[Combinatorics and NKS] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
Pages:1
Combinatorics and NKS
(Click here to view the original thread with full colors/images)
Posted by: Paul C. Meehan
Would I be correct in saying Wolframs 2-dimensional automata are inherently combinatorial in nature so far as the rules can be generated combinatorially?
The output can be defined as a discrete map of a 2-D space. Can this map be described combinatorially?
The reason I pose these questions is that I have some background in combinatorial algorithms and I am considering allocating some research time to programming projects in NKS. Specifically combinatorial views of NKS.
Any responses to my questions?
Any research out there in this area?
Posted by: Paul C. Meehan
Just realized this should have been posted to Pure NKS. Sorry!
Posted by: Tony Smith
Paul, I recently recognised that my earlier work in combinatorics was something of a precursor to my interest in CA and other discrete systems, but I would not go so far as trying to analyse one in terms of the other.
Rather I see them as parts of a larger whole which also includes the likes of solid geometry, especially tiling and packing problems.
My great problem computationally, is that most of them grow way too fast for computer emulations to provide more than the vaguest hints as to structures that might emerge in the fullness of time and space.
Posted by: Paul C. Meehan
Tony, interesting post thanks! Good to draw from the experience of someone who has already given thought to this type of view of NKS.
I had a whimsical thought that if you run something like Rule 110 long enough combinatorial structures might emerge in the output - much like order emerges from quantum randomness. Anyway enough of that!
Forum Sponsored by Wolfram Research
© 2004-2013 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. |
Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings