Designing Fractal Curves with Five-Fold Rotational Symmetry Using the Complex Number Golden Ratio

Year: 2021 Authors: Jeffrey Ventrella

Core claim

Fractal curve segments can be encoded as ζ^nφ^p, enabling algorithmic construction of five-fold symmetric curves and related Penrose-like tilings.

Topics

plane-filling fractal curves, five-fold rotational symmetry, Penrose tilings, complex number golden ratio

Domains

complex numbers, cyclotomic fields, fractal geometry, number theory, visual design, tiling art, architectural ornament, algorithmic art

Methods

recursive replacement rules, complex-number encoding, iterated curve construction, tiling-based design

Media

complex plane, fractal curve diagrams, pentagram geometry, tiling illustrations

Source status

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