3.2 What Is a Reaction-Diffusion Processor?

A reaction-diffusion processor is merely a container, or a reactor, filled with chemicals, or reagents. The reactor transforms input data to output data in a sensible and controllable way via spatial spreading and interaction of the reactants. A medium of the reactor is at rest at the beginning of a computation. Data are transformed into the configuration of a geometrical object; this configuration is cast onto the medium. After projection, the elements of the data configuration form a pattern of local disturbances in the medium's characteristics—drops of a reagent or an excitation pattern. These local disturbances generate waves. The waves spread in the medium. Eventually, the waves, originating from different data sources, meet. They somehow interact and produce either a concentration profile of a precipitate or a stationary pattern of activity. This emerging pattern represents the result of the computation.

We would rather transform our problems to make them solvable in a nonlinear media instead of trying to modify the media to solve the problems.^[1] Most problems with natural spatial parallelism, it is hoped, can be solved in a computation-efficient manner in nonlinear active media (Adamatzky 2001).

A computation in a chemical medium can be accomplished in two ways: structured or architecture-free. The structured computation is implemented in a chemical reactor subdivided into domains with different reagents. Usually the structure of the reactor imitates conventional logical circuits, where wires are simulated by tubes with flowing reagents and logical gates are realized by physical junctions of two or more tubes; alternatively, logical circuits can be drawn as channels in an excitable medium. Such implementation of reaction-diffusion information processing demonstrates the viability of chemical computing in principle but gives nothing new from the computer architecture point of view.

Architecture-free chemical processors are of much more interest. They can be classified into two subtypes: integral computers and spatial computers. In the processors of the first subtype, all spatial differentiation has been eliminated by stirring. The essence of the computation lies in the appearance and development of linked reactions and compounds in which certain characteristics of identity and concentration can be identified as outcomes of useful computation for some problem defined by the initial state and external inputs. Three remarkable examples of stirred processors include a chemical kinetic representation of a Turing machine (Hjelmfelt, Weinberger, and Ross 1991; Hjelmfelt and Ross 1993; Laplante, Pemberton, and Ross, 1995); abstract chemical reactors for parity checking and sorting (Banzhaf, Dittrich, and Rauhe 1996); and metabolic computations (Ziegler, Dittrich, and Banzhaf 1997).

The architecture-free processors of the second subtype exploit local changes and spatial differentiation in nonstirred reactors with typically simpler chemical reactions. Many basic forms of image processing are executed in parallel in such chemical computing devices (Rambidi and Chernavskii 1991; Rambidi 1992; Rambidi, Maximychev, and Usatov 1994, 1994a; Rambidi and Yakovenchuk 1999). The nonstirred active chemical media exhibit also a wide spectrum of dynamic behaviors, which could be extremely useful from a practical point of view (see Adamatzky 2001 for a detailed treatment).

Consider a Belousov-Zhabotinsky medium—the most widely known example of an active chemical medium. In the family of chemical oscillators, the BelousovZhabotinsky thin-layer reaction has been the most investigated, and thus the most appropriate for laboratory experiments. The nonstirred layer of an oscillating reaction can be seen as a massively parallel processor, where every elementary processor is represented by a microvolume reactor. The state of the microvolume can be identified with the reduced/oxidized state of the bromate component. Information processing media of the Belousov-Zhabotinsky type are specialized processors where the statement of the problem, the computational processes, and the results of the computations are all represented in the states (e.g., reagent local concentrations) of the microvolumes. The evolution over time of such reaction-diffusion processors leads to a spatiotemporal dissipative structure that can be interpreted as the solution of the problem. The computation in a Belousov-Zhabotinsky processor takes place when waves are generated, spread, and interact with each other, and perhaps result in external representations of information (e.g., light patterns). The abilities of excitable media for more complex image analysis (Rambidi, Maximychev, and Usatov 1994; Rambidi et al. 2002) and for the solution of spatially based problems (e.g., the shortest path problem; Steinbock, Toth, and Showalter 1995; Rambidi and Yakovenchuk 1998; Rambidi et al. 2002) have been well demonstrated recently.

^[1]As Lord Kelvin wrote in 1876: "It may be possible to conceive that nature generates a computable function … directly and not necessarily by approximation as in the traditional approach".