Something is fractal if it is similar at different levels of scale. An example of a non-fractal system might be the transitions we see in a game a organization between 20 people and 200 people. 20 people interact, self-organize and behave in one set of ways. 200 people have a completely and unfamiliar set of behaviour dynamics. Suddenly totally new things emerge: formal processes. In fact, if you compare a 20 person company to a 200 person company, they will look extraordinarily different.
By contrast, if you compare a school of 20 fish with a school of 2000 fish, they will look extraordinarily the same (other than sheer numbers).
The reason why this is the case is that the large scale system is composed of smaller scale systems each of which interacts with the others using the same basic mechanisms. A school of 2000 fish is like a meshwork of 200 schools of 20 fish (with every fish being part of more than one minischool).
Also importantly, the assemblies of smaller things are organized similarly into bigger things as they themselves organize the smaller things. So, like 20 schools of 20 fish becomes one unit that participates in a bigger school of 20, which again participates in something bigger.
This creating systems that are complex, in the good way, and thus potentially more resilient, flexible or resourceful than systems put together by more simplistic multiplication. Or, going in the other direction, it creates stuff that has rich depth to it. You look deeper and deeper, with greater and greater magnification, and there keeps being more variety to see. Worlds within worlds. As compared with stuff that's just the same all the way through.
Fractals have a fine structure at arbitrarily small scales.
An alternative formulation, coined by Arthur Koestler is "holon"
By contrast, if you compare a school of 20 fish with a school of 2000 fish, they will look extraordinarily the same (other than sheer numbers).
The reason why this is the case is that the large scale system is composed of smaller scale systems each of which interacts with the others using the same basic mechanisms. A school of 2000 fish is like a meshwork of 200 schools of 20 fish (with every fish being part of more than one minischool).
Also importantly, the assemblies of smaller things are organized similarly into bigger things as they themselves organize the smaller things. So, like 20 schools of 20 fish becomes one unit that participates in a bigger school of 20, which again participates in something bigger.
This creating systems that are complex, in the good way, and thus potentially more resilient, flexible or resourceful than systems put together by more simplistic multiplication. Or, going in the other direction, it creates stuff that has rich depth to it. You look deeper and deeper, with greater and greater magnification, and there keeps being more variety to see. Worlds within worlds. As compared with stuff that's just the same all the way through.
Fractals have a fine structure at arbitrarily small scales.
An alternative formulation, coined by Arthur Koestler is "holon"
http://www.worldtrans.org/essay/holarchies.html
http://www.worldtrans.org/essay/holonbook.html
See also this article on the the linkage between holons and emergence.
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