Language of fungi derived from their electrical spiking activity

Abstract

Fungi exhibit oscillations of extracellular electrical potential recorded via differential electrodes inserted into a substrate colonized by mycelium or directly into sporocarps. We analysed electrical activity of ghost fungi ( Omphalotus nidiformis ), Enoki fungi ( Flammulina velutipes ), split gill fungi ( Schizophyllum commune ) and caterpillar fungi ( Cordyceps militaris ). The spiking characteristics are species specific: a spike duration varies from 1 to 21 h and an amplitude from 0.03 to 2.1 mV. We found that spikes are often clustered into trains. Assuming that spikes of electrical activity are used by fungi to communicate and process information in mycelium networks, we group spikes into words and provide a linguistic and information complexity analysis of the fungal spiking activity. We demonstrate that distributions of fungal word lengths match that of human languages. We also construct algorithmic and Liz-Zempel complexity hierarchies of fungal sentences and show that species S. commune generate the most complex sentences.

Full text

royalsocietypublishing.org/journal/rsos
Research
Cite this article: Adamatzky A. 2022
Language of fungi derived from their electrical
spiking activity. R. Soc. Open Sci. 9: 211926.
https://doi.org/10.1098/rsos.211926
Received: 18 December 2021
Accepted: 4 March 2022
Subject Category:
Computer science and artificial intelligence
Subject Areas:
algorithmic information theory/cybernetics/
biocomplexity
Keywords:
fungi, electrical activity, action potential,
language
Author for correspondence:
Andrew Adamatzky
e-mail: andrew.adamatzy@uwe.ac.uk
Language of fungi derived
from their electrical spiking
activity
Andrew Adamatzky
Unconventional Computing Laboratory, UWE, Bristol, UK
AA, 0000-0003-1073-2662
Fungi exhibit oscillations of extracellular electrical potential
recorded via differential electrodes inserted into a substrate
colonized by mycelium or directly into sporocarps. We
analysed electrical activity of ghost fungi (Omphalotus
nidiformis), Enoki fungi (Flammulina velutipes), split gill fungi
(Schizophyllum commune) and caterpillar fungi (Cordyceps
militaris). The spiking characteristics are species specific: a spike
duration varies from 1 to 21 h and an amplitude from 0.03 to
2.1 mV. We found that spikes are often clustered into
trains. Assuming that spikes of electrical activity are used by
fungi to communicate and process information in mycelium
networks, we group spikes into words and provide a linguistic
and information complexity analysis of the fungal spiking
activity. We demonstrate that distributions of fungal word
lengths match that of human languages. We also construct
algorithmic and Liz-Zempel complexity hierarchies of fungal
sentences and show that species S. commune generate the most
complex sentences.
1. Introduction
Spikes of electrical potential are typically considered to be key
attributes of neurons, and neuronal spiking activity is interpreted
as a language of a nervous system [1–3]. However, almost all
creatures without nervous system produce spikes of electrical
potential—Protozoa [4–6], Hydrozoa [7], slime moulds [8,9] and
plants [10–12]. Fungi also exhibit trains of action-potential-like
spikes, detectable by intracellular and extracellular recordings
[13–15]. In experiments with recording of electrical potential of
oyster fungi Pleurotus djamor, we discovered two types of spiking
activity: high-frequency ( period 2.6 min) and low-frequency
(period 14 min) [13]. While studying another species of fungus,
Ganoderma resinaceum, we found that the most common width of
an electrical potential spike is 5–8 min [16]. In both species of
fungi, we observed bursts of spiking in the trains of the spike
similar to that observed in the central nervous system [17,18].
© 2022 The Authors. Published by the Royal Society under the terms of the Creative
Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits
unrestricted use, provided the original author and source are credited.

