Steampunk: Clacker animation

Mathematica, 306 281 bytes

This expects the input string to be stored in variable i

ListAnimate[ArrayPlot/@FoldList[({n,y,x,X,o,a}=#2;MapAt[IntegerDigits[o,2,4][[-1-FromDigits[{#,a},2]]]&,#,{y+1,x+1;;X+1}])&,Array[0&,{20,20}],ToExpression/@MapAt["16^^"<>#&,StringTrim/@SortBy[i~StringSplit~"\n"~StringCases~RegularExpression@"^....|..(?!.?$)|.",{#[[1]]&}],{;;,5}]]]

And here with some whitespace:

ListAnimate[ArrayPlot /@ FoldList[(
     {n, y, x, X, o, a} = #2;
     MapAt[
      IntegerDigits[o, 2, 4][[-1 - FromDigits[{#, a}, 2]]] &,
      #,
      {y + 1, x + 1 ;; X + 1}
      ]
     ) &,
   Array[0 &, {20, 20}],
   ToExpression /@ 
    MapAt["16^^" <> # &, 
     StringTrim /@ 
      SortBy[i~StringSplit~"\n"~StringCases~
        RegularExpression@"^....|..(?!.?$)|.", {#[[1]] &}], {;; , 5}]
   ]]

This got pretty damn long. This challenge contained a lot of fiddly details, and especially the input parsing takes a lot of code in Mathematica (almost half of it, 137 bytes, are just parsing the input). I ended up switching the language twice before settling on Mathematica (I thought I could save on the input parsing by using Ruby, but then I realised the result needs to be animated, so I went back to Mathematica).

Ungolfed Postscript example

This is a "protocol-prolog"-style program, so the data immediately follows in the same source file. Animated gif files can be produced with ImageMagick's convert utility (uses ghostscript): convert clack.ps clack.gif.

%%BoundingBox: 0 0 321 321

/t { token pop exch pop } def
/min { 2 copy gt { exch } if pop } def
/max { 2 copy lt { exch } if pop } def

/m [ 20 { 20 string }repeat ] def
/draw { change {
        m {} forall 20 20 8 [ .0625 0 0 .0625 0 0 ] {} image showpage
    } if } def

%insertion sort from https://groups.google.com/d/topic/comp.lang.postscript/5nDEslzC-vg/discussion
% array greater_function insertionsort array
/insertionsort
{ 1 1 3 index length 1 sub
    { 2 index 1 index get exch % v, j
        { dup 0 eq {exit} if
            3 index 1 index 1 sub get 2 index 4 index exec
            {3 index 1 index 2 copy 1 sub get put 1 sub}
            {exit} ifelse
        } loop
        exch 3 index 3 1 roll put
    } for
    pop
} def

/process {
    x X min 1 x X max { % change? x
        m y get exch  % row-str x_i
        2 copy get  % r x r_x 
        dup         % r x r_x r_x
        0 eq { 0 }{ 1 } ifelse  % r x r_x b(x)
        2 mul a add f exch neg bitshift 1 and   % r x r_x f(x,a)
        0 eq { 0 }{ 255 } ifelse  % r x r_x c(f)
        exch 1 index % r x c(f) r_x c(f)
        ne { /change true def } if
        put
    } for
    draw
} def

{ [ {
     currentfile 15 string
         dup 2 13 getinterval exch 3 1 roll
         readline not{pop pop exit}if
    pop
    [ exch
     /b exch dup 0 1 getinterval exch
     /n exch dup 1 1 getinterval exch
     /seq exch dup 2 4 getinterval exch
     /y exch dup 6 2 getinterval t exch
     /x exch dup 8 2 getinterval t exch
     /X exch dup 10 2 getinterval dup (  ) ne { t exch }{pop 2 index exch} ifelse
     /f exch dup 12 get (16#?) dup 3 4 3 roll put t exch
     /a exch 13 get 48 sub
     /change false def
    >>
}loop ]
dup { /seq get exch /seq get exch gt } insertionsort
true exch
{ begin
    b(A)eq{
        { process } if
    }{
        b(O)eq{
            not { process } if
        }{
            pop
            process
        }ifelse
    }ifelse
    change
    end
} forall
    draw
} exec
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