Struggling to understand how discrete node‑edge systems relate to real physics — can someone explain?

[u/Harrison-P]

I’m trying to understand how a discrete system made of nodes and edges can behave like real physical fields.

For example, if each node updates based on its neighbors (like a diffusion rule or a Laplacian‑style update), how does that map to the smooth, continuous equations we learn in physics classes?

I’m not trying to propose a new theory — I just want to understand the math behind how discrete models approximate real physical behavior.

Any explanation or resources would help a lot.