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Experimenting with and analysing reaction–diffusion waves on physicochemical fractal media

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  • Proskurkin, Ivan S.
  • Efimov, Alexandr A.
  • Postnikov, Eugene B.
  • Safonov, Dmitry A.
  • Malfanov, Ilya L.
  • Lavrova, Anastasia I.

Abstract

We developed a macroscopic physicochemical system based on a thin gel layer (less than 100 μ m thick) that accurately reproduces the iterative ramification process leading to the Sierpinski gasket, with four self-similar iterations originating from the base triangle. This system, filled with reagents sustaining the Belousov–Zhabotinsky (BZ) reaction in an excitable regime, made it possible to observe and investigate travelling waves propagating through a regular fractal medium—not in silico, but in the physical realm. Video recordings enabled a quantitative assessment of the spatiotemporal dynamics of wave propagation speed for each prefractal, allowing for analysis and comparison of the asymptotic behaviour with predictions derived from mathematical models. Additionally, we discovered and mathematically analysed a novel effect of wave front straightening, which suggests the potential of heterogeneous gel architectures to serve as effective transmitting elements in chemical soft-computing systems.

Suggested Citation

  • Proskurkin, Ivan S. & Efimov, Alexandr A. & Postnikov, Eugene B. & Safonov, Dmitry A. & Malfanov, Ilya L. & Lavrova, Anastasia I., 2025. "Experimenting with and analysing reaction–diffusion waves on physicochemical fractal media," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925013128
    DOI: 10.1016/j.chaos.2025.117299
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    References listed on IDEAS

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    1. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    3. Balankin, Alexander S., 2020. "Fractional space approach to studies of physical phenomena on fractals and in confined low-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Juan Manuel Parrilla-Gutierrez & Abhishek Sharma & Soichiro Tsuda & Geoffrey J. T. Cooper & Gerardo Aragon-Camarasa & Kevin Donkers & Leroy Cronin, 2020. "A programmable chemical computer with memory and pattern recognition," Nature Communications, Nature, vol. 11(1), pages 1-8, December.
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    Cited by:

    1. Zhokh, O.O. & Strizhak, P.E., 2026. "A review of non-fickian reaction-diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).

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