Fractal Game Design

Ever since I discovered (i.e. “learned about from someone else”, I didn’t invent them or anything) fractals I’ve been mildly fascinated by them.

This is not an uncommon thing.

Animated Fractal Mountain
Animated Fractal Mountain, from Wikimedia Commons

A fractal can be defined, in part (I’m not going to go into the full mathematical definition), as a “self-similar pattern”, meaning they are “the same from near as from far”.

For instance, waves in open water tend to be quite fractal. Have you ever flown in a seaplane and looked out the window, only to find that the surface of the water looks much the same from a couple thousand feet in the air as it does when you’re floating on the water’s surface?

Just as much in the real world can be described as being fractal, much of a gaming world can be described using fractal methods. It is not necessary to have entirely different processes for working at different levels of game design.

I’ll describe below a few places I find this to be so.

Campaign and Scenario Design

In my Campaign and Scenario Design series I describe a method of developing game and setting elements at the level of detail needed for the current purpose, without the developer having to delve into either too high or too low a level of detail. The same techniques work regardless of the level of detail, or scope, of the setting and scenario elements being defined. If you need something broader, you can easily move up a level, and if you need more detail you can drill down.

The Node-Based Megadungeon I designed last fall did exactly this. I started at a high level, describing the regions of the megadungeon at a high level and their relationships. I then drilled down and did the same exercise with each of the regions in turn, identifying the areas and creatures of interest in each region, and how they related to each other — mostly within the region, but at least some did interact between regions. In many cases, such as the Dwarven Safehold and the Clockwork Hell, these areas could be drilled down further. In others, such as the Goblin Warren and the Fungoid Cavern, areas in the regions are simple enough that they don’t really need further design this way.

I just realized I overlooked a very useful graph indeed: a graph showing how the megadungeon relates to other locations outside the megadungeon. In some of the regional descriptions I include hooks that could lead into or out of the megadungeon but didn’t provide the actual high-level notes that would likely come out of that.

So, by these techniques presented, it is about as easy to work at the setting level as it is at the dungeon level, and vice-versa, depending how you view such things. I think abstractly, so I like working at the setting and campaign levels, working out the major elements… but because the same techniques work at the more detailed level it is not so difficult for me to drill down as needed. Other people are more detailed-oriented and would be more comfortable at the dungeon level, but again, because the techniques work the same they can… drill up? [lame] to work at the higher levels.

Quite fractal, I think. Same techniques gets you high-level abstract development and low-level detailed development, and you can expand or contract your development to suit your need of the moment.

And like most fractals, if you try to show all the detail at once, it looks very, very fuzzy.

Demesne-Level Play

A few days ago I wrote about playing at the demesne level, ruling over huuuge tracts of land (but the small ones are nice, too).

This is something else that can be done fractally, if you look at it right. The same game mechanisms can be applied from the manor level up to the empire level, with adjustments made between them.

Consider, at the manor level you might measure land in square miles. A ‘manor’ has, for reasons that will become clear shortly, not quite two square miles allocated to it. Using medieval farming technology and techniques you might be able to support a couple hundred people this much arable land, and for the sake of convenience let’s say this is more often one hundred people in practice, what with there likely being a mix of arable and semi-arable and waste land. How convenient. There will be rules for managing a manor, and this can be done pretty much be one person, perhaps with some specific staff to help out.

At the next level up (for the sake of simplicity, because feudalism is hard — it’s a complex mess) let’s say that a barony might of some number of manors, generally up to about sixteen manors (give or take) and a total very close to 31.18 square miles (I can hear some of you go ah ha! at this number). The baron will be able to manage the barony using much the same rules as the manor lord does. He may need to have different staff arrangement and infrastructure, including depending on his manorial lords to do their part, but as far as game resolution is concerned he uses the same rules.

The next level up might be a county, which consists of, yes, about or up to 16 baronies and measure perhaps 500 square miles (for reference, perhaps 25,000 people could be expected to live here). Again, the same rules apply because the pieces the count is responsible for are larger.

Continue the process, through duchy (up to about 16 counties, 8,000 square miles) and kingdom (up to about 16 duchies and 128,000 square miles — a little more than 220 miles on a side, if fully populated; to compare, England is about 50,000 square miles, while England, Scotland, Wales, and Northern Ireland come to about 93,000 square miles), and into empire (up to about 16 kingdoms, nominally, and about 2,048,000 square miles — a little more than half the size of Canada, and about 80% the size of the Roman Empire at its height, about 2,500,000 square miles).

Wow. Serendipitous fluke, maybe.

Anyway, while the exact mechanisms of governance and the infrastructure needed to support them vary, the scope at each level and the mechanics can be very similar at each level of demesne play. The emperor makes decisions about kingdoms the way a king makes decisions about duchies, the way a duke makes decisions about counties, the way a count makes decisions about baronies, and the way barons make decisions about manorial lords (and finally, the way manorial lords make decisions about farming families).

