Voronoi crawls

Voronoi tessellations are everywhere, maybe even in your next adventure

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Last week we looked at supply and demand with Genotype: A Mendelian Genetics Game. This week we are looking at a geometric pattern that shows up seemingly everywhere!

It’s called the Voronoi pattern and might have some applications in game design!

Voronoi patterns

Bubbles and Jackfruit

Imagine blowing bubbles in milk or soapy water…

As each bubble forms, it tries to expand to fill the available space. They bump into each other. Where they meet, they press and form boundaries (i.e. partitions) that look like straight lines. Viewed in a flat, 2D plane, they look like irregular polygons vs. round bubbles.

This is called a Voronoi pattern, and it shows up throughout nature!

Just a few examples include:

• Giraffe spots

• Dragonfly wings

• Dinosaur and reptile skin

• The pattern on jackfruit

• The cracks formed in dried mud

Dragonfly, Leaf, and Giraffe

For a more technical definition:

A Voronoi diagram is a partition of a plane into regions close to each of a given set of objects… In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other.

Here’s an example of a simplified pattern generated with Affinity Photo:

A simple Voronoi pattern example

I don’t know about you, but when I see that… it instantly looks like a game map.

Let’s think about how they could be used in tabletop games!

Voronoi maps

Voronoi effect applied to an actual map with river

Voronoi patterns develop anywhere there are starting points that expand against each other. This might apply to expanding city states and their borders, and could help build a realistic world map.

If you look at the map for the original Civilization (Tresham, 1980) you can see what appears to be a Voronoi pattern on the board!

At a more tactical level, Voronoi patterns could be used to model how city districts develop and expand, pushing against each other. A large city map could have an underlying Voronoi pattern that is used to divide it up.

I could also see this pattern be used to create organic space maps showing controlled sectors in an area control game.

Voronoi crawls

Voronoi city

We could also use Voronoi patterns like a hex map but with irregular shapes.

Perhaps smaller cells could represent tougher terrain. In this way, difficult terrain would require crossing many individual cells, while larger cells could be easily traversed. Adding some color coding or map details would aid in visualization.

The other way to look at the Voronoi pattern is to have players move along the edges and vertices. In this way, it becomes a point crawl. Overlay the map on a city and you have points of interest that are spaced in a way that feels organic and natural.

Voronoi dungeon

Still another way would be to secretly overlay a Voronoi pattern over your dungeon map to determine places of connected power or the locations of artifacts. Place something special at the vertices of each cell.

Generating Voronoi patterns

Affinity Photo 2

Want to try making some patterns? The easiest way is to use the Voronoi Generator by Frederik Brasz hosted at Github.

Alternatively, if you have Affinity Photo:

1. Open a new image and add a layer that has some color. It can be a solid color or any image.

2. Under the Layer menu, select New Live Filter Layer, Colors, and Voronoi

3. Set the Cell Size and Line Width using the Live Voronoi dialog box

I’ve had some interesting results using actual maps converted to Voronoi patterns.

Learn more about Voronoi patterns

Here are a few videos that I found immensely useful while doing research for this post:

• Why this pattern shows up everywhere in nature by Dr. Trefor Bazett

• Voronoi Partitions by Khan Academy Labs

• Practical Procedural Generation for Everyone by Kate Compton

• Generating World Maps: Fun with Voronoi Graphs by Joris Dormans

• Voronoi Diagrams and the City Crawl by d4 Caltrops.

Check them out!

Conclusion

Some things to think about:

• Natural and organic feelings: Voronoi patterns are generated throughout nature. We see them all the time without giving them much thought, but instantly create an organic feeling when used.

• Multiple methods of use: The patterns can be used both as area borders (similar to a hex map) or as connected points (similar to a point crawl).

• Board games and roleplaying games: The use of Voronoi patterns isn’t limited to a single game type. They can be employed just as easily in TTRPGs as in board games, and at a large scale (e.g. space map) or tactical scale (e.g. city districts).

I’m certainly not the first person to think of this, as it’s come up many times before on various forums and blogs. That’s probably a testament to how this is a really fascinating concept waiting to be used!

As you go about your week, keep an eye out for them. You’ll be surprised how many Voronoi patterns you see!

— E.P. 💀

P.S. Thank you so much to everyone who stopped by to say hello at the Exeunt Press booth over the weekend at Save Against Fear! If you just joined, welcome!

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