A brief history of liquid computers

On complexity of colloid cellular automata

The colloid cellular automata do not imitate the physical structure of colloids but are governed by logical functions derived from them. We analyze the space-time complexity of Boolean circuits derived from the electrical responses of colloids-specifically ZnO (zinc oxide, an inorganic compound also known as calamine or zinc white, which naturally occurs as the mineral zincite), proteinoids (microspheres and crystals of thermal abiotic proteins), and their combinations in response to electrical stimulation. To extract Boolean circuits from colloids, we send all possible configurations of two-, four-, and eight-bit binary strings, encoded as electrical potential values, to the colloids, record their responses, and infer the Boolean functions they implement. We map the discovered functions onto the cell-state transition rules of cellular automata-arrays of binary state machines that update their states synchronously according to the same rule-creating the colloid cellular automata. We then analyze the phenomenology of the space-time configurations of the automata and evaluate their complexity using measures such as compressibility, Shannon entropy, Simpson diversity, and expressivity. A hierarchy of phenomenological and measurable space-time complexity is constructed.

Logical circuits in colloids

Colloid-based computing devices offer remarkable fault tolerance and adaptability to varying environmental conditions due to their amorphous structure. An intriguing observation is that a colloidal suspension of ZnO nanoparticles in dimethylsulfoxide (DMSO) exhibits reconfiguration when exposed to electrical stimulation and produces spikes of electrical potential in response. This study presents a novel laboratory prototype of a ZnO colloidal computer, showcasing its capability to implement various Boolean functions featuring two, four and eight inputs. During our experiments, we input binary strings into the colloid mixture, where a logical 'True' state is represented by an impulse of an electrical potential. In contrast, the absence of the electrical impulse denotes a logical 'False' state. The electrical responses of the colloid mixture are recorded, allowing us to extract truth tables from the recordings. Through this methodological approach, we demonstrate the successful implementation of a wide range of logical functions using colloidal mixtures. We provide detailed distributions of the logical functions discovered and offer speculation on the potential impacts of our findings on future and emerging unconventional computing technologies. This research highlights the exciting possibilities of colloid-based computing and paves the way for further advancements.

Maze-solving in a plasma system based on functional analogies to reinforcement-learning model

Maze-solving is a classical mathematical task, and is recently analogously achieved using various eccentric media and devices, such as living tissues, chemotaxis, and memristors. Plasma generated in a labyrinth of narrow channels can also play a role as a route finder to the exit. In this study, we experimentally observe the function of maze-route findings in a plasma system based on a mixed discharge scheme of direct-current (DC) volume mode and alternative-current (AC) surface dielectric-barrier discharge, and computationally generalize this function in a reinforcement-learning model. In our plasma system, we install two electrodes at the entry and the exit in a square lattice configuration of narrow channels whose cross section is 1×1 mm2 with the total length around ten centimeters. Visible emissions in low-pressure Ar gas are observed after plasma ignition, and the plasma starting from a given entry location reaches the exit as the discharge voltage increases, whose route converging level is quantified by Shannon entropy. A similar short-path route is reproduced in a reinforcement-learning model in which electric potentials through the discharge voltage is replaced by rewards with positive and negative sign or polarity. The model is not rigorous numerical representation of plasma simulation, but it shares common points with the experiments along with a rough sketch of underlying processes (charges in experiments and rewards in modelling). This finding indicates that a plasma-channel network works in an analog computing function similar to a reinforcement-learning algorithm slightly modified in this study.

Neuromorphic Engineering in Wetware: Discriminating Acoustic Frequencies through Their Effects on Chemical Waves

Some features of the human nervous system can be mimicked not only through software or hardware but also through liquid solutions of chemical systems maintained under out-of-equilibrium conditions. We describe the possibility of exploiting a thin layer of the Belousov-Zhabotinsky (BZ) reaction as a surrogate for the cochlea for sensing acoustic frequencies. Experiments and simulations demonstrate that, as in the human ear where the cochlea transduces the mechanical energy of the acoustic frequencies into the electrochemical energy of neural action potentials and the basilar membrane originates topographic representations of sounds, our bioinspired chemoacoustic system, based on the BZ reaction, gives rise to spatiotemporal patterns as the representation of distinct acoustic bands through transduction of mechanical energy into chemical energy. Acoustic frequencies in the range 10-2000 Hz are partitioned into seven distinct bands based on three attributes of the emerging spatiotemporal patterns: (1) the types and frequencies of the chemical waves, (2) their velocities, and (3) the Faraday waves' wavelengths.

