Registered: Mar 2011
Posts: 23

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?

Report this post to a moderator | IP: Logged

Registered: Mar 2011
Posts: 23

Just realized this should have been posted to Pure NKS. Sorry!

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 167

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.

__________________
Tony Smith
Complex Systems Analyst
TransForum developer
Local organiser

Report this post to a moderator | IP: Logged

Registered: Mar 2011
Posts: 23

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!

Report this post to a moderator | IP: Logged