Vincenzo De Florio‘s been tweeting lately about his research. And good thing, because this week’s been too busy for me between classes, work, and research of my own to hunt down a paper like his to write about. I showed interest in his work, he linked me to a copy of the article, and now we’re here.

De Florio et al introduce a novel sort of Complex System, called a Fractal Social Organization. Typically, when I talk about fractals it’ll be related to Chaos Theory, but today it pertains to the complex patterns that emerge from a simple set of rules.

A fractal is a geometric figure made up of an infinite number of similar copies of itself. The Sierpinski Triangle, depicted above, is a well-known example.

Constructing these figures is a recursive process. First, draw a large triangle. Second, remove the middle of the triangle, producing three smaller triangles. Third, remove the middle of each of those triangles, producing more triangles. Repeatedly remove bits of every triangle produced until unable to see change.

Fractals are important in Chaos Theory because they capture the notion of being hard to predict. For example, if I throw a dart at the Sierpinski Triangle, will it land on a white or a black pixel? This is difficult to say for certain because of the “holes” in the figure, even if the properties of the shape are perfectly known.

De Florio et al, however, have found another use for these geometric patterns, taking advantage of their natural clusters and hierarchies.

In the proposed system, a socio-technical society—that is, a society of humans, machines, and the channels they communicate through—is recursive. Just as the Sierpinski Triangle is a triangle made up of smaller triangles, these societies are made up of smaller societies.

They give an example using “smarthouse” organizations. These are made up of regions of mutual assistance communities, in turn made up of neighborhoods, made up of individual houses, made up of:

  • elderly residents,
  • general practitioners,
  • nurses, and
  • a network of tracking devices and alarms.

This could be taken further into lower or higher levels, but I feel that would be unnecessary.

De Florio et al’s system, in contrast to social networks, doesn’t track people and their interconnections. Instead, it tracks the roles played by people, devices, etc. and the actions they perform as part of these roles. This allows the same person or machine to fulfill multiple roles in the same society, or even span one society to next.

In their example, an elderly patient falls in her smarthouse. This triggers an alarm, which carries out its role by sounding. The nurse, general practitioner, and neighbor are expected to respond by carrying out their roles in turn, whatever these may be. However, there isn’t a “neighbor” in the scope of just one smarthouse—someone will have to run next door and fetch one!

The authors account for this “running next door” in the definition of their system. When a role is requested but not fulfilled, an exception process locates someone to carry it out from another society, looking first, for example, just outside, then throughout the neighborhood, within the region, and so on until it finds what it needs.

The power of this system, then, comes in two parts. First, its flexibility allows it to be adapted for various research problems. For example, a small change in how the exception process searches leads to drastic changes in the behavior of the system as a whole. And second, it has a peculiar ability, taken from its fractal-like nature, “to model collective behavior [across] complexity and scale.” Because each layer from organizations down to patients has a similar set of roles, properties at one level are closely related to those at another.

De Florio et al’s work is far from done. Their paper is interspersed with conjectures without a proof to be found. However, it is the novelty and promise of Fractal Social Organizations that makes this paper noteworthy for me. ∎

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