Plasmodium of \emph{Physarum polycephalum} is a single cell visible by unaided eye. On a non-nutrient substrate the plasmodium propagates as a traveling localization, as a compact wave-fragment of protoplasm. The plasmodium-localization travels in its originally predetermined direction for a substantial period of time even when no gradient of chemo-attractants is present. We utilize this property of \emph{Physarum} localizations to design a two-input two-output Boolean logic gates $ \to $ and $ \to $. We verify the designs in laboratory experiments and computer simulations. We cascade the logical gates into one-bit half-adder and simulate its functionality.
Plasmodium of Physarum polycephalum is a single cell with many diploid nuclei. The cell is visible by naked eye and can grow up to meters when properly cared for. The plasmodium feeds on microscopic food particles, including microbial life forms. The plasmodium placed in an environment with distributed nutrients develops a network of protoplasmic tubes spanning the nutrients' sources.
In its foraging behavior the plasmodium approximates shortest path [13], computes planar proximity graphs [5] and plane tessellations [16], exhibits primitive memory [15], realizes basic logical computing [17], and controls robot navigation [18]. The plasmodium can be considered as a general-purpose computer because the plasmodium simulates Kolmogorov-Uspenskii machinethe storage modification machine operating on a labeled set of graph nodes [4].
In 2004 Tsuda, Aono and Gunji [17] demonstrated in laboratory experiments realisation of Boolean logic negation and conjuction by plasmodium of Physarum polycephalum. In 2004 Adamatzky and De Lacy Costello esablished in numerical simulation [3] and chemical laboratory experiments [9] that by colliding localized excitations, or wave-fragments, in excitable chemical medium one can implement functionally complete set of logical gates. We merge approaches [17] and [3,9] in present paper. We adapt concepts of collision-based computing [2] to realms of Physarum behaviour, and develop experimental prototypes of two-input two-output Boolean logical gates.
The paper is structured as follows. Methods of cultivating and experimenting with plasmodium of Physarum polycephalum are described in Sect. 2. In Sect. 3 we provide experimental evidence of ‘ballistic’ behavior of traveling plasmodium localizations. Experimental Physarum gates are discussed in Sect. 4. In Sect. 5 experimental results are supported by numerical simulation of propagating localizations. The gates are cascaded in one-bit half-adder in Sect. 6. Importance of non-nutrient substrate for gate implementation is highlighted in Sect. 7.
Plasmodium of Physarum polycephalum is cultivated in large plastic boxes, on a wet paper towels and fed with oat flakes. Experiments are conducted in round Petri dishes (9 cm in diameter) and rectangular Petri dishes (12 cm × 12 cm). Channels and junctions physically representing logical gates are cut of a non-nutrient 2% agar plates (Select agar, Sigma Aldrich). The dishes are kept in room temperature (c. 25 o ) in darkness. Images of plasmodium propagating in Petri dishes are taken by Epson Perfection 4490 scanner, resolution 600. Colors are enhanced by increasing saturation and contrast.
We use two-variable Oregonator model to numerically simulate propagation of plasmodium localizations. Our choice and details of the model are outlined below.
Localized excitations in sub-excitable Belousov-Zhabotinsky (BZ) medium behave similarly to pseudopodia of P. polycephalum [6,7]. Sources of nutrients are chemo-attractants for plasmodium, gradients of shade are ‘photo-attractants’ for excitation waves in BZ medium. In [7] we shown how to navigate traveling localizations and growing parts of plasmodium by spatial configuration of attractants. We adopt the analogy developed in [7] and simulate propagating plasmodium using two-variable Oregonator equation [10] adapted to a light-sensitive BZ reaction with applied illumination [8]:
In framework of BZ reaction the variables u and v represent local concentrations of activator, or excitatory component, and inhibitor, or refractory component. With regards to plasmodium of P. polycephalum activator, u, is analogous to concentration, or ’thickness’, of the plasmodium’s cytoplasm at the propagating pseudopodium. Inhibitor, v, combines several factors, when plasmodium is concerned. These factors include rate of nutrients consumption, byproducts of biochemical chains ignited by signals on photo-and chemoreceptors, and concentration of metabolites released by the plasmodium into its substrate.
Parameter sets up a ratio of time scale of variables u and v, q is a scaling parameter depending on rates of activation/propagation and inhibition, f is a stoichiometric coefficient. Constant φ is a rate of inhibitor production. In light-sensitive BZ φ represents rate of inhibitor production proportional to intensity of illumination. In terms of plasmodium φ represents rate of inhibitor proportional to concentration of nutrients, metabolites, illumination, chemical repellents. See detailed comparison of BZ and Physarum in [6,7].
To integrate the system we use Euler method with five-node Laplacian operator, time step ∆t = 0.001 and grid point spacing ∆x = 0.25 (equivalent to 0.6 mm of physical space), = 0.0243, f = 1.4, q = 0.002. The parameter φ characterizes excitability of the simulated medium: the medium is excitable and exhibits ‘classical’ target waves when φ = 0.05 and the medium is subexcitable with propagating localizations, or wave-fragments, when φ = 0.0766.
Propos
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