TY - JOUR
T1 - Sierpinski signal generates 1/fα spectra
AU - Claussen, Jens Christian
AU - Nagler, Jan
AU - Schuster, Heinz Georg
PY - 2004/9/14
Y1 - 2004/9/14
N2 - We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1∕fα spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.
AB - We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1∕fα spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.
UR - http://www.scopus.com/inward/record.url?scp=42749101718&partnerID=8YFLogxK
UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.70.032101
U2 - 10.1103/PhysRevE.70.032101
DO - 10.1103/PhysRevE.70.032101
M3 - Article
AN - SCOPUS:42749101718
SN - 1539-3755
VL - 70
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 032101
ER -