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

Walking exhibits stride-to-stride variations. Given ongoing perturbations, these variations critically support continuous adaptations between the goal-directed organism and its surroundings. Here, we report that stride-to-stride variations during self-paced overground walking show cascade-like intermittency-stride intervals become uneven because stride intervals of different sizes interact and do not simply balance each other. Moreover, even when synchronizing footfalls with visual cues with variable timing of presentation, asynchrony in the timings of the cue and footfall shows cascade-like intermittency. This evidence conflicts with theories about the sensorimotor control of walking, according to which internal predictive models correct asynchrony in the timings of the cue and footfall from one stride to the next on crossing thresholds leading to the risk of falling. Hence, models of the sensorimotor control of walking must account for stride-to-stride variations beyond the constraints of threshold-dependent predictive internal models.

Experimental Demonstration of In-Memory Computing in a Ferrofluid System

Magnetic fluids are excellent candidates for several important research fields including energy harvesting, biomedical applications, soft robotics, and exploration. However, notwithstanding relevant advancements such as shape reconfigurability, that have been demonstrated, there is no evidence for their computing capability, including the emulation of synaptic functions, which requires complex non-linear dynamics. Here, it is experimentally demonstrated that a Fe₃ O₄ water-based ferrofluid (FF) can perform electrical analogue computing and be programmed using quasi direct current (DC) signals and read at radio frequency (RF) mode. Features have been observed in all respects attributable to a memristive behavior, featuring both short and long-term information storage capacity and plasticity. The colloid is capable of classifying digits of a 8 × 8 pixel dataset using a custom in-memory signal processing scheme, and through physical reservoir computing by training a readout layer. These findings demonstrate the feasibility of in-memory computing using an amorphous FF system in a liquid aggregation state. This work poses the basis for the exploitation of a FF colloid as both an in-memory computing device and as a full-electric liquid computer thanks to its fluidity and the reported complex dynamics, via probing read-out and programming ports.

There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-Scale Machines

The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic view. Such a view dissolves the contingent dichotomies driven by human cognitive biases (e.g., a tendency to oversimplify) and prior technological limitations in favor of a more continuous view, necessitated by the study of evolution, developmental biology, and intelligent machines. Form and function are tightly entwined in nature, and in some cases, in robotics as well. Thus, efforts to re-shape living systems for biomedical or bioengineering purposes require prediction and control of their function at multiple scales. This is challenging for many reasons, one of which is that living systems perform multiple functions in the same place at the same time. We refer to this as "polycomputing"-the ability of the same substrate to simultaneously compute different things, and make those computational results available to different observers. This ability is an important way in which living things are a kind of computer, but not the familiar, linear, deterministic kind; rather, living things are computers in the broad sense of their computational materials, as reported in the rapidly growing physical computing literature. We argue that an observer-centered framework for the computations performed by evolved and designed systems will improve the understanding of mesoscale events, as it has already done at quantum and relativistic scales. To develop our understanding of how life performs polycomputing, and how it can be convinced to alter one or more of those functions, we can first create technologies that polycompute and learn how to alter their functions. Here, we review examples of biological and technological polycomputing, and develop the idea that the overloading of different functions on the same hardware is an important design principle that helps to understand and build both evolved and designed systems. Learning to hack existing polycomputing substrates, as well as to evolve and design new ones, will have massive impacts on regenerative medicine, robotics, and computer engineering.

