Logistical nightmare

This article describes the author's implementation of the logistic map in Matlab, a simple mathematical process that leads to deterministic chaos. It explains the iterative operation x → kx(1-x), starting from x0=0.5, and discusses the convergence to a fixed point solution x = 1 - 1/k for certain values of k. The author notes the non-perturbative nature of the solution, drawing a parallel to condensed matter field theory. The article then observes a bifurcation at k=3, where the solution splits into two branches, leading to the derivation of a cubic equation to describe the new behavior. This is a technical tutorial related to mathematical modeling and programming in Matlab.