B(R,2) = 6
         CASE "011"      '7
          B(R,1) = 0
                                      B(R,2) = 7
         CASE "111"      '8
          B(R,1) = 1
                                      B(R,2) = 8
         END SELECT
       NEXT K
'****************** draw ********

           FOR L = 0 TO 639
            select case b(L,1)
             case 0
             preset (L,J)
             case 1
              select case b(l,2)      'b(R,2)
               case 0
                pset (l,j),0
               case 1
                pset (l,j),1
               case 2
                pset (l,j),2
               case 3
                pset (l,j),3
               case 4
                pset (l,j),4
               case 5
                pset (l,j),5
               case 6
                pset (l,j),6
               case 7
                pset (l,j),7
               case 8
                pset (l,j),8
              end select
            end select
          NEXT L
            if j < 477 then
             p=j+1:q=p+5
             line (0,p)-(639,q),0,bf
            end if

        ERASE A
        DIM A(0:639)
         FOR M = 0 TO 639
          A(M) = B(M,1)
         NEXT M
        ERASE B

'.......................... trap F10 to interrupt program
  $EVENT ON
   ON KEY(10) GOSUB QUIT
   KEY(10)ON

     NEXT J

  $event off

   incr COUNT&
   cycles&=count&*480
   LOCATE 3,1
   PRINT cycles&" cycles"
   GOTO 10

  END

 QUIT:
  KEY(10) OFF
  END
 RETURN

Find in the attached Zip folder a compiled executable version. I can not guarantee its behavior on your machine. Press F10 to stop it.

Good stuff Maynard!

[Turtle]

Originally Posted by Pyrotex

Dang! The 1.9 Mbyte limit got me. I need 2.9 Mbytes.

TORMOD!!!!!!!!!!!!!

THANK YOU!!!!!!!!!

OK I have the xls file loaded in Quattro. I can't for the life of me find a Run button! Little help here? Turtle down...turtle down!!!

[Pyrotex]

Originally Posted by Turtle

OK I have the xls file loaded in Quattro. I can't for the life of me find a Run button! Little help here? Turtle down...turtle down!!!

Okay, don't panic! Buttons may not be supported in Quattro.

When you got the Automaton sheet up, just click Ctrl-= (that's Control Equal Sign), to get a new run of the CA.

[Pyrotex]

I am totally sconed that no one has given any feedback on my cellular automaton, available in the #2 post of this thread. Has anyone successfully downloaded it? Does it work? Or is it just boring or what?

[Turtle]

Originally Posted by Pyrotex

I am totally sconed that no one has given any feedback on my cellular automaton, available in the #2 post of this thread. Has anyone successfully downloaded it? Does it work? Or is it just boring or what?

If you are totally sconed, I am totally sconed squared! My Quattro Pro loader takes the file and I can read it all, but no Run button or Ctrl= works. I have re-read it all thouroughly, and by all means wish to discuss it.

Mayhaps the deeper implications of such apparently gamish pursuits escapes the midling minds. No worries, there is simplicity abundant in one dimensional cellular automata.

When we say 'cellular', we mean a box, a pidgeonhole, a place to put stuff.
When we say 'one dimensional', we mean a single row of boxes.

When we say we'll be back later with more, we mean it.

Edit Post Script: Wicky on topic.

[Pyrotex]

Exactly, Turtle! Each cell of the spreadsheet is a "Cell" that can be either ON (alive, 1) or OFF (dead, 0). At any given time T-sub-(n), there exists only a single dimension (row) of Cells. In the spreadsheet, this would be a horizontal row of cells.

The vertical axis is Time. Row #1 would be T-sub-(0), let's say.
Row #2 would be T-sub-(1). Etc.

The State of any Cell, C, at any Time, T-sub-(n) is a function of three things:
--- The States of (2M-1) Cells, centered on C, at Time T-sub-(n-1);
--- A Set of Rules, R, containing (2M-1) discrete rules;
--- A pair of integers called the State Range;
where M is a positive integer > 0.

In my application, M=5, so the State of any particular Cell is a function of the 9 Cells "above" it; and 9 rules.

The rules classically are defined as either 0 or 1. The easiest way to apply the rules is by multiplying them times the corresponding Cell values of the previous Time and adding up the results, and comparing to the State Range:

C-state = 1 if rule1*cell1 + rule2*cell2 + ... + rule(2M-1)*cell(2M-1) falls within the State Range;
C-state = 0 otherwise.

I have "advanced" this scenario a bit by allowing the Set of Rules, R, to contain any integers, negative or positive. Typically, I have found that just those values from -1 to 2 produce "nice" results.

The State Range integers are typically 3 and 4, or: (3, 4). So the [sum of rulex*cellx] must be => 3 and <= 4, else C-state is zero. State Ranges (2, 3) and (2, 4) can occassionally give "nice" results.

What is a "nice" result? As Time progresses from spreadsheet row to row, there will be patterns within a row that get repeated in a subsequent row. There may be a displacement either to the left or right. This gives the visually pleasing appearance of diagonal "Gliders" of ON cells. These Gliders may slope off at 45 degrees, 30 degrees or other angles. They may collide with other Gliders or with "Lazers" -- repeating patterns with a displacement of zero, giving a vertical stream. Colliding Gliders and Lazers may produce new Gliders or Lazers, or may terminate entirely. Unstable Gliders may spit off Lazers and other kinds of Gliders as Time progresses. You can categorize the different kinds of Gliders and Lazers (collectively called Actors) to produce a Menagerie. Some Actors are rare, others are common.

[Turtle]

Originally Posted by Pyrotex

In my application, M=5, so the State of any particular Cell is a function of the 9 Cells "above" it; and 9 rules.

And so the standard nomenclature 1x9 cellular automaton. One row of cells of some arbitrary length (ringed or not), and the consideration of the state of 9 of those cells at a time. Given my proclivity to peruse complete lists, and that a 1x9 automaton has 2^9 possible states, you can see why I never ventured much beyond the 1x3.

Originally Posted by Pyrotex

I have "advanced" this scenario a bit by allowing the Set of Rules, R, to contain any integers, negative or positive.

Can we say 'understatement' ‽‽‽ I need a bit of time yet to juxtapose your 1x9 rule set calcs with my 1x3.