Research articleTowards fungal computer
Abstract
We propose that fungi Basidiomycetes can be used as computing devices: information is represented by spikes of electrical activity, a computation is implemented in a mycelium network and an interface is realized via fruit bodies. In a series of scoping experiments, we demonstrate that electrical activity recorded on fruits might act as a reliable indicator of the fungi’s response to thermal and chemical stimulation. A stimulation of a fruit is reflected in changes of electrical activity of other fruits of a cluster, i.e. there is distant information transfer between fungal fruit bodies. In an automaton model of a fungal computer, we show how to implement computation with fungi and demonstrate that a structure of logical functions computed is determined by mycelium geometry.
1. Introduction
The fungi are the largest, widely distributed and oldest group of living organisms [1]. The smallest fungi are microscopic single cells. The largest mycelium belongs to Armillaria bulbosa, which occupies 15 hectares and weights 10 tons [2], and the largest fruit body belongs to Fomitiporia ellipsoidea, which at 20 years old is 11 m long, 80 cm wide, 5 cm thick and has an estimated weight of nearly half-a-ton [3]. During the last decade, we produced nearly 40 prototypes of sensing and computing devices from the slime mould Physarum polycephalum [4], including the shortest path finders, computational geometry processors, hybrid electronic devices, see the compilation of the latest results in [5]. We found that the slime mould is a convenient substrate for unconventional computing; however, the geometry of the slime mould’s protoplasmic networks is continuously changing, thus preventing fabrication of long-living devices, and slime mould computing devices are confined to experimental laboratory set-ups. Fungi Basidiomycetes are now taxonomically distinct from the slime mould; however, their development and behaviour are phenomenologically similar: mycelium networks are analogous to the slime mould’s protoplasmic networks, and the fruit bodies are analogous to the slime mould’s stalks of sporangia. Basidiomycetes are less susceptible to infections; when cultured indoors, especially commercially available species, they are larger in size and more convenient to manipulate than slime mould, and they could be easily found and experimented on outdoors. This makes the fungi an ideal object for developing future living computing devices. Advancing our recent results on electrical signalling in fungi [6], which in a way is similar to electrical signalling in plants [7], we are exploring the computing potential of fungi in the present paper. We introduce a mycelium basis of fungal computing and define an architecture of fungal computers in §2. Findings on the electrical activity of fungi [6,8,9] are augmented in §3 by demonstrations of endogenous spiking, signalling between fruit bodies and signalling by fruit bodies about the state of the growth substrate. In experiments, we use oyster mushrooms, species pleurotus, family Tricholomataceae, because of their wide availability and interesting properties [10–12]. We imitate electrical activity of the mycelium in a discrete model in §4. There we encode logical values into presence/absence of spikes in fruit bodies and show how logical functions can be executed. We also demonstrate that a geometrical structure of mycelium, in the model this is represented by a random planar set structure, affects families of logical circuits computed. Directions of future research on fungal computing are outlined in §5.
2. Mycelium basis of fungal computer
Mycelium propagates by a foraging front and consolidations of mycelial cords behind the front [13]. The foraging front travels outward and produces fruit bodies (figure 1a,b). The front is also manifested by rings of increased vegetation and ‘exhausted’ soil (figure 1c), see historical overviews in [14,15]. Propagation/extension of the ring is due to exhaustion of nutrients necessary for fungi growth.
Figure 1. Development of mycelium in nutrient-rich (a–d) and nutrient-poor (e) substrates. (a) A cross-section of a fairy ring produced by Marasmius Oreades. Reproduced with permission from [14]. (b) A view from above: the mycelium is dark red, the fruits are red and the dried fruits are blue. (c) Vegetation profile corresponding to (b): outer stimulated (light green) and inner stimulated (dark green) zones of increased vegetation, dead zone (grey) of reduced vegetation and inside zone (yellow) of ambient vegetation. (d) Rings and fragments of rings of Agaricus campestris (dark red) inside 65 m ring of Calvatia ciathyiformi (fresh fruits are red, dry fruits are blue). Reproduced with permission from [15]. (e) A development pattern of a single mycelial system of Phanerochaete velutina. Lines are mycelial cords. Orange/grey rectangles are inoculum blocks, white rectangles decayed inoculum blocks. Scale bar, 1 m. Reproduced with permission from [16]. (f) Photo of mycelium propagating on a nutrient-rich cocoa substrate. (g) Zoomed view of the propagating front where branching is articulated. (h) Schematic architecture of a fungal computer. Fruit bodies 
are I/O interface. Mycelium network C is a distributed computing device.
