Towards 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.

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Research
Cite this article: Adamatzky A. 2018 Towards
fungal computer. Interface Focus 8: 20180029.
http://dx.doi.org/10.1098/rsfs.2018.0029
Accepted: 4 September 2018
One contribution of 10 to a theme issue
‘Computation by natural systems’.
Subject Areas:
biomathematics, biomedical engineering,
computational biology
Keywords:
natural computation, fungi, unconventional
computing
Author for correspondence:
Andrew Adamatzky
e-mail: andrew.adamatzky@uwe.ac.uk
Towards fungal computer
Andrew Adamatzky
Unconventional Computing Lab, UWE, CSCT, Bristol, UK
AA, 0000-0003-1073-2662
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 compu-
tation 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 organ-
isms [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 Phy-
sarum 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 infec-
tions; 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. Advan-
cing 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. Find-
ings 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 experiment s, we use oyster mushroom s, species pleurotus, family Tricholoma-
taceae, 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
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random planar set structure, affects families of logical cir-
cuits 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 over-
views in [14,15]. Propagation/extension of the ring is due to
exhaustion of nutrients necessary for fungi growth.
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 nutri-
ent 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 differ-
ences 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]. Explora-
tion of confined spaces by hyphae has been studied in
[28–32], and evidence of the efficiency of the exploration pro-
vided. 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
(e)
(f)
(b)(a)
(c)(d)
(g)(h)
D1
D2
D3
D8
D4D5D6
D7
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 D1,D2,... are I/O interface. Mycelium network Cis a distributed computing device.
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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 confi-
gurations of fruit bodies can be seen as outputs of a geometric
computation implemented by propagating mycelium. Consider
the following example of interacting foraging fronts. Propa-
gation 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:insomeplaces,
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 pre-
viously 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 algor-
ithms 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 min-
utes [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 A(figure 1h): a mycelium Cis a processor,
or rather a network of processors, and fruit bodies D1,D2,...
comprise I/O interface of the fungal computer. The infor-
mation is represented by spikes of electrical potential. Thus, a
state of Dt
iat a time step tcould 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 con-
sidered as input and output and the fungal computer
A:Dtþw¼F(D), where wis a positive integer. Details on
how exactly Acould 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 kits
1
of pearl oyster
mushrooms P. ostreatus. In the experiments reported seven
(b)(a)
V
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 Schu¨tte [46]; a scheme of electrodes is ours.
A
B
electrical potential (mV)
–1
0
1
2
3
4
0 20 000 40 000 60 000
–0.2
0
0.2
40 000 45 000
electrical potential (mV)
0
0.5
1.0
1.5
0 5000 10 000 15 000
electrical potential (mV)
–0.15
–0.10
–0.05
0
0.05
time (s)
35 000 40 000 45 000 50 000
(b)
(a)
(c)
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.
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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].
Eachsubstrate’sbagwas22cm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 MVon average between any two heads in the
cluster 2 MV(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 2bshows
S1 S4
S2
S3
Ch1
Ch3
Ch5
Ch7
Ch9
electrical potential (mV)
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1.0
time (s)
0 5000 10 000 15 000
Ch1
Ch3Ch5Ch7Ch9S2S1S3S4
(b)(a)
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.
AB
electrical potential (mV)
–1.0
–0.5
0
0.5
1.0
1.5
250 300 350 400 450 500 550
A
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
0.1
0.2
time (s)time (s)
3600 3650 3700
ABC
(b)
(a)
(c)
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’.
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the cross-section of a fruit body showing the translocation zone,
drawing by Schu
¨tte [46], of the cap; the distance between elec-
trodes 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 MVfor differential inputs, and offset
error is 36 mVin+1250 mV range use. We recorded the electri-
cal 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.
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).
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 begin-
ning to 0.1 mV at the eclipse. The shortest spike is 362 s
duration; the longest, in the middle of the waveform, is 705s.
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 516s (
s
¼56);
average amplitude is 0.12 mV (
s
¼0:06).
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 (
s
¼0:19), 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 withamplitudes 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 approxi-
mately 0.02 mV amplitude, approximately 6 s duration,
followed by a repolarization approximately 0.2 mV amplitude,
approximately 9 s duration. The depolarization starts approxi-
mately 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 electri-
cal 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,0:8 mV. 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
(6 mg ml1) in the substrate and recorded the electrical poten-
tial 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 (
s
¼3:5 mV). Duration of a spike
varies from 33 s to 151 s, average 71 s (
s
¼32 s). Periods
vary from 450 s to 2870 s, average duration 953 s (
s
¼559).
