Wolfram Science

Live Experiment Notebooks

The notebooks from Stephen Wolfram's live experiment at NKS 2007 last night are now available!

Download NKS2007-LiveExperiment-01.nb (76.0K)
Download NKS2007-LiveExperiment-02.nb (5124.2K)
(Right-click and select "Save Target As" or "Save Link As")

Stephen explored various interesting properties of ECA rules 18, 22 and 122.

Jesse Louis-Rosenberg, Dynamic State Networks

Jesse made a presentation about Dynamic State Networks - effectively graphs that get updated according to rules applied to a node depending on it's pattern of connections with other nodes.

The rule being applied on the nodes was an analogon of the Game of Life rule - nodes with too few neighbors die of loneliness, nodes with too many neighbors die of overcrowding, and so on. They defined classes of initial conditions according to the procedure by which the start network is constructed - vertex duplication, preferential attachment, grid exponential, ring exponential.

Then they defined two different measures of network entropy and showed how entropy varies along the time evolution of the rule. A clean computer experiment.

Live Computer Experiment by Stephen Wolfram

Posted by Joe Bolte

After the Q&A, Stephen Wolfram performed a live computer experiment from scratch. He chose to search for complex behavior in a class of systems called step registers. Starting from a blank Mathematica notebook, Wolfram generated a ruleset and combed through it for examples of complex behavior, first using a two-neighbor rule and then a three-nighbor rule. You can see that in the two-neighbor case rules 6 and 9 yielded complex behavior and in the three-nieghbor case, rules 90 and 165 were the interesting results. Wolfram had an intuition that rules 90 displayed additive behavior, but he was not able to demonstrate anything before time ran out. Please take a look at the Mathematica notebook of the experiment.

Update: Christopher Haydock noted a problem with the notebook and submitted a corrected version, with the code extensively refactored to be clearer for those following along at home. Thanks Chris!

Eric Mjolsness, "Toward a Searchable Space of Dynamical System Models"

Posted by Kathryn Cramer.

Mjolsness set out criteria for simple formal systems: expressive power, discrete labeled graph structure, & self-applicability. he showed a wide variety of examples from a number of disciplines and on multiple scales. He argued that the stochastic process operators can form the semantics of a language, and that operator algebra then leads to novel algorithms. This results in a searchable space of simple dynamical system models.

Abstract. Also, here is Eric Mjolsness's web site, which he  suggests you visit for more information, is here.

Stephen Wolfram's Keynote Address: "The core of NKS is exploring the computational universe."

Posted by Kathryn Cramer.

Stephen Wolfram gave a wide-ranging Keynote Address that touched on many (or perhaps even all) of the subjects of the papers to be presented at the conference.

The central organizing metaphor of the talk was the field of NKS as an exploration of the computational universe: The core of NKS is exploring the computational universe.

My favorite line from the talk, from the portion in which he discussed NKS and aesthetics is: We are seeing the beauty of nature but not just from our world, but from all possible worlds.

As I was listening to his talk I explored the relationship between the various items on the program today. Here is my first draft version of this. As I listen to the talks I will modify and improve upon this.

Larger versions of the graphic are available here: 1024 x 642 and 3869 x 2424.

The talk will be available later. We will post the URL when we have it.

Applying NKS minicourse talk

Posted by Todd Rowland.

Here is the pdf of the talk at the minicourse I gave about applying NKS. Download NKS-Applied-06.pdf