Abstract
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.
Highlights
Quasicrystals possess exotic and sometimes anomalous properties that have interested the scientific community since their discovery by Shechtman in 1982 [1]
The fractal properties of a one-dimensional Fibonacci chain and its variations are studied in the complex Fourier space
These results show that the fractal pattern, especially the cardioid shape, is very sensitive to any modification except changing the L/S ratio, in which case only the scaling of the fractal pattern changes
Summary
Quasicrystals possess exotic and sometimes anomalous properties that have interested the scientific community since their discovery by Shechtman in 1982 [1]. Of particular interest in this manuscript is the self similar property of quasicrystals that links them to fractal. Research on the fractal aspect of quasicrystalline properties has revolved around spectral and wave function analysis [2,3,4,5]. A new framework for analyzing the fractal nature of quasicrystals is introduced. The fractal properties of a one-dimensional Fibonacci chain and its variations are studied in the complex Fourier space. The results may be found in two and three dimensional quasicrystals that can be constructed using a network of one dimensional Fibonacci chains [10]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