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 Galle
´et al. [7]).
electrical potential (mV)
2
4
6
8
10
12
20 000 30 000 40 000 50 000 60 000
electrical potential (mV)
2
4
6
8
10
12
time (s)
43 500 44 000 44 500 45 000
(b)
(a)
Figure 6. Electrical response of a fruit body to the injection of saline solution
in the substrate.
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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 ver-
ified 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 A¼hC,Q,r,h,
u
,
d
i,whereC,Ris a planar
set, each point p[Ctakes states from the set Q¼{w,†,},
excited (w), refractory (†), resting (), and updates its state in
a discrete time depending on its current state and state of its
neighbourhood u(p)¼{q[C:d(p,q)r}; ris a neighbour-
hood radius,
u
is an excitation threshold and
d
is refractory
R
L
U
D
0
0.2
0.4
0.6
0.8
1.0
R
1.0
ratio of nodes
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
no. neighbours
0 20 40 60 80 100 120
prevaling neighbourhood size
0
10
20
30
40
50
r
510
critical threshold
0
2
4
6
8
10
12
14
r
2 4 6 8 10 12 14
p(R)
0.9
0.8
0.70.6
0.5
r = 4
r = 3
r = 5
r = 6
r = 7
r = 10
r = 12
r = 15
(e)
(b)
(a)
(c)(d)
Figure 7. Fungal computer architecture. (a) Visualization of C.(b) Probability of point in Cas a function of distance from R.(c) Distribution of a number of
neighbours for r¼3...15. A number of neighbours depending on a neighbourhood radius r.(d) Prevailing number of neighbours for r¼3...15. (e) Critical
values of excitation threshold
u
for r¼1, ..., 15.
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delay. All points update their states in parallel and by the
same rule:
ptþ1
w,if(pt¼)and
s
(p)t.
u
†,if(pt¼)or ((pt¼†)and (ht
p.0))
,otherwise
8
<
:
htþ1
p¼
d
,if(ptþ1¼†)and (pt¼w)
ht
p1, if (ptþ1¼†)and ht
p.0
0, otherwise.
8
<
:
Every resting ()pointofCexcites (w) at the moment tþ1
if a number of its excited neighbours at the moment
t—
s
(p)t¼j{q[u(p):qt¼w}j—exceeds a threshold
u
. Excited
point pt¼wtakes refractory state †at the next time step tþ1, at
the same moment a counter of refractory state hpis set to the
refractory delay
d
. The counter is decremented, htþ1
p¼ht
p1
at each iteration until it becomes 0. When the counter hp
becomes zero the point preturns to the resting state .
Architecture of Cwas chosen as follows. We randomly dis-
tributed 2 104points in a ring with small radius R¼0:5and
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
p(R)¼3:7R23:6Rþ0:9, where R[[0:5, 1] ( 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 (Land R) and vertical (Uand D)domainswith
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 r¼3, ..., 15 are shown
potential, units
–50
0
50
–50
0
50
time, iterations
0 50 100 150 200 0 50 100 150 200
potential, units
time, iterations
(b)
(a)
(c)(d)
Figure 8. Dynamics of the excitation of two fruit automaton A: in scenarios of right R(a,c) and left L(b,d) fruits excited. (a,b) Exemplar snapshots of the
dynamics. (c,d) Electrical potential measured. Dashed line is a potential measured on Rand solid line is a potential measured on L.
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in figure 7c.Wehavechosen
u
¼4 (§4.2.1),
u
¼5(§4.2.2),r¼10,
d
¼5 in the reported experiments for the following reasons.
A median radius r¼10 neighbourhood size is approxi-
mately 600 times less than a number of points in C(figure 7d);
thus a locality of the automaton state updates is assured. Exci-
tation threshold
u
¼4 is critical for Awith r¼10 (figure 7e),
i.e. it assures that excitation wavefronts propagate for at least
half of the perimeter of the ring (figure 7a).
4.1. Automaton action potential
The automaton Asupports propagation of excitation
waves, fronts of which are represented by points in the state
wand tails by points in state †. We assume a point in the
state whas higher electrical potential than a point in the
state †. To imitate a voltage difference between electrodes
inserted in fruit bodies we select two domains, D1and D2,in
each of four fruit bodies and calculate a voltage difference V
between domains as follows: V¼Pq[D1
x
(qt)Pq[D2
x
(qt),
where
x
()¼0,
x
(w)¼1, and
x
(†)¼ht
q. This imitates an elec-
trical potential difference between electrodes inserted in the
cap and the step of a fruit, as illustrated in figure 2.
We excite the fungal automaton Aby assigning points of a
selected fruit body states w. 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 auto-
mation evolution. Two examples are shown in figure 8. For
simplicity, we consider Awith only two fruit bodies: Land R.
