Here's another animated JAPH for your enjoyment!

This one optionally takes a number as an argument; save it to a file and run it with perl rotate.pl 13, for example.

The same caveats apply as for Swap JAPH; it's not expected to work on all platforms, and I concentrated on making it as compact as possible rather than as obfuscated as possible. (Although the latter does follow somewhat from the former, of course. :) 

  ($s=pop|1)>8or$s|=8;sub f{$_=.5+($h=int$s/2)+$h*$_}$|=@m=map[($")x$s
+],1..$s
   ;$j='  ,rekcah  lreP  rehtona  tsuJ  ';for(0..31){f,$_-=/-/for$x=co
+s($d=$
    _*.19635),$y=sin$d;$m[$y[$_]=$y][$x[$_]=$x]=chop$j}{$j=$m[$y[0]][$
+x[0]]
     ;print"\e[H\e[J",map"@$_\n",@m;map$m[$y[$_-1]][$x[$_-1]]=$m[$y[$_
+]][$
      x[$_]],1..31;$m[$y[-1]][$x[-1]]=$j;select$,,$,,$,,.1;redo}chipmu
+nk;

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In reply to Rotate JAPH by chipmunk

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