Wireworld

Wireworld
You are encouraged to solve this task according to the task description, using any language you may know.

Wireworld is a cellular automaton with some similarities to Conway's Game of Life. It is capable of doing sophisticated computations (e.g., calculating primeness!) with appropriate programs, and is much simpler to program for.

A wireworld arena consists of a cartesian grid of cells, each of which can be in one of four states. All cell transitions happen simultaneously. The cell transition rules are this:

Input State	Output State	Condition
empty	empty
electron head	electron tail
electron tail	conductor
conductor	electron head	if 1 or 2 cells in the neighborhood of the cell are in the state “electron head”
conductor	conductor	otherwise

To implement this task, create a program that reads a wireworld program from a file and displays an animation of the processing. Here is a sample description file (using “H” for an electron head, “t” for a tail, “.” for a conductor and a space for empty) you may wish to test with, which demonstrates two cycle-3 generators and an inhibit gate:

tH.........
.   .
   ...
.   .
Ht.. ......

While text-only implementations of this task are possible, mapping cells to pixels is advisable if you wish to be able to display large designs. The logic is not significantly more complex.

Forth

<lang forth> 16 constant w

8 constant h

rows w * 2* ;

1 rows constant row h rows constant size

create world size allot world value old old w + value new

init world size erase ;

age new old to new to old ;

foreachrow ( xt -- )

 size 0 do  I over execute  row +loop drop ;

0 constant EMPTY 1 constant HEAD 2 constant TAIL 3 constant WIRE create cstate bl c, char H c, char t c, char . c,

showrow ( i -- ) cr

 old + w over + swap do I c@ cstate + c@ emit loop ;

show ['] showrow foreachrow  ;

line ( row addr len -- )

 bounds do
   i c@
   case
   bl of EMPTY over c! endof
   'H of HEAD  over c! endof
   't of TAIL  over c! endof
   '. of WIRE  over c! endof
   endcase
   1+
 loop drop ;

load ( filename -- )

 r/o open-file throw
 init  old row + 1+  ( file row )
 begin  over pad 80 rot read-line throw
 while  over pad rot line
        row +
 repeat
 2drop close-file throw
 show cr ;

+head ( sum i -- sum )

 old + c@ HEAD = if 1+ then ;

conductor ( i WIRE -- i HEAD|WIRE )

 drop 0
 over 1- row - +head
 over    row - +head
 over 1+ row - +head
 over 1-       +head
 over 1+       +head
 over 1- row + +head
 over    row + +head
 over 1+ row + +head
 1 3 within if HEAD else WIRE then ;

\ before: empty head tail wire

create transition ' noop , ' 1+ , ' 1+ , ' conductor ,

\ after: empty tail wire head|wire

new-state ( i -- )

 dup  old + c@
 dup cells transition + @ execute
 swap new + c! ;

newrow ( i -- )

 w over + swap do I new-state loop ;

gen ['] newrow foreachrow age ;

wireworld begin gen 0 0 at-xy show key? until ;

</lang>

Output:

s" wireworld.diode" load
                
        ..      
 tH...... .Ht   
        ..      
                
                
                
                
 ok
gen show                
                
        ..      
 .tH..... Ht.   
        ..      
                
                
                
                 ok
gen show 
                
        .H      
 ..tH.... t..   
        .H      
                
                
                
                 ok
gen show 
                
        Ht      
 ...tH..H ...   
        Ht      
                
                
                
                 ok
gen show 
                
        t.      
 ....tH.t ...   
        t.      
                
                
                
                 ok
gen show 
                
        ..      
 .....tH. ...   
        ..      
                
                
                
                 ok
gen show 
                
        H.      
 ......tH ...   
        H.      
                
                
                
                 ok
gen show 
                
        tH      
 .......t ...   
        tH      
                
                
                
                 ok
gen show 
                
        .t      
 ........ H..   
        .t      
                
                
                
                 ok
gen show 
                
        ..      
 ........ tH.   
        ..      
                
                
                
                 ok
gen show 
                
        ..      
 ........ .tH   
        ..      
                
                
                
                 ok
gen show 
                
        ..      
 ........ ..t   
        ..      
                
                
                
                 ok
gen show 
                
        ..      
 ........ ...   
        ..      
                