A mycelial growth pattern is determined by nutritional conditions and temperature [13,17–21], as also demonstrated in computer models in [22,23]. A complexity of the mycelium network, as estimated by a fractal dimension, is determined by the nutrient availability and the pressure built up between various parts of the mycelial network [24]. In domains with high concentration of nutrients mycelia branch; in poor nutrient domains mycelia stop branching [25]. As indicated in [18] optimization of resources is evidenced by the inhibitory effect of contact with baits on the remainder of the colony margin, regression of mycelium originating from the inoculum associated with the renewed growth from the bait, and differences between growth patterns of large and small inocula/baits (figure 1d). Optimization of the mycelial network [20] is quite similar to that of the slime mould P. polycephalum, as evidenced in our previous studies, especially in terms of proximity graphs [26] and transport networks [27]. Exploration of confined spaces by hyphae has been studied in [28–32], and evidence of the efficiency of the exploration provided. All the above indicate that (i) fungal mycelium can solve the same range of computational geometry problems as the slime mould P. polycephalum does [5]: shortest path [33–37], Voronoi diagram [38], Delaunay triangulation, proximity graphs and spanning tree, concave hull and, possibly, convex hull, and, with some experimental efforts, the travelling salesman problem [39], and (ii) by changing environmental conditions we can reprogram a geometry and graph-theoretical structure of the mycelium networks and then use electrical activity of fungi [6,8,9] to realize computing circuits.
A mycelium is hidden underground, therefore only configurations of fruit bodies can be seen as outputs of a geometric computation implemented by propagating mycelium. Consider the following example of interacting foraging fronts. Propagation of wavefronts of fungi at large scale was described by Shantz & Piemeisel in Yuma, Colorado, on June 1916 [15]. This is illustrated in (figure 1d). There are two species of fungi, Agaricus campestris and Calvatia ciathyiformi. The ring of C. ciathyiformi was nearly 65 m in diameter with 50 fresh fruits. There are several smaller rings of A. campestris: in some places, they interrupt ‘wavefronts’ of C. ciathyiformi growth. In theory, such interaction of wavefronts of different species can be used to approximate the Voronoi diagram, as has been done previously with slime mould [38,40], when planar data points are represented by locations of fungi inoculates.
Also, notice the characteristic location of dry fruits of C. ciathyiformi (blue in figure 1b,d); this brings in an analogy with an excitable medium: the fresh fruits are analogous to the ‘excitation’ wavefront and the dried fungi to ‘refractory’ tails of the excitation waves. Fungi rings can extend up to 200 m diameter [15]. The analogy between fungi foraging fronts and excitation wavefronts indicates that already algorithms for computing with wavefronts in excitable medium [41,42] can be realized with foraging mycelium. That said, solving geometrical problems with mycelium networks does not sound feasible, because the mycelium growth rate is very low, thus the solution of any problem could take weeks and months, if not years, for problems in which spatial representation covers hundreds of metres.
In contrast to the slow growth of mycelium, fungi exhibit an electrical response to stimulation in a matter of seconds or minutes [6,8,9]. Therefore, a computation using electrical impulses propagating in and modified by the mycelium networks seems to be promising. We propose the following architecture of a fungal computer 
(figure 1h): a mycelium C is a processor, or rather a network of processors, and fruit bodies 
comprise I/O interface of the fungal computer. The information is represented by spikes of electrical potential. Thus, a state of 
at a time step t could be either binary, depending on whether a spike is present or absent at time t, or multiple valued, depending on a number of spikes in a train, duration of spikes and their amplitudes. Any fruit body can be considered as input and output and the fungal computer 
: 
, where w is a positive integer. Details on how exactly 
could compute will be analysed in §4; first let us consider, §3, a few examples from laboratory experiments on endogenous spiking, response of fungi to stimulation and evidence of communication between fruit bodies.
