The Unexpected Fractal Signatures in Fibonacci Chains

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...

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Bibliographic Details
Published inFractal and fractional Vol. 3; no. 4; p. 49
Main Authors Fang, Fang, Aschheim, Raymond, Irwin, Klee
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2019
Subjects
Chains
fibonacci chain
fourier space
Fourier transforms
fractal signature
Fractals
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Summary: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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract3040049