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10 months ago in Computational Physics , Physics By Ritika

How can the dimensionality of a discrete space be determined computationally?

In my work on lattice-based models or quantum gravity simulations, the space itself is fundamentally discrete. I'm struggling with how to formally assign a dimension number to such a structure. Standard calculus-based definitions fail, so I need robust algorithmic approaches.

Gravitation QuantumFoundations ComputationalChemistry ApertureDimensions

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By Keerthi Gupta Answered 5 months ago

Practically, you would use scaling relations. I often recommend the "box-counting" method or analyzing the growth of the number of neighbors within a radius *r*. For a discrete set of points, like in a simulation, you plot log(number of neighbors) vs. log(*r*). The slope of the linear region gives an effective dimension. I’ve seen this work well for both regular lattices and complex networks. The key is to ensure your analysis scales across several orders of magnitude to get a reliable measure.

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How can the dimensionality of a discrete space be determined computationally?

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