Langton's Loops- a self-reproducing Cellular Automaton.

This models an array of 8-state cells on a regular Cartesian grid. Synchronously, all cells update to a new set according to a rule table and their own present state & the four neighbour states.. this is four-fold symmetrical, so one rule that states '1 2345 6'is interpreted to mean that a cell currently in state 1, & with neighbours 2345 will become state 6- but so, in the other three compass directions, will '1 3452 6', '1 4523 6' and ' 1 5234 6'. This makes the rule table more comapact. A kind of 'genetic code' circulates in each loop, and as the 'genes' arrive at the active site they govern how it extends. The two main genes are one to extend and sheathe the core, and one to turn a right angle corner. The other states allow termination & disconnection of completed loops.

The starting gene-string, wrapped as shown, is ..

The Rule Table is as follows.

The 'genetic code' amounts to descriptions of the state-transition a particular neighbourhood provokes.

0    Background    Black      Empty, quiescent, 'vacuum' state.
1    Core          Blue       Fill tube & 'conduct'.
2    Sheath        Red        Form the boundary /container of the gene in the loop.
3                  Green      Support left tyrning; bonding two arms; generating new off-shoot; cap off-shoot.    4                  Yellow     Control left-turning & finishing a sprouted loop.
5                  Pink       Disconnect parent from offspring.
6                  White      Point to where new sprout should start; guide sprout; finish sprout growth.
7                  Cyan       Hold info. on straight growth of arm & offspring.

Code for a version in LB follows. LB is very slow for this kind of set-up, with two nested loops to scan the 'universe' of cells, and inside then a loop to query the neighbours' states. I've speeded it up a bit by only looking at the area of the 'iunuverse' known to include live cells, and increasing its boundaries as the pattern ( often said to look like coral) grows. I've also added code that saves the image of each generation, and if you have installed ImageMagick it turns these into an animated GIF.

I ran it for twelve hours on my 1.7G Athlon, and got 320 generations. The GIF can replay these at several per second....

While I've a few speed-up ideas, including 'boosting', but it's never going to be real-time. There are good Java simulations of Langton's Loops out there, and I also recommend the versatile 'Golly', freeware that generates most of the investigated Cellular Automata.

nomainwin

dim p( 128, 128), q( 128, 128)

y     = 0
itern = 1
colour$ = "black blue red green yellow pink white cyan"
global i, horizMin, horizMax, vertMin, vertMax, flag$

while a$ <>"="
  read a$
  for x =1 to len( a$ )
    p( x +64, y +64 ) =val( mid$( a$, x, 1))
  next x
  y = y +1
wend

data " 22222222"    '   initial conditions
data "2170140142"
data "2022222202"
data "272    212"
data "212    212"
data "202    212"
data "272    212"
data "21222222122222"
data "20710710711111"
data " 2222222222222"
data "="

dim r$( 400)

open "langton-.txt" for input as #in
  i =0
  while not( eof( #in))
    line input #in, r$( i)
    i =i +1
  wend
close #in

max = i -1
vertMin =63: vertMax =74: horizMin =64: horizMax =79

WindowWidth  =860: WindowHeight =780
UpperLeftX   = 10: UpperLeftY   =  1

button #m.b1, "Make Animation", [makeAnimGIF], LR, 150, 720, 130, 40

open "Langton's loop" for graphics_nsb_nf as #m
  #m "trapclose [quit]"
  #m "down ; size 11 ; fill 140 140 140 ; backcolor 200 210 70 ; font Arial 9 11"

do                                                      '   Display old cells while calculating new data.

  for x =horizMin to horizMax                           '   copy old cell data array p() to array q() to be updated.
    for y =vertMin to vertMax
      q( x, y) =p( x, y)
    next y
  next x

  flag$ =""
  for x =horizMin to horizMax                           '   calc new data from q() and put in array p().
    for y =vertMin to vertMax

      for i =0 to max                                   '   check all rules against current situation of cell & surroundings.
        old =val( mid$( r$( i), 1, 1))                  '   try matching first digits 2 to 5 of rule for match against cell.
        n   =val( mid$( r$( i), 2, 1))                  '   current, N, E, S, W for matching against rules array r()..
        e   =val( mid$( r$( i), 3, 1)): s   =val( mid$( r$( i), 4, 1)): w   =val( mid$( r$( i), 5, 1))

        call rule x, y, old, n, e, s, w                 '   check the four symmetry variants
        call rule x, y, old, e, s, w, n: call rule x, y, old, s, w, n, e: call rule x, y, old, w, n, e, s

        #m "color "; word$( colour$, q( x, y) +1)       '   display old data while calc'g new
        #m "set "; x *10 -300; " "; y *11 -304
        scan

      next i

    next y
  next x

  #m "font Courier_New 20 bold ; color white": #m "place 10 20": #m "\Gen'n "; str$( itern)
  #m "font Arial 9 11 ; flush": #m "getbmp scr 260 160 500 390"
  bmpsave "scr", "C:\Temp\scr" +right$( "000" +str$( itern), 3) +".bmp"    ' These will be made into an animated GIF later.
  itern =itern +1
  bmpsave "scr", "R:\scr.bmp"
  #m "cls"
  loadbmp "scr", "R:\scr.bmp"
  #m "drawbmp scr 260 160"
loop until itern =999

[quit]
  close #m
end

sub rule x, y, old, n, e, s, w
  if q( x, y ) = old _
  and q(   x,             ( y -1) and 127)  =n _
  and q( ( x -1) and 127,   y)              =w _
  and q(   x ,            ( y +1) and 127)  =s _
  and q( ( x +1) and 127,   y )             =e then
        p( x, y) =val( mid$( r$( i), 6, 1))
        if i <>0 and p( x, y) <>0 then
            '   We've changed a cell not originally empty. If it is on existing H & V limits, need to increase range for next generation....
            if x =horizMin then horizMin =horizMin -1
            if x =horizMax then horizMax =horizMax +1
            if y =vertMin  then vertMin  =vertMin  -1
            if y =vertMin  then vertMax  =vertMax  +1
        end if
  end if
end sub

[makeAnimGIF]
    IM$ ="cd C:\Program Files\ImageMagick-6.7.1-Q16"
    'run "cmd.exe /c "; chr$( 34); IM$; chr$( 34), HIDE
    IM$ ="convert -delay 50 C:\Temp\scr*.bmp R:\aniL2.gif"
    'run "cmd.exe /c "; chr$( 34); IM$; chr$( 34), HIDE
        '   Give it 60 seconds to execute (may not be enough for large images)
    'timer 20000, [on]
    'wait
  [on]
    'timer 0
    close #m
    end

Contact me if you have problems... mr.john.f@gmail.com