Squares and Hexes

Squares and Hexes

By Brian Lancaster (Jan. 2021, updated Dec. 2023)

Website: www.laughingcoyote.net


You'll find tons of articles regarding game design about how hexagons are better than squares, as they allow a more realistic representation of space. In real life there are no spaces, unless you are playing Realpolitik with nations like Kissinger on a Risk board (or Axis and Allies, which is way better than Risk). In real life, space is uncountable.

But in games and simulations, you have to count it -- no matter how infinitesimal, representations are always rounded off. The simplest example is in chess, where the queen can move diagonally across the board, or non-diagonally, but clearly moving diagonally across the board the same number of spaces is, in real space, much farther. Therefore (the dirty hexagonians argue), squares are inferior to hexes.

I am here to argue against hexagons, you blind fools, if this single minor tweak is implemented on the square system: diagonal movement costs 1.5 of an adjacent move. The real square root of 2 is 1.414213562373095, but rounding it to 1.5 does the trick.

You can pull this off in different ways, either adjusting movement speed in real time or using action points in turn-based gameplay. It works better than hexes, and I'll explain why, starting with turn-based games like Fallout 1 and 2.

 

Fallout 1 and 2 used hexagons. Amazing games, but when you moved directly north or south, the character zig-zagged in a really annoying way. You could move west/east in a straight and easy line, but not north/south. Four cardinal directions make for simpler strategy than hexagons, and it represents how we think in real life better.

Now, applying this to a real-time game (like the upcoming Warlordocracy, shameless plug), instead of action points, you use pixel movement speed. Make diagonal movement cost 1.5 times the time as an adjacent move, just slow down the pixel progression. It's still not perfect, but it looks better than hexagon zig-zagging like in Fallout 1 and 2.

The problem with diagonal movement has been a long-term issue in gaming. In N64 Golden Eye and Perfect Dark, moving both forward and sidestepping at the same time while turning your camera to a 45 degree angle makes you move faster. This is because engines and math functions in general round things off in a 3D space. My old project, Brigand, was 3D and it still it had this problem. My new one is 2D and tile-based.

Warlordocracy: https://store.steampowered.com/app/1748160/Warlordocracy/