                
                
                 ok

Haskell

<lang Haskell> import Data.List import Control.Monad import Control.Arrow import Data.Maybe

states=" Ht." shiftS=" t.."

borden bc xs = bs: (map (\x -> bc:(x++[bc])) xs) ++ [bs]

  where r = length $ head xs
        bs = replicate (r+2) bc

take3x3 = ap ((.). taken. length) (taken. length. head) `ap` borden '*'

  where taken n =  transpose. map (take n.map (take 3)).map tails

nwState xs | e =='.' && noH>0 && noH<3 = 'H'

          | otherwise = shiftS !! (fromJust $ findIndex (==e) states) 
  where e = xs!!1!!1
        noH = length $ filter (=='H') $ concat xs

runCircuit = iterate (map(map nwState).take3x3) </lang> Example executed in GHCi: <lang Haskell> oscillator= [" tH ",

            ".  ....",
            " ..    "
           ]

example = mapM_ (mapM_ putStrLn) .map (borden ' ').take 9 $ runCircuit oscillator </lang> Ouptput:

*Main> example

  tH
 .  ....
  ..


  .t
 .  H...
  ..


  ..
 .  tH..
  .H


  ..
 .  .tH.
  Ht


  ..
 H  ..tH
  t.


  H.
 t  ...t
  ..


  tH
 .  ....
  ..


  .t
 .  H...
  ..


  ..
 .  tH..
  .H

(0.01 secs, 541764 bytes)

J

The example circuit: <lang J> circ0=:}: ] ;. _1 LF, 0 : 0 tH........ . .

  ...    

. . Ht.. ..... ) </lang> A 'boarding' verb board and the next cell state verb nwS: <lang J>

board=: ' ' ,.~ ' ' ,. ' ' , ' ' ,~ ]

nwS=: 3 : 0

 e=. (<1 1){y
 if. ('.'=e)*. e.&1 2 +/'H'=,y do. 'H' return. end.
 ' t..' {~ ' Ht.' i. e

) </lang> The 'most' powerful part is contained in the following iterating sentence, namely the dyad cut ;. [1]. In this way verb nwS can work on all the 3x3 matrices containing each cell surrounded by its 8 relevant neighbors. <lang J> (3 3 nwS;. _3 board)^: (<10) circuit</lang> Example run:

   (3 3 nwS;. _3 board)^: (<10) circ0
tH........
.   .     
   ...    
.   .     
Ht.. .....

.tH.......
H   .     
   ...    
H   .     
t... .....

H.tH......
t   .     
   ...    
t   .     
.H.. .....

tH.tH.....
.   H     
   ...    
.   .     
HtH. .....

.tH.tH....
H   t     
   HHH    
H   .     
t.tH .....

H.tH.tH...
t   .     
   ttt    
t   .     
.H.t .....

tH.tH.tH..
.   H     
   ...    
.   .     
HtH. .....

.tH.tH.tH.
H   t     
   HHH    
H   .     
t.tH .....

H.tH.tH.tH
t   .     
   ttt    
t   .     
.H.t .....

tH.tH.tH.t
.   H     
   ...    
.   .     
HtH. .....

Python

<lang python> Wireworld implementation.

from io import StringIO from collections import namedtuple from pprint import pprint as pp import copy

WW = namedtuple('WW', 'world, w, h') head, tail, conductor, empty = allstates = 'Ht. '

infile = StringIO(\ tH......... . .

  ...

. . Ht.. ......\ )

def readfile(f):

   'file > initial world configuration'
   world  = f.readlines()
   world  = [row.rstrip('\r\n') for row in world]
   height = len(world)
   width  = max(len(row) for row in world)
   # fill right and frame in empty cells
   nonrow = [ " %*s " % (-width, "") ]
   world  = ( nonrow
              + [ " %*s " % (-width, row) for row in world ]
              + nonrow[:] )    
   world = [list(row) for row in world]
   return WW(world, width, height)

def newcell(currentworld, x, y):

   istate = currentworld[y][x]
   assert istate in allstates, 'Wireworld cell set to unknown value "%s"' % istate
   if istate == head:
       ostate = tail
   elif istate == tail:
       ostate = conductor
   elif istate == empty:
       ostate = empty
   else: # istate == conductor
       n = sum( currentworld[y+dy][x+dx] == head
                for dx,dy in ( (-1,-1), (-1,+0), (-1,+1),
                               (+0,-1),          (+0,+1),
                               (+1,-1), (+1,+0), (+1,+1) ) )
       ostate = head if 1 <= n <= 2 else conductor
   return ostate

def nextgen(ww):