It is possible for a ruler to manage an incredibly large area as long as he has good support and infrastructure, including a strong ability and means to delegate. The same sorts of problems can apply at many levels, they differ primarily in scope. A manorial lord might have to deal with a problem on a single farm, the king might have to deal with a problem with a single duchy. Or, feudalism being what it was, several… but let’s keep the model simple for play purposes.

Notes on Demesne Sizes

I chose the geographic sizes because they should work pretty well for play purposes. Many people have adopted the six-mile hex for hex crawling, which has an area of about 31.18 square miles. You can subdivide each hex into sixteen smaller hexes (almost; three of them end up split into six halves, but you can still tessellate if shift things a little) to get the ‘manorial hexes’, and conversely combine them to get the ‘county hexes’.

You can see how I picture the hexes fitting together for the 16:1 scaling in Richard’s Hex Crawl Worksheet at the Save Vs. Dragon download page. The split hexes can be resolved, for my purposes, by either ignoring them, or treating the ‘north edges’ hexes to be considered complete (and going outside this parent hex) and the ‘south edges’ hexes being absent (and being removed from this parent hex).

A bit of research via Wikipedia suggests that the various demesne sizes that evolved from this aren’t even terribly unrealistic, if you want to stick to managing things with hexes. I’m rather pleased by that.

Notes on Demesne-Management Rules

As I recall, the rules from Book of the River Nations: Complete Player’s Reference for Kingdom Building have you apply modifiers to your governance checks based on the number of hexes you control (unless that was An Echo, Resounding: A Sourcebook for Lordship and War; honestly I’m reading these things fast enough and synthesizing them in my mind that they are very much blurring together). As much as I would probably continue to use hexes for movement and exploration at the personal level, I think for managing governance I would depend more on how many direct vassals there are.

A lord rules over farmers, and might have modifiers based on how many families of farmers are involved. A baron rules over lords (and might rule over farm families — but more likely delegates to a steward or headman or the like), a count rules over barons, and so on. If at any time a liege has too many vassals to manage well, he might be wise to add a layer of management below to handle part of the load. This may cost him some ability to directly control things, and some income, but will simplify his life quite a bit.

Help, help, I’m being digressed!

Closing Comments

It is not always necessary to have different procedures for handling game elements at different levels. If the right abstractions are used, the same or similar methods and techniques can be applied at multiple levels of design and development.

In the case of setting and scenario design, entities are defined in much the same way, regardless of scope, and will generally have similar sorts of relationships between them. It may seem odd to say that a particular nation hates another, as a person hates another person, but understanding that this describes the general attitude rather than the attitude of specific people or groups within the nation can make it palatable — and introduce factional behavior as you drill down into the game entity (nation, in this case).

When it comes to demense-level play, much the same rules for resolving situations and actions can be applied at multiple levels. The in-world infrastructure needed to support them differs, the in-world effect of an action may have vastly different scope, but the rules and mechanics can be very, very similar indeed.


  1. When I started reading this I thought of the hierarchy of nobility as an example of this self-similar structure, and lo and behold you then went on to discuss it!

    You may like to look into the early history of petitioning, including its existence in the British Bill of Rights. Essentially it’s a way for the “dirt farmers” to appeal to the monarch for aid against oppressive nobles (Magna Carta did something similar earlier but was intended to benefit lesser nobles rather than the general populace). It’s an extreme measure for the monarch to step in and overrule a lesser noble’s authority, but a very effective sledgehammer for dealing with corruption. It might be an interesting subject to deal with in-game.

    • It’s not only fractal, but it’s a complex fractal. What I described here is a very, very simplified and simplistic view of feudalism.

      Having a mechanism for jumping the queue is probably actually pretty easily implemented. As the ruler, a realm event indicating corruption or injustice could mean (explicitly or implicitly) such a petition. As the one about to get the kinghammer, it could be caused either by malicious activity on the lord’s part (accumulating too much people-are-angry points), or by botching the handling of a particular problem (whereupon the petitioners escalate the problem looking for help).

      • David Lamb

        One thing that complicates the feudal “self-similar” structure is having overlapping hierarchies for the Church(es) and (in some campaigns) other power structures like mages. That’s one way in which oppression or malfeasance by one hierarchy might be opposed or reported by another. So the local lord is robbing his peasants, and a local priest raises a complaint at a higher level. Or perhaps intervenes directly if the lord is of the same church.

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  3. To add further to the digression inherent in the system:
    You mentioned a count as a noble rank; in the British system there actually isn’t a rank of Count, but the term “Earl” is used instead (from Scandinavian “Jarl”). There is a rank of Viscount, however. Oh, and if this doesn’t sound weird enough to you yet, the Earl’s wife? A Countess!

    I wrote an article about royalty and nobility some time back. I posted it up on google+ as well in case anybody had a use for it.

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