[Announcing a new simpler evolving network] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Announcing a new simpler evolving network
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Posted by: Tony Smith
Prior to this, NKS-style studies of evolving networks have seemed generally unsatisfying, even as, for other reasons, evolving networks became an increasingly popular choice as the most likely underlying model for our world.
Over the last three months I have finally had a chance to tackle this question head on and discovered a very simple generative rule which produces some spectacularly suggestive outcomes which I have started to present on a dedicated website.
Beyond exploring evolution of simple graphs, my other design goal was a generative rule which would solve locally the global synchronisation problem which prevents CAs and other simple programs being taken too seriously as models of our world.
My discovery, which I have named Tick Tock, meets both those goals and is the unique simplest system which does so. Being as simple as possible, it is unsurprising that it is strictly Class 2, but it does point the way to simple enough extensions with, say, coloured links and corresponding rule dependencies, which can be expected to exhibit the full range of behaviour that we see emerge from other simple rules.
Before clicking the link below, you should be aware that the website makes use of a mix of technologies which may test your browser in places, though each individual technology used has significant support. (The attached file is a graphical representation of the Tick Tock rule for those cursed with a browser which understands object tags but not SVG.)
Also please be aware that I am continuing to add to the site, but I suspect there is already enough there that it is time others had a chance to offer some feedback, right here for preference at this stage.
The Tick Tock website!
Have fun!
Posted by: Bram Boroson
That's nifty! You seem to be a pioneer here. I was lamenting the dearth of network physics simulations.
At first I thought, "Don't those rules destroy more edges each time step than they create?" but then visualizing a tetrahedron helped--a triangle's other edges are already destroyed by other double-triangles.
The interactive 3-d was also helpful!
The 2-d projections reminded me of Julia set fractals and also the "Gplot" graph on page 143 of Hofstadter's Godel, Escher, Bach. Part of that may have been the sparse dotted nature of the projection.
Though this is a pretty basic model, you've taken the plunge!
Posted by: Tony Smith
Last night was the monthly get together of a small but very persistent group of now mostly aging mostly men where I have a regular sparing partner on amateur cosmology who I had prealterted about the Tick Tock website so as to at least have one person to talk to about it in this not small city.
One sticking problem for those thrown in the deep end with Tick Tock is our chronic communal unfamiliarity with the likes of tetrahedral geometry, let alone simple graphs. At least with regard to the packing problems of tetrahedral geometry, my friend had an unexpected advantage. As a youngster, his father had been head of the local manufacturer of Jubbly orange drink with its unique tetrahedral packaging and my friend had a vacation job packing them. (For those who are too young, the Jubbly pack can be seen amongst a few of somebody else's Faded Memories.)
I've been playing with related geometrical examples since school days and have a bad habit of forgetting how difficult it can be for most people to think outside the square/cube, but this isn't the place to go into that story in any more detail, although I should at least add a page on visualisation issues to the Tick Tock site in due course.
On that subject, I did add a page on Deterministic Breaking of Symmetry to the Tick Tock site a few days after the original announcement here, but before the run generating comprehensive t+7 structural data for a 6-simplex finally finished after tying up my old G4 for ten days. I now need to take a break to reflect (and get some real work done) before I push any deeper with the research program, although I may still add the odd commentary page whenever my mind so dictates.
After an evening of hand waving over dinner, my friend now feels a bit more comfortable about trying to get his head around Tick Tock, but if that's what it is going to take with every potentially interested individual, I might need to explore some other ways of communicating.
Posted by: Tony Smith
This is in response to Mike's questions prompted by my response to his announcement in News & Announcements:1. Are you simply adding more nodes to the graph or are you actually increasing the relative sizes of nodes from one step to the next? Can you show where this is addressed... in simple simple terms... in your explanations?
Nodes, by definition do not have size. The Tick Tock rule creates a new generation of nodes (and edges) based on the local state of nodes and edges at the previous tick. This very simple rule from some very simple seed configurations generates a process that is in some ways reminiscent of cosmological inflation.
The page which discusses the relationship in more depth is still in preparation. I raised it only because I believe it was specifically relevant to Mike's concern than NKS needs a steady state universe.2. According to the Big Bang models the rate of inflation changes. It used to be slowing down, now it appears to be accelerating. Is your idea compatible with these observations? How?
Inflation is only postulated at the first moment of the Big Bang, as a period of exponential growth which smooths out any variations in the pre inflationary seed to levels consistent with the observed cosminc microwave background. After that brief moment, the continuing growth from the Big Bang is known as (Hubble) expansion. It is this which is purported to be now accelerating.
The real difference with inflation, as with Tick Tock, is that the growth of space/the network is incomparably faster that the speed at which messages can move through space/the network. And, no, as mentioned on the site's front page, a mechanism as simplistic as Tick Tock has no way of stopping/slowing inflation. It is intended only as a suggestive starting point that opens up the possibility of further research in a corner (evolving networks) widely acclaimed as a good candidate model, but one which human minds have great difficulty coming to terms with.
Posted by: Tony Smith
The research which got this far with Tick Tock was primarily done using programs written in Perl, so the story of that development provided the basis for a paper presented at the first Australian Open Source Developers' Conference held in Melbourne in the week just gone.
For anyone interested in that side of the project, I have put up my paper and slides on the Tick Tock site and will no doubt link them from the main site in due course.
In appendices to the main paper I have also included a bit more about a couple of my cellular automata projects which should evetually get sites of their own.
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