## Tuesday, September 3, 2024

### Numerical Solution to Strings Theory. ðŸ˜‡

Dynamic Foam is the Numerical solution to solve String Theory vs Analytically. Simply because Voronoi already has the basic String-fibers, read edges.

They only need be tied into Knots. ðŸª¢

Voronoi ☯ Delaunay

Kaluza-Klein theories (an important precursor to string theory) shows how you can get Electro-Magnetism from Einstein's GR if you assume an extra (5th) dimension which is a circle (Torus). A particle moving around this circle (i.e. with momentum in the 5th dimension) appears to a 4-dimensional observer (us) to have electric charge. It is quantised because the circle has a finite size.

*The Red cells contain a sharp < 90° angle where the distribution
of the pressure (flow) in the edges is cut-off.

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Short Recap:

Markov-Chains in Voro-X calculate the pressure-flow for each edge based on the number of connections. It's like Google’s Page-rank looking for connected websites, as a result we get for each Voronoi-edge a value.

First we check the gates/angles if the are open or closed, based on the 90° angle rule:
> 90° is open
< 90° is closed

Next we calculate the connections:
(A) is open to (B) and (C)
(B) is open to (A) but closed to (C)
(C) is open to (A) but closed to (B)

We use a local connection-tree to calculate the value for each individual edge.

These values make their dual Delaunay-edges contract or expand,
and as a result we get cells shrink or expand.