   'compute next generation of wireworld'
   world, width, height = ww
   newworld = copy.deepcopy(world)
   for x in range(1, width+1):
       for y in range(1, height+1):
           newworld[y][x] = newcell(world, x, y)
   return WW(newworld, width, height)

def world2string(ww):

   return '\n'.join( .join(row[1:-1]).rstrip() for row in ww.world[1:-1] )

ww = readfile(infile) infile.close()

for gen in range(10):

   print ( ("\n%3i " % gen) + '=' * (ww.w-4) + '\n' )
   print ( world2string(ww) )
   ww = nextgen(ww)

</lang>

Sample Output

  0 =======

tH.........
.   .
   ...
.   .
Ht.. ......

  1 =======

.tH........
H   .
   ...
H   .
t... ......

  2 =======

H.tH.......
t   .
   ...
t   .
.H.. ......

  3 =======

tH.tH......
.   H
   ...
.   .
HtH. ......

  4 =======

.tH.tH.....
H   t
   HHH
H   .
t.tH ......

  5 =======

H.tH.tH....
t   .
   ttt
t   .
.H.t ......

  6 =======

tH.tH.tH...
.   H
   ...
.   .
HtH. ......

  7 =======

.tH.tH.tH..
H   t
   HHH
H   .
t.tH ......

  8 =======

H.tH.tH.tH.
t   .
   ttt
t   .
.H.t ......

  9 =======

tH.tH.tH.tH
.   H
   ...
.   .
HtH. ......

Ruby

Library: Ruby/Tk

The GUI is somewhat "halfway", in that it animates a text widget so it's not "real" graphics. <lang ruby>require 'tk'

class WireWorld

 EMPTY = ' '
 HEAD = 'H'
 TAIL = 't'
 CONDUCTOR = '.'

 def initialize(string)
   max_row = 0
   @grid = string.each_line.collect do |line|
             line.chomp!
             max_row = [max_row, line.length].max
             line.each_char.collect do |char| 
               case char
               when EMPTY, HEAD, TAIL, CONDUCTOR then char
               else EMPTY
               end 
             end
           end
   @original_grid = Marshal.restore(Marshal.dump @grid)   # this is a deep copy
   @width = max_row
   @height = @grid.length
   pad_grid
 end

 # initialize from a file
 def self.open(filename)
   self.new(File.read(filename))
 end

 def reset
   @grid = @original_grid
 end

 # ensure all rows are the same length by padding short rows with empty cells
 def pad_grid
   @grid.each do |row|
     if @width > row.length
       row.concat(Array.new(@width - row.length, EMPTY))
     end
   end
 end

 # the "to_string" method
 def to_s
   @grid.inject() {|str, row| str << row.join() << "\n"}
 end

 # transition all cells simultaneously
 def transition
   @grid = @grid.each_with_index.collect do |row, y| 
             row.each_with_index.collect do |state, x| 
               transition_cell(state, x, y)
             end
           end
 end

 # how to transition a single cell
 def transition_cell(current, x, y)
   case current
   when EMPTY then EMPTY
   when HEAD  then TAIL
   when TAIL  then CONDUCTOR
   else neighbours_with_state(HEAD, x, y).between?(1,2) ? HEAD : CONDUCTOR
   end
 end

 # given a position in the grid, find the neighbour cells with a particular state
 def neighbours_with_state(state, x, y)
   count = 0
   ([x-1, 0].max .. [x+1, @width-1].min).each do |xx|
     ([y-1, 0].max .. [y+1, @height-1].min).each do |yy|
       next if x == xx and y == yy
       count += 1 if state(xx, yy) == state
     end
   end
   count
 end

 # return the state of a cell given a cartesian coordinate
 def state(x, y)
   @grid[y][x]
 end

 # run a simulation up to a limit of transitions, or until a recurring
 # pattern is found
 # This will print text to the console
 def run(iterations = 25)
   seen = []
   count = 0
   loop do
     puts self
     puts

     if seen.include?(@grid)
       puts "I've seen this grid before... after #{count} iterations"
       break
     end
     if count == iterations
       puts "ran through #{iterations} iterations"
       break
     end

     seen << @grid
     count += 1
     transition
   end
 end

 # the gui version
 def run_tk
   $root = TkRoot.new("title" => "WireWorld")

   $text = TkText.new($root) {font 'courier'}
   $text.width(@width)
   $text.height(@height)
   $text.insert('end', self.to_s)
   $text.state('disabled')
   $text.pack(:expand => 1, :fill => 'both')

