Wireworld: Difference between revisions
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import Control.Arrow |
import Control.Arrow |
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import Data.Maybe |
import Data.Maybe |
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states=" Ht." |
states=" Ht." |
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Example executed in GHCi: |
Example executed in GHCi: |
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<lang Haskell> |
<lang Haskell> |
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example = mapM_ (mapM_ putStrLn) .map (borden ' ').take 9 $ runCircuit oscillator |
example = mapM_ (mapM_ putStrLn) .map (borden ' ').take 9 $ runCircuit oscillator |
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</lang> |
</lang> |
Revision as of 18:19, 10 September 2009
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
Text only.
<lang ruby>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 @width = max_row @height = @grid.length pad_grid end
# initialize from a file def self.open(filename) self.new(File.read(filename)) 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 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
end
ww = WireWorld.open('wireworld.data') ww.run
puts "---------------"
program = DATA.read ww = WireWorld.new(program) ww.run
__END__ > .. > tH...... .Ht > .. </lang>
Outputs
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.tH . H ... . . HtH. ...... .tH.tH.tH.t H t HHH H . t.tH ...... H.tH.tH.tH. t . ttt t . .H.t ...... I've seen this grid before... after 11 iterations --------------- .. tH...... .Ht .. .. .tH..... Ht. .. .H ..tH.... t.. .H Ht ...tH..H ... Ht t. ....tH.t ... t. .. .....tH. ... .. H. ......tH ... H. tH .......t ... tH .t ........ H.. .t .. ........ tH. .. .. ........ .tH .. .. ........ ..t .. .. ........ ... .. .. ........ ... .. I've seen this grid before... after 13 iterations
Tcl
<lang tcl>package require Tcl 8.6 package require Tk
- The color scheme.
- The order is: empty, conductor, electronTail, electronHead
set colors "#000000 #000080 #8080ff #ffffff"
- 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 }
}
}
- 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
}
- 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]
}
- 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>