FINDING: Renormalization group fixed points determine universal critical exponents and fractal dimensions in phase transitions, with Feigenbaum's constants emerging from period-doubling universality. | MATH: Fixed-point equation \ (R_ (f) = f \) in function space; Feigenbaum constants \ (= 4. 669201609. . . \) (bifurcation scaling) and \ (= 2. 502907875. . . \) (width scaling) ; critical exponents \ (, , \) related to eigenvalues of linearized RG operator; fractal dimension \ (D = d - /\) for Ising class; anomalous dimension \ (\) from fixed-point coupling. | CONNECTION: Feigenbaum's \ (2. 5029\) is near \ (2. 618\) (golden ratio squared \ (²\) ) and \ (4. 669\) is close to \ (4. 618\) (\ (³ + 1\) ) ; period-doubling cascade ratio \ (\) relates to universal scaling of fractal attractors; p-adic fractal strings link to Minkowski dimension and explicit tube formulas, echoing base-p number systems (base-60 analogue). | DEPTH: 9 — Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Fri,) studied this question.