Turing's cascade instability supports the coordination of the mind, brain, and behavior

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Periodic Motion in the Chaotic Phase of an Unstirred Ferroin-Catalyzed Belousov Zhabotinsky Reaction

The Belousov Zhabotinsky reaction, a self-organized oscillatory color-changing reaction, can show complex behavior when left unstirred in a cuvette environment. The most intriguing behavior is the transition from periodicity to chaos and back to periodicity as the system evolves in time. It was shown that this happens thanks due to the decoupling of reaction, diffusion and convection. We have recently discovered that, as the so-called chaotic transient takes place, periodic bulk motions in form of convective cells are created in the reaction solution. In this work we investigated this phenomenon experimentally by changing cuvette size and reaction volume, in order to allow different types of convection patterns to appear. So far, we have observed single and double convection cells in the system. There are indications that the convection patterns are connected to the duration of the chaotic phase. A simplified mathematical model confirms the form and dynamics of the observed convection cells and explains the connection between chemical chaos and hydrodynamical order.

Ferrofluids and bio-ferrofluids: looking back and stepping forward

Ferrofluids investigated along for about five decades are ultrastable colloidal suspensions of magnetic nanoparticles, which manifest simultaneously fluid and magnetic properties. Their magnetically controllable and tunable feature proved to be from the beginning an extremely fertile ground for a wide range of engineering applications. More recently, biocompatible ferrofluids attracted huge interest and produced a considerable increase of the applicative potential in nanomedicine, biotechnology and environmental protection. This paper offers a brief overview of the most relevant early results and a comprehensive description of recent achievements in ferrofluid synthesis, advanced characterization, as well as the governing equations of ferrohydrodynamics, the most important interfacial phenomena and the flow properties. Finally, it provides an overview of recent advances in tunable and adaptive multifunctional materials derived from ferrofluids and a detailed presentation of the recent progress of applications in the field of sensors and actuators, ferrofluid-driven assembly and manipulation, droplet technology, including droplet generation and control, mechanical actuation, liquid computing and robotics.

Identification of the best medium for experiments on chemical computation with Belousov–Zhabotinsky reaction and ferroin-loaded Dowex beads

Our study is focused on identification of the best medium for future experiments on information processing with Belousov–Zhabotinsky reaction proceeding in Dowex beads with immobilized catalyst inside. The optimum medium should be characterized by long and stable nonlinear behavior, mechanical stability and should allow for control with electric potential. We considered different types of Dowex ion-exchange resins, bead distributions and various initial concentrations of substrates: malonic acid and 1,4-cyclohexanedione. The electric potential on platinum electrodes, stabilized by a potentiostat is used to control medium evolution. A negative electric potential generates activator species HBrO2 on the working electrode according to the reaction: BrO3−  + 2e−  + 3H+  → HBrO2 + H2O, while positive electric potential attracts inhibitor species Br− to the proximity of it. We study oscillation amplitude and period stability in systems with ferroin loaded Dowex 50W-X2 and Dowex 50W-X8 beads during experiments exceeding 16 h. It has been observed, that the above mentioned resins generate a smaller number of CO2 bubbles close to the beads than Dowex 50W-X4, which makes Dowex 50W-X2 and Dowex 50W-X8 more suitable for applications in chemical computing. We report amplitude stability, oscillation frequency, merging and annihilation of travelling waves in a lattice of Dowex 50W-X8 beads (mesh size 50–100) in over 19 h long experiments with equimolar solution of malonic acid and 1,4-cyclohexanedione. This system looks as a promising candidate for chemical computing devices that can operate for a day.

Novel, Emerging Chip Models of the Blood-Brain Barrier and Future Directions

The use of microfluidic chips is now allowing for more advanced modelling of the blood-brain barrier (BBB) in vitro, recapitulating heterotypic interactions, 3D architecture, and physiological flow. This chapter will give an introduction to these new technologies and how they are being applied to model the BBB and neurovascular unit (NVU). A foundational understanding of the fluid dynamics germane to the effective use of these chips will be set and an overview of how physical phenomena at the microscale can be exploited to enable new possibilities to control the cell culture environment. The four main approaches to construct microfluidic blood vessel mimetics will be discussed with examples of how these techniques are being applied to model the BBB and more recently to study specific neurovascular disease processes. Finally, practical guidance will be given for researchers wishing to adopt these new techniques along with a summary of the challenges, limitations faced, and new opportunities opened up by these advanced cell culture systems.

Shape-Changing Particles: From Materials Design and Mechanisms to Implementation

Demands for next-generation soft and responsive materials have sparked recent interest in the development of shape-changing particles and particle assemblies. Over the last two decades, a variety of mechanisms that drive shape change have been explored and integrated into particulate systems. Through a combination of top-down fabrication and bottom-up synthesis techniques, shape-morphing capabilities extend from the microscale to the nanoscale. Consequently, shape-morphing particles are rapidly emerging in a variety of contexts, including photonics, microfluidics, microrobotics, and biomedicine. Herein, the key mechanisms and materials that facilitate shape changes of microscale and nanoscale particles are discussed. Recent progress in the applications made possible by these particles is summarized, and perspectives on their promise and key open challenges in the field are discussed.

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

The bibliography includes 250 references.

Native Chemical Computation. A Generic Application of Oscillating Chemistry Illustrated With the Belousov-Zhabotinsky Reaction. A Review

Computing with molecules is at the center of complex natural phenomena, where the information contained in ordered sequences of molecules is used to implement functionalities of synthesized materials or to interpret the environment, as in Biology. This uses large macromolecules and the hindsight of billions of years of natural evolution. But, can one implement computation with small molecules? If so, at what levels in the hierarchy of computing complexity? We review here recent work in this area establishing that all physically realizable computing automata, from Finite Automata (FA) (such as logic gates) to the Linearly Bound Automaton (LBA, a Turing Machine with a finite tape) can be represented/assembled/built in the laboratory using oscillatory chemical reactions. We examine and discuss in depth the fundamental issues involved in this form of computation exclusively done by molecules. We illustrate their implementation with the example of a programmable finite tape Turing machine which using the Belousov-Zhabotinsky oscillatory chemistry is capable of recognizing words in a Context Sensitive Language and rejecting words outside the language. We offer a new interpretation of the recognition of a sequence of chemicals representing words in the machine's language as an illustration of the “Maximum Entropy Production Principle” and concluding that word recognition by the Belousov-Zhabotinsky Turing machine is equivalent to extremal entropy production by the automaton. We end by offering some suggestions to apply the above to problems in computing, polymerization chemistry, and other fields of science.

Integration of capillary-hydrodynamic logic circuitries for built-in control over multiple droplets in microfluidic networks

Here, we show the successful implementation of advanced sequential logic in droplet microfluidics, whose principles rely on capillary wells establishing stationary states, where droplets can communicate remotely via pressure impulses, influencing each other and switching the device states. All logic operations perform spontaneously due to the utilization of nothing more than capillary-hydrodynamic interactions, inherent for the confined biphasic flow. Our approach offers integration feasibility allowing to encode unprecedentedly long algorithms, e.g., 1000-droplet counting. This work has the potential for the advancement of liquid computers and thereby could participate in the development of the next generation of portable microfluidic systems with embedded control, enabling applications from single-cell analysis and biochemical assays to materials science.

Energy Harvesting and Storage with Soft and Stretchable Materials

This review highlights various modes of converting ambient sources of energy into electricity using soft and stretchable materials. These mechanical properties are useful for emerging classes of stretchable electronics, e-skins, bio-integrated wearables, and soft robotics. The ability to harness energy from the environment allows these types of devices to be tetherless, thereby leading to a greater range of motion (in the case of robotics), better compliance (in the case of wearables and e-skins), and increased application space (in the case of electronics). A variety of energy sources are available including mechanical (vibrations, human motion, wind/fluid motion), electromagnetic (radio frequency (RF), solar), and thermodynamic (chemical or thermal energy). This review briefly summarizes harvesting mechanisms and focuses on the materials' strategies to render such devices into soft or stretchable embodiments.

Distance dependent types of coupling of chemical micro-oscillators immersed in a water-in-oil microemulsion

A system of micro-spheres immersed in a water-in-oil microemulsion (ME) is studied both theoretically and experimentally.