   $quit = TkButton.new($root) do
     text 'close gui'
     command do
       $root.after_cancel($after_id)
       $root.destroy
     end
   end.pack(:fill => 'x')

   $after_id = $root.after(500) {self.animate}
   Tk.mainloop
 end

 def animate
   transition 
   $text.state('normal')
   $text.delete('1.0','end')
   $text.insert('end', self.to_s)
   $text.state('disabled')
   $after_id = $root.after(150) {self.animate}
 end

end

ww = WireWorld.open(ARGV.shift) ww.run ww.reset ww.run_tk puts 'bye'</lang>

Tcl

Works with: Tcl version 8.6

Library: Tk

<lang tcl>package require Tcl 8.6 package require Tk

1. The color scheme.
2. The order is: empty, conductor, electronTail, electronHead

set colors "#000000 #000080 #8080ff #ffffff"

1. Encapsulate the per-cell logic in a class to simplify it

oo::class create wireCell {

   variable X Y S0 S1 Neighbours

   constructor {x y state} {

global cells colors upvar 1 at at

set X $x set Y $y

switch -- $state conductor { set S0 1 } electronTail { set S0 2 } electronHead { set S0 3 } default { return -code error "invalid state name \"$state\"" } lappend cells [self] set at($x,$y) [self] pixels put [lindex $colors $S0] -to $x $y

   }

   # Method used to allow each (non-background) cell to know about its
   # surrouding non-background cells. This makes the connectivity
   # calculations much simpler and faster!
   method initConnectivity {} {

upvar 1 at at foreach dx {-1 -1 -1 0 0 1 1 1} dy {-1 0 1 -1 1 -1 0 1} { set pos [expr {$X+$dx}],[expr {$Y+$dy}] if {[info exists at($pos)]} { lappend Neighbours $at($pos) } }

   }

   method state {} {return $S0}

   # Perform the transition in two stages, so that we can do the transition
   # "simultaneously" across all cells. The transition0 method calculates
   # what state we're going to change to, and the transition1 method actually
   # moves to the state.
   method transition0 {} {

if {$S0 == 3} { set S1 2 } elseif {$S0 == 2} { set S1 1 } else { set count 0 foreach n $Neighbours { incr count [expr {[$n state] == 3}] } set S1 [expr {($count == 1 || $count == 2) ? 3 : 1}] }

   }
   method transition1 {} {

if {$S0 != $S1} { global colors set S0 $S1 pixels put [lindex $colors $S0] -to $X $Y }

   }

}

1. How to load a layout/program from a file

proc loadWires filename {

   global cells colors

   # Read the file in
   set f [open $filename]
   set data [read $f]
   close $f

   # Initialize the list of interacting cells and the connectivity map
   set cells {}
   array set at {}

   # Calculate the width of the program
   set lines [split $data \n]
   set len 0
   foreach line $lines {

if {[string length $line] > $len} { set len [string length $line] }

   }

   # Create the arena image
   image create photo pixels

   # Initialize the image to "empty cell"s; interacting parts will be overlaid
   pixels put [lindex $colors 0] -to 0 0 $len [llength $lines]

   # Parse the input data and create the interacting cells
   set y 0
   foreach line $lines {

set x 0 foreach char [split $line {}] { switch $char { H { wireCell new $x $y electronHead } t { wireCell new $x $y electronTail } . { wireCell new $x $y conductor } } incr x } incr y

   }

   # Now inform each cell about its connectivity
   foreach cell $cells {

$cell initConnectivity

   }
   unset at

}

1. How to perform the animation timestep

proc timeStep {t} {

   global cells

   # Arm the transition for all interacting cells
   foreach cell $cells {

$cell transition0

   }
   # Perform the transition for all interacting cells
   foreach cell $cells {

$cell transition1

   }

   # Reschedule
   after $t [list timeStep $t]

}

1. Initialize the GUI (such as it is) and load and start the animation

wm title . "Wireworld: [lindex $argv 0]" loadWires [lindex $argv 0] pack [label .l -image pixels] after 1000 timeStep 250</lang>