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The Unexpected Fractal Signatures in Fibonacci Chains

Quantum Gravity Research, Los Angeles, CA 90290, USA
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Fractal Fract 2019, 3(4), 49; https://doi.org/10.3390/fractalfract3040049
Received: 2 August 2019 / Revised: 11 October 2019 / Accepted: 29 October 2019 / Published: 6 November 2019
In this paper, a new fractal signature possessing the cardioid shape in the Mandelbrot set is presented in the Fourier space of a Fibonacci chain with two lengths, L and S, where L / S = ϕ . The corresponding pointwise dimension is 1.7. Various modifications, such as truncation from the head or tail, scrambling the orders of the sequence and changing the ratio of the L and S, are done on the Fibonacci chain. The resulting patterns in the Fourier space show that that the fractal signature is very sensitive to changes in the Fibonacci order but not to the L / S ratio. View Full-Text
Keywords: Fibonacci chain; fractal signature; Fourier space Fibonacci chain; fractal signature; Fourier space
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Fang, F.; Aschheim, R.; Irwin, K. The Unexpected Fractal Signatures in Fibonacci Chains. Fractal Fract 2019, 3, 49.

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