void _connectRegions() {
    // Find all of the tiles that can connect two (or more) regions.
    var connectorRegions = <Vec, Set<int>>{};
    for (var pos in bounds.inflate(-1)) {
      // Can't already be part of a region.
      if (getTile(pos) != Tiles.wall) continue;

      var regions = new Set<int>();
      for (var dir in Direction.CARDINAL) {
        var region = _regions[pos + dir];
        if (region != null) regions.add(region);
      }

      if (regions.length < 2) continue;

      connectorRegions[pos] = regions;
    }