Seems like the method display as written would actually print all the cells in one row -- method iterate doesn't have an explicit hook for "reached end of line". That's fine, since we have $.max available within the object.

I think method display should actually look like this:

 method display
  {
    iterate 
    { 
      print $.grid[$^x][$^y] ?? '+' :: '.';
      print "\n" if ($^x == $.max);
         # print each row on own line
    }
    print "\n"; # blank line follows grid
    print "Turn $(++$.count), press enter to continue"
    print " or ctl-c to quit";
    <$*IN>;
    .calculate();
  } # end method display
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A separate style comment: wouldn't it be a bit cleaner to remove the .calculate(); line from method display and change the loop at the top so that it reads:

loop { $life.display(); $life.calculate(); }
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Then there's no nasty surprise when someone does:

  # somewhere far, far, away
  $life.display;
  `shell-script;clear`; # weird stuff on screen tty
  $life.display; # refresh terminal *only*
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later. I recognize that's personal preference, but Side Effects Are Scary.