Fractal geodesic networks

[Ray Dillinger]

On Fri, 8 Dec 2000, Jim Choate wrote:

>
>Fractal simply means non-integer dimension.
>

Yeah, that's where it started.  But I'm using it more in the 
sense of meaning the properties that fractal structures have; 
self-similarity across scales, for one, as in the big nodes 
work the same way as the little nodes and larger patterns are 
emergent from the interaction of simple rules.  

>Computer networks, at least copper or fiber based, can't be fractal. 

Physically, true.  There is a minimum size feature, in the sense 
that some computing hardware and memory is required of every node.  
In terms of the flow of information, I'm not as sure.

>The
>traffic patterns can have fractal patterns (e.g. Foucault Dust
>periodicity) but that isn't the same thing at all.

The traffic patterns *ARE* the network.  If the network has 
fractal traffic patterns, the network is fractal.

>'fractal geodesic network' is spin doctor bullshit.

Yup.  Mutually exclusive sets of properties. 

>And the Internet is most certainly NOT(!) geodesic with respect to packet
>paths.

At the lower levels in user-land and very small ISP's, it seems to be 
hierarchical (eg, I have an "uplink" who connects me to the rest of 
the Internet, and people who connect through my system treat me as 
their uplink...).  But at major nodes like big ISP's and server farms, 
it's more like a distributed or peer-to-peer network (eg, my uplink 
has several dozen peers, each with independent connections to other 
points on the internet, and they each maintain independent connections 
to several different "backbone sites", and the backbone sites are 
connected both via dedicated links peer-to-peer *and* via all the 
ISP's that have connections to more than one of the backbone sites
....)

Anyway, once you get up out of hierarchy levels, I think the Internet 
starts looking a lot more fractal -- self-similarity across scales  
in traffic flow, emergent bandwidth and load patterns, etc. 

				Bear