2026/07/25 by Goktug Islamoglu
Physics and Astronomy · #nlin.CG
To model high-risk traffic densities a cellular automaton model is constructed, exhibiting Ising model-like properties. The attraction-repulsion forces between vehicles are evaluated as coupling, and the coupling function p(1-p)=g/8, where p is the initial distribution of cells with state 1, and g is the Moore neighbor count, which has roots cos2(π/8) and sin2(π/8) for g=1. This is achieved without the use of any trigonometric functions in the code. From the roots, the tangent polynomial tan2(x) + tan(x) emerges. Kramers-Wannier duality is recovered and it is conjectured that the 1/√(2) difference between the roots serves as a fixed point for a projection mechanism from the 2-dimensional Ising model onto a 1-dimensional Ising chain through the Gudermannian function. The sigmoid evaluated at the proposed fixed point is substituted into the derivative of the logistic coupling function, σ(1/√(2))(1-σ(1/√(2))), yielding a numerical approximation to the three-dimensional Ising inverse critical coupling. Finally, the results are linked to risk densities in traffic and vehicle types, accounting for the amplification of fatal accidents.