Octogrid

The "octogrid" is a concept I've developed to address the disadvantages of using a square grid (square tiling) or hex map (hexagonal tiling) for strategic mapping. (Those disadvantages are explained in the Wikipedia article for "hex map"). In other words, I wanted a "map" that worked for the eight cardinal and intercardinal directions, allowing a "unit" on the map to have eight sides. Unfortunately, the disadvantages of this system start adding up.

Disadvantage #1 - Mathematically, representing the 45° directions with the same "length" as the 90° directions resulted a scaling factor of $\sqrt{2}$ (See here) - not simple. Essentially, for every $x$ length in N, S, E, or W, the equivalent length in NE, SE, NW, or SW would be $x\sqrt{2}$.

This chart shows whole number (integer) approximations of $x\sqrt{2}$
$x$

(N, S, E, W)
$x\sqrt{2}$
rounded
(NE, SE, NW, SW)
1 1
2 3
3 4
4 6
5 7
6 8
7 10
8 11
9 13
10 14

(The 4:6 ratio is highlighted as being the most optimal for our purposes: easy to remember and easy to manipulate mathematically).

The resulting "grid" below uses dots to show line segments that approximately fit the ratios above (also see table below).

An "octogrid"
octogrid.pngAn "octogrid cell"
octogrid_cell.png
Minimum ranges
(# of dots from center dot)
N, S, E, W NE, SE, NW, SW
Personal space 2 dots 3 dots
Melee/Movement* 4 dots 6 dots
*The "movement" minimum is debatable
Here is an example of an octogrid with some 8-sided units on it.
octogrid_example.png

Here, another disadvantage (#2) of an octogrid map becomes apparent: either units must be comparatively larger, or the cells comparatively smaller than normal square or hex maps. A unit takes up the equivalent of 14 cells.

Also evident in the example above is disadvantage #3 - A single 8-sided unit cannot be "surrounded" by eight other 8-sided units without overlap. A square gap is produced between units that are separated by an edge of the unit they are "surrounding" (see between the yellow and blue units surrounding the red unit, or between the red and magenta units surrounding the green unit). (Apparently, this is called truncated square tiling).

Though this all may seem to be an exercise in futility (especially after reading about regular tilings), I still find the octogrid to be an interesting concept that I'd like to playtest sometime.

The Next Step

See Square Grid enhanced with trigonometry

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