perhaps the scale larger than the highest layer nodes is no longer recognisable as being part of the fractal. Likewise the nodes at each ppp have some organization as to how they handle data internaly. The shape of a shoreline is often used to illustrate fractal self similarity, but you quickly reach a point where it is hard to call it a shoreline anymore, it becomes grains of sand, pebbles, or boulders. So say you -could- estimate a fractal dimension for the internet. What would the number be good for? ----- Original Message ----- From: "Jim Choate" <ravage@einstein.ssz.com> To: <cypherpunks@einstein.ssz.com> Sent: Friday, December 08, 2000 8:33 PM Subject: Re: Fractal geodesic networks
On Fri, 8 Dec 2000, Bill Stewart wrote:
....more like a geodesic dome filled with boiled spaghetti...
If you think about it this is actually one way to view the Internet. Consider the highest layer nodes. Place them equidistant on a sphere and interconnect them with links. Whether they are geodesic or not isn't relevant (unless you'r using a shortest-path algorithm, which we don't).
Anyway. The next thing you do is connect each single user machine to it's appropriate node. Cluster them in a similar manner. You get a globe with little partial globe 'bumps' centered on each 'parent' node. Then from each of these parent nodes, using a different length path for distinguishing, list the multi-user nodes. Then interconnect these nodes. Repeat add infinitum (well you can't realy since the lowest level link, a single ppp link for example can't be broken down into smaller physical links, the net is pseudo-fractal at best at this scale).
You can also do them as 'sea urchins'.
The reality is that the Internet, as big as it is, is simply too small by several orders of magnitude to be modelled by anything approaching a true fractal. However, by looking at it from the perspective of emergent behaviour from simple rules we can probably gain more understanding and control over its use. Something akin to cellular automatons with simple neighborhood rules interconnected by 'small network' models.
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