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Acoustic manifestations of symmetry breaking in self-similar signals

• Piotr Zielinski

(2024). ECMS 2024, 38th Proceedings
Edited by: Daniel Grzonka, Natalia Rylko, Grazyna Suchacka, Vladimir Mityushev, European Council for Modelling and Simulation.
DOI: http://doi.org/10.7148/2024
ISSN: 2522-2422 (ONLINE)
ISSN: 2522-2414 (PRINT)
ISSN: 2522-2430 (CD-ROM)
ISBN: 978-3-937436-84-5
ISBN: 978-3-937436-83-8 (CD) Communications of the ECMS Volume 38, Issue 1, June 2024, Cracow, Poland June 4th – June 7th, 2024

https://doi.org/10.7148/2024-0291

Piotr zielinski (2024). Acoustic Manifestations of Symmetry Breaking in Self-Similar Signals, ECMS 2024, Proceedings Edited by: Daniel Grzonka, Natalia Rylko, Grazyna Suchacka, Vladimir Mityushev, European Council for Modelling and Simulation. doi:10.7148/2024-0291

A gradual construction of signal based on the Weierstraß-Mandelbrot function starting from a single pure tone up to a fully developed self-similar waveform allows one to aurally perceive gain/loss of self-similarity symmetry. A numerically synthesized example involves a scaling transformation with the value of scaling factor increasing continuously from unity to the value defining the self-similarity of the full Weierstraß-Mandelbrot function. In the case of partially self-similar signals the sequence of a sequential repetition of  this transformation is readily perceptible, whereas for the fully self-similar signal the repetitions manifest themselves as an ever-ascending glissando specific to Shepard tones. The usefulness of the concept of self-similarity in the condensed matter physics is discussed.