The XOROR sequence

Mathematica, 133 bytes

FromCharacterCode@Nest[BlockMap[If[#>126,#~Mod~127+32,#]&[BitXor[#,#2]~BitOr~#3]&@@#&,ArrayPad[#,1,32],3,1]&,ToCharacterCode@#,#2+1]&

It would be nice to make a CellularAutomaton[] solution work, but I kept coming up short. Anyone?

Edit: some pretty pictures (click to enlarge)

plotCA[str_, n_] := ArrayPlot[NestList[foo[str],n], ColorFunction -> "Rainbow"]

plotCA["Hello, World!", 60]:

plotCA[bXORnotb, 100]:

plotCA[raven, 100]:

Java, 193 185 bytes

Because Java.

-8 bytes by switching to looping rather than recursing to make it an anonymous function

Returns the n'th iteration of XOROR on s.

(s,n)->{String o=s;for(;n-->=0;){o="";for(int i=0;i<s.length();i++){char c=(char)((i>1?s.charAt(i-1):' ')^s.charAt(i)|(i<s.length()-1?s.charAt(i+1):' '));o+=c>126?' ':c;}s=o;}return o;}

Readable version:

static BiFunction<String, Integer, String> f = (s,n)->{
    String o=s;
    for(;n-->=0;) {
        o = "";
        for (int i=0;i<s.length();i++) {
            char c=(char)((i>1?s.charAt(i-1):' ')^s.charAt(i)|(i<s.length()-1?s.charAt(i+1):' '));
            o+=c>126?' ':c;
        }
        s=o;
    }
    return o;
};

public static void main(String[]a) {
    System.out.println(f.apply("Hello, World",1));
}

Pretty much a literal implementation of the spec, with a recursive loop to apply the operation n times. Some bytes were saved, however, with my observation that the CHARCODE>126 clause will only ever happen with CHARCODE==127, which results in saving SPACE instead of DEL.

I ran my code over a few arbitrarily chosen strings and found this wonderful cycle:

oook$ok$ok$ok$
ook$ok$ok$ok$o
oo$ok$ok$ok$ok
oook$ok$ok$ok$

CJam, 38 bytes

lri){2S*\*3ew{)\:^|_'~>{i127%' +}&}%}*

Test it here.

Explanation

l                e# Read string.
ri               e# Read n.
){               e# Run this block n+1 times...
  2S*\*          e#   Wrap in two spaces.
  3ew            e#   Get all (overlapping) substrings of length 3.
  {              e#   Map this block over all those substrings...
    )\           e#     Pull off the third character and put it below the other two.
    :^           e#     Take XOR of the other two.
    |            e#     OR with the third one.
    _'~>         e#     Duplicate and check if it's greater than '~'.
    {i127%' +}&  e#     If so, mod 127, add to space.
  }%
}*