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 Fractal structures in human coordination

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ambiguousmartingale:
Hey all,

I have been thinking about instances of fractal patterns in human collective behavior and I'm hoping I can get some new ideas from you. Here are three examples of what I mean roughly, but you can interpret the question as you like:

1. Have various political structures ever occurred fractal to you? Most parliamentary democracies have similar structures on all levels of cooperation. There is a federal parliament, state parliaments, city councils and sometimes even district councils. Similarly for the judiciary and executive branches. This analogy is by no means perfect and maybe even a bit trivial since society needs to make decisions on every level and these are just the tools that a democracy uses. I would love to hear how you could make it more concrete.

2. City planning. I'm not from the US but there seem to be a lot of cities planned very rigorously in a block pattern. Zoom into Houston on Google Maps and you will know what I mean. This block pattern is pretty explicitly a fractal design if you think about large highways on a big scale, 4-lane streets on the next scale and smaller residential streets on the smallest scale. It is a quite effective (although not very aesthetic) way to plan a city with short car drives, so it's also not surprising that humans coordinate this way.
Even non-planned cities like Paris seem fractal to me. Not in a self-similar sense but in the sense of constant complexity while zooming (i.e. non-integer Hausdorff dimension).

3. If you look at the area around Ludhiana, India, you can see that cities of different sizes grew in a fractal pattern to fill the space of agricultural land. (Use the satellite images for this.) This would also be a sensible way to "plan" the use of space, but I believe this phenomenon might be entirely emergent and not top-down imposed.

I would be really interested in your ideas. They don't have to be visible on a map. It could be societal behavior or something within companies for example.

Linkback: https://fractalforums.org/index.php?topic=4245.0

hobold:
Your examples 1 and 2 are instances of an abstract tree structure. In example 1, the tree is used to facilitate efficient communication. Governments rely heavily on communication and coordination. In other words, they depend on the flow of information.

If there were N citizens in the nation, and they would all talk anybody to anybody, the total bandwidth required would be proportional to N*N. If instead the citizens were organized in some sort of tree, each individual would have, in the simplest case, only two lines of communication: upwards and downwards the hierarchy. Messages between any two individuals would travel up the tree until they reach an upward node which both individuals have in common. From that common node, the message can travel down the tree towards the other receiver.

Total communication bandwidth is then proportional to N*(depth of tree); and the depth of the tree is proportional to the logarithm of N (the tree's branching factor determines the specific base of the logarithm, but that's not important for considering what it is proportional to).

In other words, trees can reduce communication overhead from N*N to N*log(N), which is why they are being utilized.


In example 2, a very similar argument can be made about the efficiency of travel and transport, when you try to connect any house to any other house, but don't want to expend a lot of real estate for roads.

Biological trees in the forest have their shape because they want to transport nutrients from and to every leaf, and because they want to reach a large volume to collect air, and because they want to cover a large surface area to collect sunlight, and because they want to expend as little material and mass to reach all these goals.


Fractals are simply the most efficient shapes known in nature for some tasks performed by organisms.

ambiguousmartingale:
Ah yes, I really like your explanation! Most of the things I had in mind can be translated into some sort of hierarchy and hence a tree structure.

I would still love to hear about more examples, even if they're all related in principle.

youhn:
See for example https://roneglash.org/ > Current Research > African Fractals



ambiguousmartingale:
Good stuff, thanks!

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