3. Electrical activity of fungi
3.1. Experimental procedure
We used commercial mushroom growing kits1 of pearl oyster mushrooms P. ostreatus. In the experiments reported seven growing kits were used. For each kit, we recorded electrical activity of the first flush of fruiting bodies only because the first flush usually provides the maximum yield of fruiting bodies [43] and the growing mycelium in the substrate was less affected by products of fungi metabolism [44,45]. Each substrate’s bag was 22 cm × 10 cm × 10 cm, 800–900 g in weight. The bag was cross-sliced 10 cm vertical and 8 cm horizontal and placed in a cardboard box with 8 cm × 10 cm opening. Experiments were conducted at room temperature in constant (24 h) ambient lighting of 10 lux. Electrical potential of fruit bodies was recorded from the second to third day of their emergence. Resistance between cap and stalk of a fruit body was 1.5 MΩ on average between any two heads in the cluster 2 MΩ (measured by Fluke 8846 A). We recorded the electrical potential difference between cap and stalk of the fruit body. We used sub-dermal needle electrodes with twisted cable.2 A recording electrode was inserted into the stalk and a reference electrode in the translocation zone; figure 2b shows the cross-section of a fruit body showing the translocation zone, drawing by Schütte [46], of the cap; the distance between electrodes was 3–5 cm. In each cluster, we recorded four to six fruit bodies simultaneously (figure 2a) for 2–3 days. Electrical activity of fruit bodies was recorded with an ADC-24 High-Resolution Data Logger.3 The data logger employs differential inputs, galvanic isolation and software-selectable sample rates—these contribute to a superior noise-free resolution; its 24-bit A/D converter maintains a gain error of 0.1%. Its input impedance is 2 MΩ for differential inputs, and offset error is 36 μV in ±1250 mV range use. We recorded the electrical activity one sample per second; during the recording the logger made as many measurements as possible (typically up 600) per second then saved the average value.
Figure 2. Experimental set-up. (a) Photographs of fruit bodies with electrodes inserted. (b) Position of electrodes in relation to a translocation zone. Drawing of fruit body is from Schütte [46]; a scheme of electrodes is ours.
3.2. Endogenous spiking
As we previously discussed in [6] fruits show a rich family of endogenous, i.e. not caused by purposeful stimulation during experiments, spiking behaviour. Spiking patterns of several types have been observed during simultaneous recording from the different fruits of the same cluster. Recordings of four fruit bodies during nearly 20 h are shown in figure 3. Most pronounced patterns are the trains of large amplitude spikes (figure 3b) and the wave-packets (figure 3c).
Figure 3. Co-existence of various types of electrical activity in fruit bodies of the same cluster. (a) Electrical potential recorded for over 16 h on four fruits. (b) Zoomed in area marked ‘A’ in (a). Large amplitude spikes. (c) Zoomed in area marked ‘B’ in (a). Two wave-packets.
Large amplitude spikes (figure 3b) have average amplitude 0.77 mV, s.d. 0.29. The spikes are usually observed in pairs. Average distance between spikes in a pair is 238 s, s.d. 81 s. Time interval between the two largest, over 0.8 mV, spikes varies from 20 to 48 min. Two wave-packets are shown in figure 3c. The first wave-packet, roughly 91 min long, consists of 10 spikes. Their amplitude varies from 0.05 mV at the beginning to 0.1 mV at the eclipse. The shortest spike is 362 s duration; the longest, in the middle of the waveform, is 705 s. The second most pronounced wave-packet consists of 19 spikes and lasts for 163 min. Amplitudes of the spikes vary from 0.05 mV at the beginning of the wave-packet to 0.2 mV in the middle. The shortest spike is 457 s long, and the longest spike is 609 s long. Average spike duration is 516 s (
); average amplitude is 0.12 mV (
).
3.3. Signalling between fruits
To check if fruits in a cluster would respond to stimulation of their neighbours, we conducted the experiments illustrated in figure 4. Note, fruits which electrical potential recorded were not stimulated (figure 4a). Recording on one of the fruiting bodies (Ch3) shows periodic oscillations: average amplitude 0.47 mV ( Figure 4. Stimulation of fruits. (a) Set-up of recording, sites of stimulation and location of electrode pairs corresponding to channels Ch1–Ch9. (b) Electrical potential recording on five mushrooms. Channel Ch1 is shown by black, Ch3 red, Ch5 blue, Ch7 green and Ch9 orange. The following stimuli have been applied to fruiting bodies. (S1) 3450 s: start open flame stimulation for 20 s. (S2) 5310 s: start open flame stimulation for 60 s. (S3) 7000 s: ethanol drop is placed on a cap of the fruit. (S4) 10440 s: 15 mg of table salt is placed on a cap of one of fruiting bodies.
