Fractal geodesic networks

[Jim Choate]

On Sat, 9 Dec 2000, Carol A Braddock wrote:

> Could you explain 'saturated'?

Sure, I meant it as the actual level of capacity/usage approached the
maximal capacity/usage. The 'channel' is saturated, it reaches a point
where it can't grow. This is a small grain observation about the
capacity/cost ratio for individual links.

Another way the 'channel' might get saturated is with respect to 'common'
services such as DNS. As the consumer layer grows the load increases and
can become problematic (ie DNS time outs become very common). So, one
could compare the percentage of requests at each layer of the network and
then compare their time series.

> I am not sure this isn't related to a more simple surface - to - volume type
> number, but I only have three or so hands to wave at the difference.

In a way that's what a fractal dimension is. In the case of say a Koch
snowflake we're talking of a function part way between a line and a plane.
In the context of the Internet we're talking about the complexity moving
from 2d to 3d, we've already moved from 1d (direct connect ala BBS's) to
2d. With the growth of space based Internet assets you'll see this number
approach 3.

> How about the average number of links to get to a destination vs the total
> network size? Plot that the way you would Minkowski sausage volume vs
> diameter to get fractal dimension. I saw an article pointing out that the
> average number of links was not growing as fast as the network size would
> predict, and blaming the expert and portal type sites for the difference.
> That is a cypherpunkish type observation, it is a number indicating
> intelligient intervention in the organization of the network.

The network can't exist without 'intelligent intervention", at least I've
never heard of a bridge (for example) self-assembling. It could happen but
I suspect the odds are pretty slim.

With respect to the growth of links, it doesn't surprise me that it's
saturating faster than expected. After all 80% of the planets population
hasn't ever made a telephone call (or that's the urban legend anyway).

I saw an article somewhere the other day (no clue where) stating that the
youngest kids (say 8 to 12) are not using the net as much as predicted
either.

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