When right fruit Ris stimulated (see first spike in figure 8c)an
excitation wave propagates into the mycelium ring Cand
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 lat-
tice) the excitation wavefronts would annihilate each other
when colliding. However, the disorganized structure of the con-
ductive 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 stimulationof the left and the right fruits are differ-
ent. This can be employed in designs of computing schemes
with fungal automata, as outlined in the next section.
4.2. Logical functions computed by A
Dynamics of excitation wave propagation and interaction in C
is determined by exact configuration of the planar set. The con-
figurations 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.
AlogicalinputT
RUE, 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 wintroduced in §2) of automaton evolution,
after stimulation and stopped recording 130 iterations. Let us
consider two examples. The sets Care 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 Cshown in
figure 9a. Excitation dynamics for inputs R¼0, U¼1, D¼0,
L¼1 is shown in figure 9 and for inputs R¼1, U¼0, D¼1,
L¼0 in figure 10. When fruits Uand Dare stimulated
t =5 t =15 t =35
t =71 t =73 t =82
(e)(f)
(b)(a)(c)
(d)
Figure 9. (a–f) Snapshots of excitation dynamics in a four-fruit fungal automaton for inputs R¼0, U¼1, D¼0, L¼1.
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(figure 9) the fungal automaton Aresponds with spikes on fruits
Land R(figure 11a). Excitation dynamics is less trivial when
fruits Land Rare stimulated (figure 10): automaton Aresponds
with two voltage spikes at fruit D, and a single spike at fruits U
and R(figure 11b). When only fruit Ris stimulated the automa-
ton Aresponds withpairs of spikes on all fruits but L(figure12b).
The automaton Aresponds with a spike on fruit Ljust before cut-
off time 150. After the 150th iteration, two centres of spiral waves
are formed and thusthe fungal automaton exhibits regular trains
of spikes on all fruit bodies (figure 12a), similar to the dynamics
ofexcitationshowninfigure4b.
We stimulated the fungal automaton with 16 combi-
nations of input variables and constructed a tabular
representation of a function realized by the automaton
(table 1), where R,U,L,Dare values of input variables,
and Rw
,Uw
,Lw
,Dware values of output variables.
Assuming one or two impulses on the fruits represent
TRUE we have the following functions implemented by the
fungal automaton:
Rw¼
R(UþLþD)þR
D,
Uw¼
U(LþUþR),
Lw¼
L(DþUþR)
and Dw¼
D(LþUþR),
9
>
>
>
>
>
>
=
>
>
>
>
>
>
;
(4:1)
t=5 t=15 t=28
t=49
t=88 t=95 t= 103
t= 137 t= 176 t= 193
t=67 t=79
(e)(f)
(b)(a)(c)
(d)
(i)
(k)(l)( j)
(g)(h)
Figure 10. (a–l) Snapshots of excitation dynamics in a four-fruit fungal automaton for inputs R¼1, U¼0, D¼0, L¼1.
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with the equivalent circuit for fruit Dshown in figure 13. If
we assume that only two impulses represent TRUE we have
Rw¼Uw¼Lw¼0 and Dw¼R
D.
4.2.2. Second example
In the second example, discussed below, we used a random
configuration of points C
4
and the automaton Awith
d
¼5, r¼10 and
u
¼5. Frames and videos of the experi-
ments 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 illus-
trated 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:
Rw¼0,
Uw¼LþD,
Lw¼
LD(RþU)þR
UL
D
and Dw¼L(
RþDþU):
9
>
>
>
>
>
>
=
>
>
>
>
>
>
;
(4:2)
Assuming only two impulses on the fruits symbolize ‘1’,
we have the following functions recorded on each of the
potential, units
–200
–100
0
100
200
time, iterations
020 40 60 80 100
–200
–100
0
100
200
time, iterations
0 20 40 60 80 100 120 140 160
(b)(a)
Figure 11. Voltage measured on four fruits for inputs (a)R¼0, U¼1, D¼0, L¼1, see dynamics in figure 9, and (b)R¼1, U¼0, D¼1, L¼0, see
dynamics in figure 10. Voltage recorded on fruit Ris plotted with red colour, Ublue, Lgreen and Dmagenta.
potential, units
–80
–60
–40
–20
0
20
40
60
80
time, iterations
0 50 100 150 200 250 300
(b)(a)
Figure 12. Response of the fungal automaton for input values R¼1, U¼0, D¼0, L¼0. (a) A snapshot of the automaton taken at 350th step of evolution.
(b) Voltage recorded on the fruit Ris plotted with red colour, Ublue, Lgreen and Dmagenta.
Table 1. Table of a function realized by four-fruit automaton A
(figure 9a). One impulse on a fruit is shown by ‘1’, two impulses by ‘2’
and no impulses by ‘0’.