), average duration of a spike is 1669 s (s.d. 570) and average period 1819 s (s.d. 847) (figure 4b). Other recorded fruiting bodies also show substantial yet non-periodic changes in the electrical potential with amplitudes up to 1 mV. A thermal stimulation, S1 and S2, in figure 4b, leads to a temporal disruption of oscillation of the fruit Ch3, and low-amplitude short-period spikes in other recorded fruits Ch1, Ch2, Ch4–Ch9. The response of an intact fruit to stimulation of another fruit with an open flame consists of a depolarization approximately 0.02 mV amplitude, approximately 6 s duration, followed by a repolarization approximately 0.2 mV amplitude, approximately 9 s duration. The depolarization starts approximately 3 s after start of stimulation. This might indicate that it is caused by action potential-like fast dynamical changes. High-amplitude repolarization takes place at approximately 13 s after start of stimulation, when a substantial loci of a fruit cap becomes thermally damaged. Application of ethanol (S3, figure 4) and salt (S4, figure 4) leads to a 0.15–0.45 mV drop in electrical potential; recovery occurs in approximately 1200 s.
In the experiment illustrated in figure 5, we stimulated fruits with an open flame, salt and sugar, and recorded electrical responses from non-stimulated neighbours. Application of sugar did not cause any response, and thus can be seen as a control experiment on mechanical stimulation. No responses to a short-term (approx. 1–2 s) mechanical stimulation were recorded. Fruits respond to thermal stimulation of a member of their cluster by a couple of action-potential like impulses (figure 5b). The amplitude of the response differs from fruit to fruit, and more likely depends not only on the distance between the recorded fruit and the stimulated fruit but also on the position of electrodes. The fruits respond to saline stimulation of their neighbour in a more uniform manner (figure 5c). In 12–15 s after the application of salt, the electrical potential of the recorded fungi drops by approximately 0.2, Figure 5. Response of fruits to stimulation of neighbouring fruits. (a) Photo of the fruit cluster taken after experiments were completed. The stimulated fruits are indicated by arrows: 20 mg of salt (A), open flame of a butane lighter, temperature 600–800°C for 60 s (B), 20 mg sugar (C). (b) Electrical potential of five non-stimulated fruits during stimulation of a fruit from their cluster with an open flame: start of the thermal stimulation is shown by arrow ‘A’, end of the stimulation by arrow ‘B’. (c) Electrical potential of five fruits recorded during stimulation of a fruit from their cluster with salt, moment when salt was placed on a cap is shown by arrow labelled ‘A’.
. The potential recovers in approximately 30 s.
3.4. Signalling about state of growth substrate
To test the response of fruits to environmental changes in the growth substrate, we injected 150 ml of sodium chloride ( Figure 6. Electrical response of a fruit body to the injection of saline solution in the substrate.
) in the substrate and recorded the electrical potential of a fruit. The moment of injection is reflected in the spike of electrical potential with amplitude 9 mV. This spike might be caused by mechanical stimulation of mycelium (figure 6). Four hours after injection, the recorded fruit exhibited trains of spiking activity. Amplitude of spikes vary from 0.29 to 12.3 mV, average 4.1 mV (
). Duration of a spike varies from 33 s to 151 s, average 71 s (
). Periods vary from 450 s to 2870 s, average duration 953 s (
). The spikes might be caused by an osmotic function of mycelium due to intake of saline solution and transported into the caps of fruits [47] (cited by Gallé et al. [7]).
4. Automaton model of a fungal computer
To imitate propagation of depolarization waves in the mycelium network, we adopt an automaton model. The automaton models are proved to be appropriate discrete models for spatially extended excitable media [48–50] and verified in models of calcium wave propagation [51], propagation of electrical pulses in the heart [52–54] and simulation of action potential [55,56]. We represent a fungal computer by an automaton 
, where 
is a planar set, each point 
takes states from the set 
, excited (
), refractory (•), resting (○), and updates its state in a discrete time depending on its current state and state of its neighbourhood 
; r is a neighbourhood radius, θ is an excitation threshold and δ is refractory delay. All points update their states in parallel and by the same rule:
) at the moment 
if a number of its excited neighbours at the moment t—
—exceeds a threshold 
. Excited point 
takes refractory state • at the next time step 
, at the same moment a counter of refractory state 
is set to the refractory delay 
. The counter is decremented, 
at each iteration until it becomes 0. When the counter 
becomes zero the point p returns to the resting state ○.
