Re: Fractal geodesic networks
On Fri, 8 Dec 2000, Carol A Braddock wrote: So say you -could- estimate a fractal dimension for the internet. What would the number be good for? If it could be shown that a consistent estimate exists and it was calculated, it would probably affect the scaling properties of the Net - after all, what are fractal dimensions but numbers relating linear scale changes to changes in measures? Sampo Syreeni [EMAIL PROTECTED], aka decoy, student/math/Helsinki university
Re: Re: Re: Re: Fractal geodesic networks
At 3:57 PM -0800 12/8/00, Ray Dillinger wrote: 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. Argg. Anyone claiming that something "can't be fractal," as Choate apparently does in the section you quote, just doesn't understand the meaning of fractal. Or, in Choateworld, "Since all physical things have three spatial dimensions, there are no non-integer dimensions, and hence fractals cannot exist." Like Choatian physics, Choatian economics, Choatian law, and Choatian history, such crankish ideas are neither useful nor interesting. --Tim May -- (This .sig file has not been significantly changed since 1992. As the election debacle unfolds, it is time to prepare a new one. Stay tuned.)
Re: Re: Fractal geodesic networks
At 5:49 PM -0800 on 12/8/00, Bill Stewart wrote: At 02:47 PM 12/8/00 -0600, Jim Choate emetted: 'fractal geodesic network' is spin doctor bullshit. Well, buzzword bingo output anyway. :-). "Neological" is so much more... euphemisitic... And the Internet is most certainly NOT(!) geodesic with respect to packet paths. more like a geodesic dome filled with boiled spaghetti... Depends on what dimension you're measuring. For fun, I pick time. I leave a definition of fractal time to the more mathematically creative out there. Cheers, RAH -- - R. A. Hettinga mailto: [EMAIL PROTECTED] The Internet Bearer Underwriting Corporation http://www.ibuc.com/ 44 Farquhar Street, Boston, MA 02131 USA "... however it may deserve respect for its usefulness and antiquity, [predicting the end of the world] has not been found agreeable to experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire'
Re: Fractal geodesic networks
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" [EMAIL PROTECTED] To: [EMAIL PROTECTED] 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. Before a larger group can see the virtue of an idea, a smaller group must first understand it. "Stranger Suns" George Zebrowski The Armadillo Group ,::;::-. James Choate Austin, Tx /:'/ ``::/|/ [EMAIL PROTECTED] www.ssz.com.', `/( e\ 512-451-7087 -~~mm-'`-```-mm --'-
