1/f Noise in Fractal Quaternionic Structures

Details 1/f Noise in Fractal Quaternionic Structures 1/f Noise in Fractal Quaternionic Structures

2005-11-25

arxiv.org/abs/math-ph/0511074v2

AIP Conf. Proc. 780 (2005) 91-94

Physics

Mathematical Physics

Corrected figures, 5 pages, 4 figures, ICNF 2005

Scientific paper

10.1063/1.2036706

We consider the logistic map over quaternions $\mathbb{H}\sim\mathbb{R}^4$
and different 2D projections of Mandelbrot set in 4D quaternionic space. The
approximations (for finite number of iterations) of these 2D projections are
fractal circles. We show that the point process defined by radiuses $R_j$ of
those fractal circles exhibits pure 1/f noise.

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