Initial *mDnD* Essay HERE

**Introduction**

We need a simple way to divide up space, so that an entire globe may be easily generated, preferably mostly as the party of adventurers makes their way through it.

I propose a set of nested increasingly large triangles that ultimately reach the size of an entire planet, in the form of an icosahedron (same shape as a d20).

A macromemetic-like system is needed to generate the next blob of terrain as the party enters it. Crossing the boundary from one triangle to the next, we could ask whether one needs to know where the given triangle (whatever its size) is located in the larger one. Perhaps this is not the case.

In a given terrain, such as town, kind of town, desert, forest, hilliness, mountains, the weather, winter, where is the seashore and so on, the next tiny step in any direction is going to tend to be more of the same.

So our requirements for this system are that:

- it be scalable from person size to whole world size
- it be easy to dynamically generate the next grid as the party approaches it.

**The Icosahedron (d20) as Globe**

Quick overview: the Earth has a surface area of approximately 200 million square miles. Thus each face of an icosahedron (d20 solid shape) would contain 10 million square miles.

fig 1. icosahedron (20 faces) as approximate globe |

This means that the edge of each face would be some 5,000 miles.

We can endlessly tile a gigantic equilateral triangle thusly:

fig 2. triangular face tiled into four, then each of four into four, etc. |

In other words, the first "cutting" or "tiling" gives us four equilateral triangles inside the original one, and each edge is *half* the edge length of the original. This dividing by two property is intriguing. It makes things simple and clean if we just use multiples of two. In other words, if we just say that the largest edge is 4,096 miles, then we can go all the way down to one foot, which we call the "zeroth tiling level" (1).

To extend from the scale of the very small to the very large, i.e., the level at which characters might experience a town or dungeon up to planet size, we have tiling level and edge length:

**How to Generate the Next Bit of Terrain?**

fig 4.1. triangles that abut upon the party's triangle |

Every triangle is surrounded on three sides by three other triangles, as well as three triangles which only touch on the points. There must be continuity between triangles that abut one another. Or must there?

fig 4.2. What terrain transitions look like |

A terrain tile triangle is either solid, i.e., a continuation of the current terrain, be it grasslands, forest, town, dungeon, or whatever, or it's two-thirds one terrain and a third some new one, with the line of division going between the midpoints of two of its sides. When a party enters a new grid space, they will still have the same terrain, but they may or may not face a boundary ahead of them, as in figure 4.2.

fig. 4.3. terrain of smaller area determined by surrounding area |

**Terrain Intersections and Boundaries**

fig. 5.1a. two bordering terrain regions |

Now, if we have three regions intersecting we have two choices: 1. disallow certain terrains to border one another, e.g., no mountains next to sea shore, no forests next to deserts, and so on, or 2. have tiles that connect three different regions. This basically translates into things like needing a solid band of grassland that you have to cross to get from the ocean to the mountains and such. Figure 5.3. shows how two or more regions of terrain can meet. Note the red exes depict where more than two regions touch, and where we would need special tiles beyond the "tip bitten off" tiles from figure 5.2.

fig. 5.2a. Four sections of terrain and how they meet |

fig. 5.2b. Triangular Tile Dividing between three regions |

You might object that there has to be a tile that has a different region on each corner and a fourth type of tile in the center.

**K.I.S.S (Keep it Simple and Spiritual, Dummy)**

**Summary & Conclusions**

**Addendum**

## No comments:

## Post a Comment