For readers new to Mad Brew Labs, I have been working on a rank-based d20 system called Echelon. During Echelon’s development, I took another look at the use of square grids during tactical play in Dungeons & Dragons. When making decisions when designing game mechanics, I try to maximize realism without sacrificing too much efficiency. If you could graph realism and efficiency of a mechanic on a chart, the point where the two cross each other is the magic intersection called fun, at least from my perspective.

I like detailed combat systems with a plethora of options, but I also do not want play to grind to a halt while players and gamemasters try to do big calculations. It would seem that detailed combat and ease of use are sometimes mutually exclusive. Perhaps without any other constraints they might be. If the rules can be executed swiftly after a modicum of familiarity, then I am happy. This requirement also tends to shape the target audience of my game.

So the question I posed to myself was, “Are square grids accurate enough for my tastes?” So I decided to look at other methods of creating tiled maps, but only ones that used regular tessellations. Then I measured the pros and cons of each method and finally decided on supporting two methods which I reveal at the end of this article.

**Tessellations**

A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps (Wikipedia). This means the a pattern of two dimensional shapes that repeat without leaving space between each other or intersect each other. The works of M.C. Escher often dealt with tessellating shapes and patterns.

A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. These symmetric tiles are the most appropriate patterns for use in miniature combat. There were four elements that I used when testing mapping styles: miniature base compatibility, spell effect templates, flanking, and accurate movement

**Triangles**

Looking at tessellated triangles reminds me of creating custom maps for Unreal Tournament. Many video games use tessellations to render terrain and objects. I found several issues with attempting to use equilateral triangles for tactical combat maps.

The first problem is there is a *facing* issue in that the tiled triangles alternate from point up to point down. There was also a question of how one moved from space to space. Can one only move to a triangle that shares a side or merely a vertex.

I also found that there is not a good size to use to take advantage of current miniature scales. A triangle large enough to fit a 1 inch inscribed circle leaves too much wasted space at the corners of the triangle. When using larger sized minis, this problem intensified.

**Squares**

The default dungeon tile since I can remember. I do not think Advanced Dungeons & Dragons 2^{nd} Edition officially supported squared tiles, but I do remember extensively using grid paper to draw practically all my dungeons. From 3^{rd} Edition on, the square has been the de facto method of presenting dungeons.

Squares obviously work well with the standard 1″ miniature base and its larger bases since D&D miniatures were designed for use with square grids. Flanking is also cut and dry, as the 3.5 rules have clearly covered the topic when using a square grid. Spell effects can be somewhat chunky in nature I sometimes think that targets in squares that would be partially affected in the radius of a spell should get something.

Squares allow movement in eight directions as well as making the construction of dungeons simple and clean. In 3.5 D&D a character moving diagonal would count every other diagonal square as two squares to proximate the true distance travelled (remember the Pythagorean Theorem?). I never did the math before, but it is a surprisingly close approximation. Movement of 5 diagonal 1″ squares actually equals 7.0710 squares of horizontal or vertical movement (which would have been counted as 7 squares under the 3.5 method).

The 4^{th} Edition of D&D eliminates the need to count squares twice in the name of simplicity, but I do not think it is that difficult to count a square twice in the name of accuracy.

**Hexes**

Hex maps have been a mainstay of many wargames as well as the default grid for overland maps from the older editions of Dungeons & Dragons. I can still remember getting the hex transparencies in the old box sets from 1^{st} and 2^{nd} edition.

The primary strength of hex tessellations is that the distance from the center of a hex to any adjacent hex is the same, so we do not encounter any issues where you need to counter every other move twice. A hex map does limit movement to only six axes, but it does represent spell template radii as there are not any partially effected spaces.

The primary weaknesses of hex mapping are issues with compatibility of mini bases of the large and gargantuan sizes and by extension flanking. These sizes look odd when demarked on a hex map and resemble triangles with their tips truncated (see the d20 Hypertext SRD for more).

**Gridless**

Many skirmish games simply use rulers or measuring tape to determine distance. This of course provides the most accuracy, but also allows for more disputes (“my base was barely touching the area of effect!”).

It is fully compatible with any scale of miniature base, spell templates are accurate. Though it produces more questions, such as how much of a base must be within the template to be affected. Movement is not confined to a grid and is very accurate.

The biggest problem I see with abstaining from grids is determining flanking positions. My solution is if you can draw a line through the center of the target mini’s base and the line touches any part of the bases of threatening minis on opposite sides of the target, then that target is flanked. Of course, it could be a hassle visually checking this rule, but a laser pointer could be your best friend.

**Conclusion**

Obviously triangles are not conducive to tactical miniature combat. For the Echelon Gaming System I am going to stick with 1″ squares as the preferred method of mapping. Squares provide the most flexibility in movement, are the easiest to use, and are fairly accurate. Not to mention most roleplayers are familiar with it.

I also plan on providing rules for going gridless with full miniature terrain. I think I will call it the Hardcore method as it requires the most work but, in my opinion, provides the best accuracy and immersion. I love the freedom is gives players to move around well constructed terrain.

I think that the hex may also find a home with the Dead Wastes campaign setting as the preferred method of identifying areas on overland maps. This way when I am describing a location, I can refer to its coordinates on the hex map for easy referencing.

WELCOME BACK!!!

jonathan’s last blog post..New 4E Ritual FeatsThanks! Yeah it has been too long since my last post, 2 weeks! Been busy tearing down an engine I want to rebuild this summer for one of my cars.

This is a good summary of available options. I’ve thought about going without a grid several times. Like you said, there are some issues that crop up that put that option as experimental only. Maybe when I start my Classic Traveller game in the next month or so, I’ll try out not using a grid.

Bonemaster’s last blog post..My Failed Open Call Attempt@Bonemaster: Yeah, I like the whole wargaming approach of no grid and just measuring, but it is not for feint of heart.