From Mathematics to Art: A Petri Net Representation of the Fibonacci Sequence and Its Fractal Geometry

Mathematics, as Bertrand Russell noted, possesses both truth and beauty. In this work, we revisit the classical Fibonacci recurrence thanks to a minimal Petri net. Starting from a minimal layered construction that mirrors the second-order additive rule Fn=Fn−1+Fn−2, we show that the marking dynamics of the associated net generate a combinatorial triangle whose parity structure reveals a self-similar, Sierpiński-like pattern. To the best of our knowledge, this oblique fractal geometry has never been formally documented. We provide a formal definition of the underlying Petri net, analyse its computational properties, and explore the emergence of higher-order harmonics when token markings are considered modulo primes. The study highlights how a classical recurrence gives rise to previously unnoticed geometric regularities at the intersection of mathematics and art. Beyond its mathematical interest, the construction illustrates how minimal Petri net dynamics can be used as formal specification patterns for distributed, event-driven systems.

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Publication Details

Journal
Fractal and Fractional
Published
2026-01-13
DOI
https://doi.org/10.3390/fractalfract10010053
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
Field-Weighted Citation Impact
0.00
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article

From Mathematics to Art: A Petri Net Representation of the Fibonacci Sequence and Its Fractal Geometry

Iwona Grobelna, David Mailland
Fractal and Fractional
Advanced Mathematical Theories and Applications
article

From Mathematics to Art: A Petri Net Representation of the Fibonacci Sequence and Its Fractal Geometry

Iwona Grobelna, David Mailland
article en

Abstract

Mathematics, as Bertrand Russell noted, possesses both truth and beauty. In this work, we revisit the classical Fibonacci recurrence thanks to a minimal Petri net. Starting from a minimal layered construction that mirrors the second-order additive rule Fn=Fn−1+Fn−2, we show that the marking dynamics of the associated net generate a combinatorial triangle whose parity structure reveals a self-similar, Sierpiński-like pattern. To the best of our knowledge, this oblique fractal geometry has never been formally documented. We provide a formal definition of the underlying Petri net, analyse its computational properties, and explore the emergence of higher-order harmonics when token markings are considered modulo primes. The study highlights how a classical recurrence gives rise to previously unnoticed geometric regularities at the intersection of mathematics and art. Beyond its mathematical interest, the construction illustrates how minimal Petri net dynamics can be used as formal specification patterns for distributed, event-driven systems.

Fractal and FractionalVol. 10(1)
Oldham Council (GB), University of Zielona Góra (PL)
Openalex Percentile: Top 88%
Advanced Mathematical Theories and Applications
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