I am thinking about the heuristic rules we can apply in the Wolfram Physics Project. And I'd like to share my idea with you guys. What if we cluster some closely related nodes (a sub-network) as a new node in a larger scale network (Maybe iterating the k-means algorithm with different k on a different scale)? The network may be nested somehow on a different scale. But in a way, it may be fractal-like. On the one hand, we can simplify the original network by this. On the other hand, the computational universe may resemble a fractal (in a sense, our real world is a fractal). Many more interesting properties may emerge after it, e.g. self-organizing. And the cross-scale feedback seems to be more obvious in this structure. Welcome to discuss, and thanks in advance!

The k-means algorithm does not apply here. K-Means is useful for vector quantization. Our nodes are not vectors, and are quantifiable. Let me explain, k-means is define by this: The problems are: We have no - defined between nodes. It is not a vector space/field. You suppose more mathematically structure than we have. We also have no \|\| . \|\| defined since our nodes are not in some metric space.

Thanks a lot for your insight! Those are really what I missed. It seems that we may need to somehow define a coordinate system in the computational universe. Do you have some ideas to solve the problem? I think we may need to define a kind of coordinate system that relies on some characters of the network itself. Or... can we set a standard to measure all the universes?

It seems that we may need to somehow define a coordinate system in the computational universe. Do you have some ideas to solve the problem? Your question doesn't make that much sense. This is mostly due to the loose way you used terms with strict mathematical definition before. What attributes do you hope your coordinate system might have? Or... can we set a standard to measure all the universes? What do you mean by standard, what do you mean by measure and what do you mean by all the universes?

Scaling - an idea to extract network features