Liquid brains, solid brains

Cognitive networks have evolved a broad range of solutions to the problem of gathering, storing and responding to information. Some of these networks are describable as static sets of neurons linked in an adaptive web of connections. These are 'solid' networks, with a well-defined and physically persistent architecture. Other systems are formed by sets of agents that exchange, store and process information but without persistent connections or move relative to each other in physical space. We refer to these networks that lack stable connections and static elements as 'liquid' brains, a category that includes ant and termite colonies, immune systems and some microbiomes and slime moulds. What are the key differences between solid and liquid brains, particularly in their cognitive potential, ability to solve particular problems and environments, and information-processing strategies? To answer this question requires a new, integrative framework. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Liquid metal droplet solves maze

A room temperature liquid metal features a melting point around room temperature. We use liquid metal gallium due to its non-toxicity. A physical maze is a connected set of Euclidean domains separated by impassable walls. We demonstrate that a maze filled with sodium hydroxide solution is solved by a gallium droplet when direct current is applied between start and destination loci. During the maze solving the droplet stays compact due to its large surface tension, navigates along lines of the highest electrical current density due its high electrical conductivity, and goes around corners of the maze's corridors due to its high conformability. The droplet maze solver has a long life-time due to the negligible vapour tension of liquid gallium and its corrosion resistance and its operation enables computational schemes based on liquid state devices.

Numerical Study on the Characteristics of Boger Type Viscoelastic Fluid Flow in a Micro Cross-Slot under Sinusoidal Stimulation

The cross-slot geometry plays an important role in the study of nonlinear effects of viscoelastic fluids. The flow of viscoelastic fluid in a micro cross-slot with a high channel aspect ratio (AR, the ratio of channel depth to width) can be divided into three types, which are symmetric flow, steady-state asymmetric flow and time-dependent flow under the inlet condition with a constant velocity. However, the flow pattern of a viscoelastic fluid in the cross-slot when a stimulation is applied at inlets has been rarely reported. In this paper, the response of cross-slot flow under an external sinusoidal stimulation is studied by numerical simulations of a two-dimensional model representing the geometry with a maximum limit of AR. For the cases under constant inlet velocity conditions, three different flow patterns occur successively with the increase of Weissenberg number (Wi). For the cases under sinusoidal varying inlet velocity conditions, when the stimulation frequency is far away from the natural frequency of a viscoelastic fluid, the frequency spectrum of velocity fluctuation field shows the characteristics of a fundamental frequency and several harmonics. However, the harmonic frequency disappears when the stimulation frequency is close to the natural frequency of the viscoelastic fluid. Besides, the flow pattern shows spatial symmetry and changes with time. In conclusion, the external stimulation has an effect on the flow pattern of viscoelastic fluid in the 2D micro cross-slot channel, and a resonance occurs when the stimulation frequency is close to the natural frequency of the fluid.

Modeling somatic computation with non-neural bioelectric networks

The field of basal cognition seeks to understand how adaptive, context-specific behavior occurs in non-neural biological systems. Embryogenesis and regeneration require plasticity in many tissue types to achieve structural and functional goals in diverse circumstances. Thus, advances in both evolutionary cell biology and regenerative medicine require an understanding of how non-neural tissues could process information. Neurons evolved from ancient cell types that used bioelectric signaling to perform computation. However, it has not been shown whether or how non-neural bioelectric cell networks can support computation. We generalize connectionist methods to non-neural tissue architectures, showing that a minimal non-neural Bio-Electric Network (BEN) model that utilizes the general principles of bioelectricity (electrodiffusion and gating) can compute. We characterize BEN behaviors ranging from elementary logic gates to pattern detectors, using both fixed and transient inputs to recapitulate various biological scenarios. We characterize the mechanisms of such networks using dynamical-systems and information-theory tools, demonstrating that logic can manifest in bidirectional, continuous, and relatively slow bioelectrical systems, complementing conventional neural-centric architectures. Our results reveal a variety of non-neural decision-making processes as manifestations of general cellular biophysical mechanisms and suggest novel bioengineering approaches to construct functional tissues for regenerative medicine and synthetic biology as well as new machine learning architectures.