Architecture of C was chosen as follows. We randomly distributed Figure 7. Fungal computer architecture. (a) Visualization of C. (b) Probability of point in C as a function of distance from R. (c) Distribution of a number of neighbours for 
points in a ring with small radius 
and large radius 1 (figure 7a). To reflect the higher density of mycelium near the propagation front and decay of mycelium inside the propagating disc we distributed points with a probability described by a quadratic function 
, where 
(figure 7b); the function reflects biomass distribution in a cross-section of a fairy ring [57,58]. To imitate fruit bodies, we distributed points in horizontal (L and R) and vertical (U and D) domains with size 0.27 by 0.023 (figure 7a); each domain contains 370 points distributed randomly. Distributions of a point’s number of neighbours for neighbourhood radius 
are shown in figure 7c. We have chosen 
(§4.2.1), 
(§4.2.2), 
, 
in the reported experiments for the following reasons. A median radius 
neighbourhood size is approximately 600 times less than a number of points in C (figure 7d); thus a locality of the automaton state updates is assured. Excitation threshold 
is critical for 
with 
(figure 7e), i.e. it assures that excitation wavefronts propagate for at least half of the perimeter of the ring (figure 7a).
. A number of neighbours depending on a neighbourhood radius 
. (d) Prevailing number of neighbours for 
. (e) Critical values of excitation threshold 
for 
.
4.1. Automaton action potential
The automaton 
supports propagation of excitation waves, fronts of which are represented by points in the state 
and tails by points in state •. We assume a point in the state 
has higher electrical potential than a point in the state •. To imitate a voltage difference between electrodes inserted in fruit bodies we select two domains, 
and 
, in each of four fruit bodies and calculate a voltage difference V between domains as follows: 
, where 
, 
, and 
. This imitates an electrical potential difference between electrodes inserted in the cap and the step of a fruit, as illustrated in figure 2.
We excite the fungal automaton Figure 8. Dynamics of the excitation of two fruit automaton 
by assigning points of a selected fruit body states 
. This is equivalent to thermal or mechanical stimulation of fruits in our laboratory experiments. We record voltage on fruit bodies at every iteration of the automation evolution. Two examples are shown in figure 8. For simplicity, we consider 
with only two fruit bodies: L and R. When right fruit R is stimulated (see first spike in figure 8c) an excitation wave propagates into the mycelium ring C and splits into two waves (figure 8a). Excitation waves enter fruit bodies when they reach them, which is reflected in spikes of the calculated potential. If the medium was regular (as e.g. a lattice) the excitation wavefronts would annihilate each other when colliding. However, the disorganized structure of the conductive medium leads to formation of the new excitation waves (see train of three spikes in figure 8c). New waves travel along the ring but eventually die out. Excitation of the left fruit L (figure 8b) generate two waves propagating along the ring. However, in this case, due to irregularity of the excitable medium a temporary wave generator is born in the upper part of the ring (2nd snapshot in figure 8b). The generator produces pairs of waves (3rd snapshots in figure 8b). The transition from sparse spiking to wave-packets is similar to experimental results shown in figure 3. In this example, we witness that fungal responses to stimulation of the left and the right fruits are different. This can be employed in designs of computing schemes with fungal automata, as outlined in the next section.
: in scenarios of right R (
) and left L (
) fruits excited. (
) Exemplar snapshots of the dynamics. (
) Electrical potential measured. Dashed line is a potential measured on R and solid line is a potential measured on L.
4.2. Logical functions computed by 
Dynamics of excitation wave propagation and interaction in C is determined by exact configuration of the planar set. The configurations are generated at random; therefore we expect fungal automaton to implement different functions for each, or nearly, configuration. This is illustrated by the two following examples. Here we use four fruit bodies acting as both inputs and outputs. A logical input True, or ‘1’, is represented by excitation of a chosen fruit body. A logical output True, or ‘1’, is recognized as one or more impulses recorded at the fruit body some time interval after stimulation: we started recording 40 iterations (the parameter w introduced in §2) of automaton evolution, after stimulation and stopped recording 130 iterations. Let us consider two examples. The sets C are generated randomly, therefore the dynamics of excitation is expected to be different in these examples.
