Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices

Year: 2005 Authors: Jay Kappraff; Slavik Jablan; Gary Adamson; Radmila Sazdanovich

Core claim

Diagonals of odd n-gons generate golden fields through generalized Fibonacci recurrences whose associated matrices and Mandelbrot operators exhibit periodic trajectories.

Topics

regular polygons, generalized Fibonacci sequences, matrix operators, Mandelbrot dynamics, golden fields

Domains

algebraic fields, recurrence relations, eigenvalues, Chebyshev polynomials, combinatorics of polygons, geometry, visualization, pattern

Methods

polygon diagonal identities, polynomial recurrences, matrix eigenanalysis, sequence indexing

Media

regular n-gons, triangular matrices, glass plates

Source status

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