RULDRwUwLwDw
0000 0 0 0 0
0001 1 1 1 0
0010 1 1 0 1
0011 1 1 0 0
0100 1 0 1 1
0101 1 0 1 0
0110 1 0 0 1
0111 1 0 0 0
1000 1 1 1 2
1001 0 1 1 0
1010 1 1 0 2
1011 0 1 0 0
1100 1 0 1 2
1101 0 0 1 0
1110 1 0 0 2
1111 0 0 0 0
L
U
R
D
D*
Figure 13. Equivalent logical circuit for fruit Dimplemented by the fungal
automaton A, with configuration of Cshown in figure 9a.
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fruit bodies:
Rw¼0,
Uw¼LþD(RþU),
Lw¼R
U
LD
and Dw¼L
D(
RþU):
9
>
>
>
>
>
>
=
>
>
>
>
>
>
;
(4:3)
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 signal-
ling in fungi, previously evidenced during intracellular
recording of electricalpotential [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 spikestravelling alongmycelium 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
potential, units
–100
–50
0
50
100
–100
–50
0
50
100
–100
–50
0
50
100
–100
–50
0
50
100
–100
–50
0
50
100
–100
–50
0
50
100
–100
–50
0
50
100
0 50 100 150 200
0001
0 50 100 150 200
0010
0 20 40 60 80 100 120 140 160
0 20 40 60 80 100 120 140 160
0011
potential, units
–50
0
50
–50
0
50
–50
0
50
010 20 30 40 50 60 70 80 90
0100
0 50 100 150 200
0101 0110
potential, units
–100
–50
0
50
100
–100
–50
0
50
100
–100
–50
0
50
100
0 50 100 150 200
0111
010 20 30 40 50
1000
0 50 100 150 200
1001
potential, units
–100
–50
0
50
100
0 50 100 150 200
0 50 100 150 200
1010
020 40 60 80 100 120 140
0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160
1011
0 1020304050
1100
potential, units
–100
–50
0
50
100
time, iterations
1101
time, iterations
1110
time, iterations
1111
(e)(f)
(b)(a) (c)
(d)
(i)
(k)
(m)(n)(o)
(l)( j)
(g)(h)
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 (RULD). Spikes appearing during first 10– 15 iterations are input spikes. All other spikes are outputs. Voltage recorded on fruit Ris
plotted with red colour, Ublue, Lgreen and Dmagenta.
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memory [81,82], wave-based counters [83] and other infor-
mation 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 con-
strained 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], poly-
morphic logical gates [101], and experimental laboratory
prototype of four-bit input, two-bit output integer square root
circuits based onalternating ‘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 proto-
plasmic 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 proces-
sor of a distributed multi-processor computing network. We
assume the numberof 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 mm2. Considering that the largest known
fungi, Armillaria bulbosa, populates over 15 hectares [2], we
could assume that there could be 75 1011 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 0:5mms
1(this is several orders slower than the speed
of a typical action potential in plants: from 0:005 mm s1to
0:2mms
1[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
thigmotacticand thigmomorphogeneticresponses,whichmight
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
Table 2. Table of a logical function realized by four-fruit automaton A.One
impulse on a fruit is shown by ‘1’, two impulses by ‘2’ and no impulses by ‘0’.
RULDRwUwLwDw
0000 0 0 0 0
0001 0 2 1 0
0010 0 2 0 2
0011 0 2 0 1
0100 0 0 0 0
0101 0 2 1 0
0110 0 2 0 2
0111 0 2 0 1
1000 0 0 0 0
1001 0 2 2 0
1010 0 2 1 0
1011 0 2 0 1
1100 0 0 0 0
1101 0 2 1 0
1110 0 2 0 2
1111 0 2 0 1
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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 exper-
imental 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 prin-
ciple, 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 neigh-
bouring fruits. An example of the recorded activity is shown
in figure 15b. Average distance between spikes is 4111 s
(
s
¼2140). Average duration of a spike is 287 s (
s
¼1515).
Average amplitude is 0.25 mV (
s
¼0:06). There is a possi-
bility 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
electrical potential (mV)
–0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
time (s)
30 000 40 000 50 000 60 000
(b)(a)
(c)
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.
D1
D2
D3
D4
D5
D6
D7
D
8
C
Figure 16. Representation of a mycelium by relative neighbourhood graph
with 2000 nodes. Black discs are fruit bodies.
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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. Con-
nection 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.
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.
Endnotes
1
Copyright qEspresso Mushroom Company, Brighton, UK.
2
Copyright qSPES MEDICA SRL Via Buccari 21 16153 Genova, Italy.
3
Pico Technology, St Neots, Cambridgeshire, UK.
4
File with coordinates is available here https://drive.google.com/
open?id=1wcmo8DkcKN49rDSRFGm9hnIjJj5LTbDL.
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