4.2.1. First example
In the first example, we consider the configuration C shown in figure 9a. Excitation dynamics for inputs Figure 9. (a–f) Snapshots of excitation dynamics in a four-fruit fungal automaton for inputs Figure 10. (a–l) Snapshots of excitation dynamics in a four-fruit fungal automaton for inputs Figure 11. Voltage measured on four fruits for inputs (a) Figure 12. Response of the fungal automaton for input values 
, 
, 
, 
is shown in figure 9 and for inputs 
, 
, 
, 
in figure 10. When fruits U and D are stimulated (figure 9) the fungal automaton 
responds with spikes on fruits L and R (figure 11a). Excitation dynamics is less trivial when fruits L and R are stimulated (figure 10): automaton 
responds with two voltage spikes at fruit D, and a single spike at fruits U and R (figure 11b). When only fruit R is stimulated the automaton 
responds with pairs of spikes on all fruits but L (figure 12b). The automaton 
responds with a spike on fruit L just before cut-off time 150. After the 150th iteration, two centres of spiral waves are formed and thus the fungal automaton exhibits regular trains of spikes on all fruit bodies (figure 12a), similar to the dynamics of excitation shown in figure 4b.
, 
, 
, 
.
, 
, 
, 
.
, 
, 
, 
, see dynamics in figure 9, and (b) 
, 
, 
, 
, see dynamics in figure 10. Voltage recorded on fruit R is plotted with red colour, U blue, L green and D magenta.
, 
, 
, 
. (a) A snapshot of the automaton taken at 350th step of evolution. (b) Voltage recorded on the fruit R is plotted with red colour, U blue, L green and D magenta.
We stimulated the fungal automaton with 16 combinations of input variables and constructed a tabular representation of a function realized by the automaton (table 1), where R, U, L, D are values of input variables, and 
, 
, 
, 
are values of output variables. Assuming one or two impulses on the fruits represent True we have the following functions implemented by the fungal automaton:
and 
.
Figure 13. Equivalent logical circuit for fruit D implemented by the fungal automaton 
, with configuration of C shown in figure 9a.
| R | U | L | D |  |
 |
 |
 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 2 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 2 |
| 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 2 |
| 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 1 | 0 | 0 | 2 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
4.2.2. Second example
In the second example, discussed below, we used a random configuration of points C4 and the automaton 
with 
, 
and 
. Frames and videos of the experiments are available at https://drive.google.com/open?id=1XSTQt7lD2KGUHCuJchJ--ah6CO-XUSap. Dynamics of electrical potential for 15 combinations of input values is shown in figure 14. The response of the automaton is illustrated in table 2. Assuming one impulse or two impulses on the fruits symbolize ‘1’, we have the following functions realized on each of the fruit bodies:
Figure 14. (a–o) Dynamics of electrical potential on fruits, in experiment with random seed 357556317, in response to stimulation of inputs. The inputs are shown in the captions in the format 
. Spikes appearing during first 10–15 iterations are input spikes. All other spikes are outputs. Voltage recorded on fruit R is plotted with red colour, U blue, L green and D magenta.
| R | U | L | D |  |
 |
 |
 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 2 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 | 2 | 0 | 2 |
| 0 | 0 | 1 | 1 | 0 | 2 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 2 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 2 | 0 | 2 |
| 0 | 1 | 1 | 1 | 0 | 2 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 2 | 2 | 0 |
| 1 | 0 | 1 | 0 | 0 | 2 | 1 | 0 |
| 1 | 0 | 1 | 1 | 0 | 2 | 0 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 | 2 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 2 | 0 | 2 |
| 1 | 1 | 1 | 1 | 0 | 2 | 0 | 1 |
5. Discussion
We proposed that fungi can be used as computing devices: information is represented by spikes of electrical activity, a computation is implemented in a mycelium network and an interface is realized via fruit bodies. In laboratory experiments, we demonstrated that fungi respond with spikes of electrical potential to stimulation of their fruit bodies. Thus, we can input data into a fungal computer via mechanical, chemical and electrical stimulation of the fruit bodies. Electrical signalling in fungi, previously evidenced during intracellular recording of electrical potential [8,9], is similar to the signalling in plants [7,59]. The experimental results provided in the paper are of illustrative nature with focus on architectures of potential computing devices; a statistical analysis of spontaneous spiking behaviour of the fungi can be found in [6]. Further extensive studies will be necessary to obtain statistical results on fungal response to a stimulation, particularly on the response’s dependence on a strength of stimuli and inter-species differences in their responses.
