# The Metrics of Space: Molecule Design

**January 15, 2013**

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# Introduction

Game spaces provide a context for the game's rules and systems, and a space for the game agents to perform mechanics. When we go about designing game spaces, sometimes thinking in pure spatial terms clouds what a designer needs to achieve with a certain game space.

For FPS games, sitting yourself down with your favorite prototyping tool kit and drawing corridors and rooms is a recipe for disaster. It is difficult to design interesting spatial puzzles when you are creating game spaces using the rules of reality. How many office blocks are fun to navigate?

Molecule design is a way of applying graphing theory for concepting and fine-tuning of various types of game spaces. This rational approach to design is a means to design spaces without thinking about the representational elements of space itself. This article still accepts the importance of planar maps; however, we need better tools to help us create these first.

This article will examine some useful tools gathered from the field of graphing theory that designers can use to conceptualize various game components. The latter half of this article will examine a real-world application of these tools. By doing so, we will examine how iterations of a level design benefited from this abstracted means of realizing space.

# The Basics of Graphing

Graphing theory is a broad and diverse field of mathematics; however, this article discusses graphs that *can *explain spatial relationships. Core to graphs that explain spatial relationships are nodes and edges (Figure 1). Nodes can represent game spaces / rooms, pickups, spawn points and AI pathing nodes. Edges define relationships between nodes.

**Figure 1 **

Figure 2 is a simple molecule consisting of several nodes, linked by edges. In this example, we have defined a set of tokens around the players spawn point. This is a literal depiction of space using a graphing approach. Nodes become linked by edges, and these define the shortest possible distance between the player and other node. The more powerful a token is, the longer the edge should become.

This approach works well for PvP games -- to create a game space with roughly similar distributions of pickups, to achieve game balance. Repeating and rotating a molecule leads to symmetrical distributions throughout the game space. Edges are abstract ways of defining relationships but not necessarily hallways or any other level geometry. To explain this further, we need to look at weighted and directed graphs.

**Figure 2 **

We can manipulate the physical appearance of our edges to help communicate different types of relationships between the nodes. In Figure 3, the edge between nodes A and C is thicker than the rest. If we are using graphing theory to create spaces, and the nodes represent particular game spaces, then the larger edge does not imply a bigger space between the two nodes, but rather a more direct route.

**Figure 3 **

Figure 4 takes our molecule from Figure 3 and uses weighted edges as a guideline to place out level geometry. In this example, heavy weighted edges create a path between nodes A and C that is direct and unimpeded. Alternatively, the thin edge connecting nodes A and B results in a meandering pathway that is complex in nature. This example shows that edges do not depict geometry, but rather the relationship between nodes.

**Figure 4 **

We can further increase the information that an edge communications by adding direction. Figure 5 is an example of a graph that has directed and weighted edges. Figure 5 uses directed and weighted edges to communicate two different ways to get between node A and node B. The thicker edge is more direct than the other. Linking nodes B and C is an indirect one-way gate. The thick edge linking nodes A and C is another one-way gate. The thickness of this edge shows a direct and unimpeded relationship between the nodes.

**Figure 5 **

Nodes and edges can represent nearly any feature of game level design. For example, we could use a system whereby the weight of the lines also tells us about the difficulty of getting between nodes. By using edges to depict vertical space, we could say that node C is the highest point of the map. Node C is then transitive in the sense that it can only be accessed from node B. The one-way direction between nodes B and C might be achieved by having a "jump pad" at node B, pointing towards node C, but not in the opposite direction. It is really at the discretion of the designer and their team to define a key for their particular molecule system.

To further explain the concept of using spatial molecules to create play spaces, let us consider one example molecule and how it should and should not be implemented. The molecule represented in Figure 6 is a simple spatial molecule that defines a linear level progression, suitable for single player type maps. Weighted edges have not been used in this example; however directed edges have been used to create interesting spatial puzzles.

**Figure 6 **

Figure 7 is an example of what not to do with a spatial molecule. The reason to use a molecule-based approach is to free your creative process from thinking in purely spatial terms, and instead think about creating interesting spatial relationships. Although the planar map in Figure 7 does follow the spatial relationships of the molecule, it is a boring, linear space.

There are also a number of other flaws that demonstrate why designing maps from a planar perspective is problematic. First, the linear, room-by-room layout of the map is a direct product of drawing maps out in planar space. When your imaginative space is two-dimensional, your maps will be two-dimensional also. As such, there are no interesting vertical spaces and, more importantly, the objective is not clearly visible from the beginning of the map.

**Figure 7 **

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