On architectures of circuits implemented in simulated Belousov–Zhabotinsky droplets
Introduction
The design of logical gates in chemical systems can be traced back to the early 1990s when Hjemfelft et al. suggested a theoretical coupled mass flow system for implementing logic gates and finite-state machines (Hjelmfelt and Ross, 1995) and Lebender and Schneider proposed logical gates utilising a series of flow rate coupled continuous stirred tank reactors and a bistable chemical reaction (Lebender and Schneider, 1994). No experimental prototypes were implemented at that time. Mass-kinetic based computing is appealing theoretically but laboratory experiments are cumbersome to undertake. The implementation of mass-kinetic networks is inefficient as most designs require the use of programmable pumping devices. In 1994 the Showalter Laboratory presented the first ever experimental implementation of logical gates in the Belousov–Zhabotinsky (BZ) system (Tóth et al., 1994, Tóth and Showalter, 1995). The logical gates were based on the geometrical configuration of channels in which excitation waves propagate. The ratio between the channel diameter and the critical nucleation radii of the excitable media allowed various logical schemes to be realised. These original findings led to several innovative designs of computational devices, based on geometrically constrained excitable substrates. Designs incorporating assemblies of channels for excitation wave propagation were used to implement logical gates for Boolean and multiple-valued logic (Sielewiesiuk and Górecki, 2001, Motoike and Adamatzky, 2005, Górecki et al., 2009, Yoshikawa et al., 2009). All these chemical computing devices were realised in geometrically constrained media where excitation waves propagate along defined catalyst loaded channels or tubes filled with the BZ reagents. The waves perform computation by interacting at the junctions between the channels. Despite its apparent novelty the approach is just an implementation of conventional computing architectures in novel materials—namely excitable chemical systems. There is however another way to undertake computation—by employing the principles of collision-based computing (Adamatzky, 2003). Wave-fragments collide in a ‘free’ space and change their velocity vectors as a result of the collision. When input and output waves are interpreted as logical variables, the site of the waves’ collision can be seen as a logical gate (Adamatzky et al., 2005). We explore the collision-based approach in the paper.
Section snippets
BZ-vesicles
A BZ-vesicle is a spherical compartment encapsulating BZ medium in an lipid membrane (NeuNeu., 2010, Szymanski et al., 2011, King et al., 2011); the BZ-vesicles can be arranged into a regular lattice. We physically imitate BZ-vesicles by projecting patterns and boundaries on a flat chemical reactor, and simulate the vesicles assembles in computer models.
When the BZ reaction is in a sub-excitable mode asymmetric perturbations lead to the formation of propagating localised excitation, or
Binary Adder Made of Uniform BZ-vesicles
Let us consider how to build a one-bit half-adder using BZ-vesicles of the same size. BZ mixtures inside each vesicle is connected to the mixtures in neighbouring vesicles with the pores of the same size. The assembles of BZ-vesicles are fully synchronised.
Let several wave-fragments enter a vesicle. If at least two wave-fragments have opposite velocity vectors all wave-fragments annihilate. Otherwise the wave-fragments merge and the velocity vector of the newly formed wave-fragment is a sum of
Elaborate Arrangements of BZ Discs
In the previous section we have shown how arithmetical circuits can be implemented in a regular arrangements of BZ vesicles, as if they were packed in a hexagonal lattice. Let us assume now that we can manipulate BZ vesicles and are capable for arranging them in the irregular structures. Fig. 2 illustrates how and and xor gates can be created using interconnected BZ discs. In the and gate the collision between the two inputs results in two perpendicular fragments, one of which develops in the
Conclusion
In the Belousov–Zhabotinsky (BZ) medium in a sub-excitable state localised travelling excitation waves are formed. We interpret these localisations as quanta of information, values of logical variables. When two or more localisations collide they annihilate or form a new localisations. We interpret post-collision trajectories of the localisations as the results of a computation. We demonstrate that by colliding wave-fragments in an encapsulated excitable chemical medium we can realise a number
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2019, BioSystemsCitation Excerpt :We conclude that the network is capable of correctly transitioning from any input state to any other input state, in each case, rapidly converging on the correct output values. The Belousov–Zhabotinsky (BZ) medium (Zhabotinsky and Zaikin, 1973) is an oscillating chemical reaction that has been identified and investigated as a potential complex non-linear system capable of computational tasks see e.g. (Adamatzky et al., 2012; Adamatzky, 2013, 2001). In this section we present our application of the RERUN-method to identify NAND-gates in chemical “neural networks” of artificial BZ-medium containing droplets (Jones et al., 2015; Chang et al., 2016).
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2015, BioSystemsCitation Excerpt :Nevertheless, implementation of Boolean operations and more complex circuitry does demonstrate universality that is a characteristic feature of classical schemes. In recent years there have been numerous examples of individual gates and more complex circuits implemented in unconventional substrates, including Belousov–Zhabotinsky medium (Costello et al., 2011; Adamatzky et al., 2011, 2012; Zhang et al., 2012), competing patterns in Game-like cellular automata (Martí nez et al., 2010a,b), patterns of crystallisation (Adamatzky, 2009), disordered ensembles of carbon nanotunes (Broersma et al., 2012), liquid crystals (Harding and Miller, 2005; Miller et al., 2014; Adamatzky et al., 2011), organic molecular layers (Bandyopadhyay et al., 2010), spiking memristors (Gale et al., 2013), nuclear magnetic resonance (Bechmann et al., 2012), precipitating reaction–diffusion chemical systems (Adamatzky and De Lacy Costello, 2002), enzymatic systems (Zavalov et al., 2012; MacVittie et al., 2012; Pedrosa et al., 2010). Limitations faced by unconventional substrates include the fact that planar arrangements of circuits necessitate crossing or bridging points (where signal ‘wires’ must cross paths but not interfere with either independent signal).
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