Voltage spikes travelling along mycelium networks might be seen as analogous, but of different physical and chemical nature, to oxidation wavefronts in a thin-layer Belousov–Zhabotinsky (BZ) medium [60,61]. Thus, in future, we could draw some useful designs of fungal computers based on an established set of experimental laboratory prototypes of BZ computing devices. The prototypes produced are image processes and memory devices [62–64], logical gates implemented in geometrically constrained BZ medium [65,66], approximation of shortest path by excitation waves [67–69], memory in BZ micro-emulsion [64], information coding with frequency of oscillations [70], on-board controllers for robots [71–73], chemical diodes [74,75], neuromorphic architectures [42,76–80] and associative memory [81,82], wave-based counters [83] and other information processors [84–87]. First steps have been already made towards prototyping arithmetical circuits with BZ: simulation and experimental laboratory realization of gates [41,65,66,88–90], clocks [91] and evolving logical gates [92]. A one-bit half-adder, based on a ballistic interaction of growing patterns [93], was implemented in a geometrically constrained light-sensitive BZ medium [94]. Models of multi-bit binary adder, decoder and comparator in BZ are proposed in [95–98]. These architectures employ crossover structures as T-shaped coincidence detectors [99] and chemical diodes [75] that heavily rely on heterogeneity of geometrically constrained space. By controlling excitability [100] in different loci of the medium, we can achieve impressive results, as it is demonstrated in works related to analogues of dendritic trees [79], polymorphic logical gates [101], and experimental laboratory prototype of four-bit input, two-bit output integer square root circuits based on alternating ‘conductivity’ of junctions between channels [102].
Spikes of electrical potential are not the only means of implementing information processing in fungal computers. Microfluidics could be an additional computational resource. Eukaryotic cells, including slime moulds and fungi, exhibit cytoplasmic streaming [103,104]. In experiments with the slime mould P. polycephalum, we found that when a fragment of protoplasmic tube is mechanically stimulated, cytoplasmic streaming in this fragment halts and the fragment’s resistance substantially increases. Using this phenomenon, we designed a range of logical circuits and memory devices [105]. These designs can be adopted in prototypes of fungal computers; however, more experiments would be necessary to establish optimal ways of mechanical addressing of strands of mycelium.
5.1. Programmability
To program fungal computers, we must control the geometry of the mycelium network. The geometry of the mycelium network can be modified by varying nutritional conditions and temperature [13,21–23], especially the degree of branching is proportional to the concentration of nutrients [25], and a wide range of chemical and physical stimuli [106]. Also, we can geometrically constrain it [28–32]. The feasibility of shaping similar networks has been demonstrated in [107]: high-amplitude, high-frequency voltage applied between two electrodes in a network of protoplasmic tubes of P. polycephalum leads to abandonment of the stimulated protoplasmic without affecting the non-stimulated tubes and low-amplitude, low-frequency voltage applied between two electrodes in the network enhances the stimulated tube and encourages abandonment of other tubes [107].
5.2. Parameters of fungal computers
Interaction of voltage spikes, travelling along mycelium strands, at the junctions between strands is a key mechanism of fungal computation. We can see each junction as an elementary processor of a distributed multi-processor computing network. We assume the number of junctions is proportional to the number of hyphal tips. There are estimated to be 10–20 tips per 1.5–3 mm [108] of a substrate. Without knowing the depth of the mycelial network, we go for the safest lower margin of two-dimensional estimation: 50 tips 
. Considering that the largest known fungi, Armillaria bulbosa, populates over 15 hectares [2], we could assume that there could be 
branching points, that is nearly a trillion of elementary processing units. With regards to a speed of computation by fungal computers, Olsson & Hansson [9] estimated that electrical activity in fungi could be used for communication with message propagation speed 
(this is several orders slower than the speed of a typical action potential in plants: from 
to 
[109]). Thus, it would take about half an hour for a signal in the fungal computer to propagate 1 m. The low speed of signal propagation is not a critical disadvantage of potential fungal computers, because they never meant to compete with conventional silicon devices.
