Sierpinski signal generates 1/f alpha spectra.

Area of Science:

• * Computational mathematics
• * Dynamical systems theory
• * Signal analysis

Background:

• * The Sierpinski automaton generates complex binary patterns.
• * Such patterns can exhibit fractal properties and power-law scaling.
• * Understanding their spectral properties is key to modeling natural phenomena.

Purpose of the Study:

• * To analytically compute the power spectrum of the Sierpinski signal.
• * To characterize the spectral properties of the Sierpinski automaton's row sums.
• * To explore its potential as a model for 1/f(alpha) spectra.

Main Methods:

• * Analytical calculation of the power spectrum.
• * Time series interpretation of the generated binary pattern.
• * Investigation of the row sum properties.

Main Results:

• * A unique, rugged fine structure was observed in the power spectrum.
• * An underlying power-law decay with an exponent of approximately 1.15 was identified.
• * The Sierpinski signal exhibits characteristics of 1/f(alpha) noise.

Conclusions:

• * The Sierpinski automaton generates signals with power-law spectral decay.
• * This model can represent 1/f(alpha) spectra found in natural systems.
• * Applications include modeling catalytic reactions and biological patterns.