Finding the optimal path with the aid of chemical wave

doi:10.1016/S0167-2789(97)00049-3

Physica D: Nonlinear Phenomena

Volume 106, Issues 3–4, 1 August 1997, Pages 247-254

https://doi.org/10.1016/S0167-2789(97)00049-3 Get rights and content

Abstract

It is shown that the optimal path in a two-dimensional vector field is deduced by the use of chemical wave in the Belousov-Zhabotinsky reaction (BZ reaction). We also reproduced our experimental result in a numerical simulation based on a two-variable reaction-diffusion equation. The present result provides a simple model for the future application of excitable media to parallel computing, i.e., an excitable medium serves as a self-organized parallel processor.

References (16)

K. Agladze et al.
Physica D
(1995)
V.I. Krinsky et al.
Physica D
(1983)
R.R. Aliev et al.
Physica D
(1991)
K.I. Agladze et al.
L. Kuhnert et al.
Nature
(1989)
R.R. Aliev
J. Phys. Chem.
(1994)
C.Y. Lee
IRE Tr. Elec. Comput.
(1961)
L. Kuhnert
Nature
(1986)

There are more references available in the full text version of this article.

Cited by (85)

Light sensitive Belousov–Zhabotinsky medium accommodates multiple logic gates
2021, BioSystems
Citation Excerpt :
This chemical computational substrate has been utilized in several types of problems. Namely, implementing basic Boolean logic gates (Tóth and Showalter, 1995; Steinbock et al., 1996; Adamatzky, 2004; Costello and Adamatzky, 2005; Toth et al., 2009; Adamatzky et al., 2011b; Sun and Zhao, 2013; Adamatzky et al., 2012; Sielewiesiuk and Górecki, 2001; Fyrigos et al., 2020), Fredkin and Toffoli gates (Adamatzky, 2017), binary adders (Adamatzky et al., 2011b; Dourvas et al., 2017), multi-bit binary decoders (Sun and Zhao, 2013) and even more complicated problems, like implementing binary Correlation Matrix Memory (Stovold and O’Keefe, 2017), solving labyrinths (Steinbock et al., 1995), calculating the shortest path in an area avoiding hurdles (Agladze et al., 1997; Adamatzky and de Lacy Costello, 2002), analyzing transport infrastructure (Adamatzky et al., 2018), implementing dataset classifier (Gizynski and Gorecki, 2017a; Gizynski et al., 2017) and performing pattern recognition (Parrilla-Gutierrez et al., 2020). The fact that the BZ reaction is photosensitive was utilized as a key mechanism in studies of chemical computers (Gizynski and Gorecki, 2017b).
Computational functionality has been implemented successfully on chemical reactions in living systems. In the case of Belousov–Zhabotinsky (BZ) reaction, this was achieved by using collision-based techniques and by exploiting the light sensitivity of BZ. In order to unveil the computational capacity of the light sensitive BZ medium and the possibility to implement re-configurable logic, the design of multiple logic gates in a fixed BZ reservoir was investigated. The three basic logic gates (namely NOT, OR and AND) were studied to prove the Turing completeness of the architecture. Namely, all possible Boolean functions can be implemented as a combination of these logic gates. Nonetheless, a more complicated logic function was investigated, aiming to illustrate further capabilities of a fixed size BZ reservoir. The experiments executed within this study were implemented with a Cellular Automata (CA)-based model of the Oregonator equations that simulate excitation and wave propagation on a light sensitive BZ thin film. Given that conventional or von Neumann architecture computations is proved possible on the proposed configuration, the next step would be the realization of unconventional types of computation, such as neuromorphic and fuzzy computations, where the chemical substrate may prove more efficient than silicon.
An adaptive and robust biological network based on the vacant-particle transportation model
2011, Journal of Theoretical Biology
Citation Excerpt :
The developing model equipped with the vacant-particle, VP-D, also shows a balance between exploitation and exploration. Since it was shown that the BZ reaction can solve the minimal path of a maze, biochemical reactions have been regarded as natural computational devices (Steinbock et al., 1995; Agladze et al., 1997). Physarum is also regarded as a computational device, being a closed tube containing a biochemical reaction (Nakagaki et al., 2000a, b; Nakagaki, 2001).
A living system reveals local computing by referring to a whole system beyond the exploration–exploitation dilemma. The slime mold, Physarum polycephalum, uses protoplasmic flow to change its own outer shape, which yields the boundary condition and forms an adaptive and robust network. This observation suggests that the whole Physarum can be represented as a local protoplasmic flow system. Here, we show that a system composed of particles, which move and are modified based upon the particle transformation that contains the relationship between the parts and the whole, can emulate the network formed by Physarum. This system balances the exploration–exploitation trade-off and shows a scale-free sub-domain. By decreasing the number of particles, our model, VP-S, can emulate the Physarum adaptive network as it is attracted to a food stimulus. By increasing the number of particles, our model, VP-D, can emulate the pattern of a growing Physarum. The patterns produced by our model were compared with those of the Physarum pattern quantitatively, which showed that both patterns balance exploration with exploitation. This model should have a wide applicability to study biological collective phenomena in general.
Biomimetic Cardiac Tissue Models for In Vitro Arrhythmia Studies
2023, Biomimetics
Chemical Computers and Computing Based on Chemical Reactions: Current Status and Outlook
2022, Advanced Journal of Chemistry, Section A
Information Processing Using Networks of Chemical Oscillators
2022, Entropy
Computing With Networks of Chemical Oscillators and its Application for Schizophrenia Diagnosis
2022, Frontiers in Chemistry

View all citing articles on Scopus

View full text

Finding the optimal path with the aid of chemical wave

Abstract

Physica D

Physica D

Physica D

Nature

J. Phys. Chem.

IRE Tr. Elec. Comput.

Nature