5.3. Application domains
Likely application domains of fungal devices could be large-scale networks of mycelium which collect and analyse information about environment of soil and, possibly, air and execute some decision-making procedures. Fungi ‘possess almost all the senses used by humans’ [106]. Fungi sense light, chemicals, gases, gravity and electric fields. Fungi show a pronounced response to changes in a substrate pH [110], demonstrate mechanosensing [111]; they sense toxic metals [112], CO2 [113] and direction of fluid flow [114]. Fungi exhibit thigmotactic and thigmomorphogenetic responses, which might be reflected in dynamic patterns of their electrical activity [115]. Fungi are also capable of sensing chemical cues, especially stress hormones, from other species [116], thus they might be used as reporters of health and well-being of other inhabitants of the forest. Thus, fungal computers can be made an essential part of distributed large-scale environmental sensor networks in ecological research to assess not just soil quality but the overall health of the ecosystems [117–119].
5.4. Further studies
In automaton models of a fungal computer, we have shown that a structure with Boolean functions realized depends on the geometry of a mycelial network. In further studies, we will tackle four aspects of fungal computing as follows.
First, ideas developed in the automaton model of a fungal computer should be verified in laboratory experiments with fungi. In the automaton model developed, we did not take into account a full range of parameters recorded during experimental laboratory studies: origination and propagating of impulses have been imitated in the dynamics of the final state machines. To keep the same physical nature of inputs and outputs, we will consider stimulating fruit bodies with alternating electrical current. To cascade logical circuits implemented in clusters of fruit bodies, we might need to include amplifiers in the hybrid fungi-based electrical circuits.
Second, in experiments we evidenced electrical responses of fruits to thermal and chemical stimulation; in some cases, we observed trains of spikes. This means we could, in principle, apply experimental findings of Physarum oscillatory logic [120], where logical values are represented by different types of stimuli, apply threshold operations to frequencies of the electrical potential oscillations, and attempt to implement logical gates. Another option would be to adopt ideas of oscillatory threshold logic reported in [121]; however, this might require unrealistically precise control of the geometry of mycelial networks.
Third, we might consider measuring electrical potential between fungal bodies. In the set-up shown in figure 15a,b, we recorded the electrical potential difference between neighbouring fruits. An example of the recorded activity is shown in figure 15b. Average distance between spikes is 4111 s ( Figure 15. Electrical potential difference between two neighbouring fruits. (a) Position of electrodes when measuring potential different between fungal bodies. (b) Part of experimental set-up. (c) Exemplar plot of electrical potential.
). Average duration of a spike is 287 s (
). Average amplitude is 0.25 mV (
). There is a possibility that patterns of oscillation will be affected by stimulation of other fruit bodies in the cluster. This might lead to a complementary method of computing with fungi.
Fourth, we must learn how to programme the geometry of mycelial networks to be able to execute not arbitrary, as demonstrated in the automaton model, but predetermined logical circuits. The computer modelling approach may be based on formal representation of mycelial networks as a proximity graph, e.g. relative neighbourhood graph [122] (figure 16), and then dynamically updating the graph structure till a desired logical circuit is implemented on the graph. Connection rules in proximity graphs are fixed, therefore the graph structure can be updated only by adding or removing nodes. A new set of nodes can be added to a living mycelial network by placing sources of nutrients. However, due to the very slow growth rate of mycelium, this could be unfeasible. Thus, the best way would be to focus only on removing parts of the mycelial network. When parts of a network are removed the network will re-route locally, and the set of logical functions implemented by the network will change.
Figure 16. Representation of a mycelium by relative neighbourhood graph with 2000 nodes. Black discs are fruit bodies.
Data accessibility
Videos of computer experiments are accessible at https://doi.org/10.5281/zenodo.1451496.
Competing interests
I declare I have no competing interests.
Funding
I received no funding for this study.
Acknowledgements
I acknowledges pearl oyster mushrooms P. ostreatus for their cooperation in the studies.
Footnotes
Endnotes
4 File with coordinates is available here https://drive.google.com/open?id=1wcmo8DkcKN49rDSRFGm9hnIjJj5LTbDL.