While the similarity could be just phenomenological, this indicates a possibility that mycelium networks
transform information via interaction of spikes and trains of spikes in manner homologous to neurons.
First evidence has been obtained that indeed fungi respond to mechanical, chemical and optical
stimulation by changing pattern of its electrically activity and, in many cases, modifying characteristics
of their spike trains [19,20]. There is also evidence of electrical current participation in the interactions
between mycelium and plant roots during formation of mycorrhiza [21]. In [22], we compared
complexity measures of the fungal spiking train and sample text in European languages and found that
the ‘fungal language’exceeds the European languages in morphological complexity.
In our venture to decode the language of fungi, we first uncover if all species of fungi exhibit similar
characteristics of electrical spiking activity. Then we characterize the proposed language of fungi by
distributions of word length and complexity of sentences.
There is an emerging body of studies on language of creatures without a nervous system and
invertebrates. Biocommunication in ciliates [23] include intracellular signalling, chemotaxis as expression
of communication, signals for vesicle trafficking, hormonal communication and pheromones. Plants
communication processes are seen as primarily sign-mediated interactions and not simply an exchange
of information [24,25]. Evidences of different kinds of chemical ‘words’in plants are discussed in [26,27].
Moreover, a modified conception of language of plants is considered to be a pathway towards ‘the de-
objectification of plants and the recognition of their subjectivity and inherent worth and dignity’[28]. A
field of the language of insects has been developed by Karl von Frisch and resulted in his Nobel Prize
for detection and investigation of bee languages and dialects [29,30]. An issue of the language of ants,
and how species hosted by ants can communicate the ants language, was firstly promoted in 1971 [31].
In the early 1980s, analysis of the ants’language using information theory approaches was proposed
[32]. The approach largely succeeded in analysis of ants’cognitive capacities [33–36].
We recorded and analysed, as detailed in §2, electrical activity ofghost fungi (Omphalotus nidiformis), Enoki
fungi (Flammulina velutipes), split gill fungi (Schizophyllum commune) and caterpillar fungi (Cordyceps militaris).
The phenomenological characteristic of the spiking behaviour discovered are presented in §3. Linguistic
analysis and information and algorithmic complexity estimates of the spiking patterns are given in §4.
2. Experimental laboratory methods and analysis
Four species of fungi have been used in experiments: Omphalotus nidiformis and Flammulina velutipes,
supplied by Mycelia NV, Belgium (mycelium.be), Schizophyllum commune, collected near Chew Valley
lake, Somerset, UK (approximate coordinates 51.34949164156282,−2.622511962302647), Cordyceps
militaris, supplied by Kaizen Cordyceps, UK (kaizencordyceps.co.uk).
Electrical activity of the fungi was recorded using pairs of iridium-coated stainless steel sub-dermal
needle electrodes (Spes Medica S.r.l., Italy), with twisted cables and ADC-24 (Pico Technology, UK) high-
resolution data logger with a 24-bit A/D converter, galvanic isolation and software-selectable sample
rates all contributing to a superior noise-free resolution. Each pair of electrodes reported a potential
difference between the electrodes. The pairs of electrodes were pierced into the substrates colonized by
fungi or, as in the case of S. commune, in the sporocarps, as shown in figure 1. Distance between
electrodes was 1–2 cm. We recorded electrical activity one sample per second. We recorded eight
electrode pairs simultaneously. During the recording, the logger has been doing as many measurements
as possible (typically up to 600 per second) and saving the average value. The acquisition voltage range
was 78 mV. Schizophyllum commune has been recorded for 1.5 days, other species for ca 5 days. The
experiments took place at temperature 21°C, ca 80% humidity, in darkness.
Spikes of electrical potential have been detected in a semi-automatic mode as follows. For each sample
measurement x
i
, we calculated average value of its neighbourhood as ai¼ð4wÞ1Pi2wjiþ2wxj.
The index iis considered a peak of the local spike if |x
i
|−|a
i
|>δ. The list of spikes were further
filtered by removing false spikes located at a distance dfrom a given spike. Parameters were species
specific, for C. militaris and F. velutipes,w= 200, δ= 0.1, d= 300; for S. commune, w = 100, δ= 0.005, d= 100;
for O. nidiformis, w = 50, δ= 0.003, d= 100. An example of the spikes detected is shown in figure 2. Over
80% of spikes have been detected by such a technique.
3. Characterization of the electrical spiking of fungi
Examples of electrical activity recorded are shown in figure 3. Intervals between the spikes and
amplitudes of spikes are characterized in figure 4 and table 1.
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Cordyceps militaris shows the lowest average spiking frequency among the species recorded ( figures 3a
and 4a): average interval between spikes is nearly 2 h. The diversity of the frequencies recorded is highest
among the species studied: standard deviation is over 5 h. The spikes detected in C. militaris and
F. velutipes have highest amplitudes: 0.2 and 0.3 mV, respectively. Variability of the amplitudes in both
species is high, standard deviation nearly 0.3.
Enoki fungi F. velutipes show a rich spectrum of diverse patterns of electrical activity which combines
low- and high-frequency oscillations (figure 3b). Most commonly exhibited patterns are characterized by
low-frequency irregular oscillations: average amplitude 0.3 mV (figure 4d) and average interval between
two spikes is just over 1.5 h (figure 4cand table 1). There are also bursts of spiking showing a transition
from a low-frequency spiking to high frequency and back, see recording in blue in figure 3b. There are
12 spikes in the train, average amplitude is 2.1 mV, σ= 0.1, average duration of a spike is 64 min, σ= 1.7.
(a)
(b)
(c)
Figure 1. Photographs of pairs of differential electrodes inserted in (a)C. militaris, the block of a substrate colonized by the fungi
was removed from the plastic container to make a photo after the experiments, (b)S. commune, the twig with the fungi was
removed from the humid plastic container to make a photo after the experiment, (c)F. velutipes, the container was kept
sealed and electrodes pierced through the lid.
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3

Omphalotus nidiformis also show low amplitude and low-frequency electrical spiking activity with the
variability of the characteristics highest among species recorded ( figure 3aand table 1). Average interval
between the spikes is just over 1.5 h with nearly 2.5 h standard variation (figure 4g). Average amplitude is
0.007 mV but the variability of the amplitudes is very high: σ= 0.006 ( figure 4h).
Schizophyllum commune electrical activity is remarkably diverse (figures 3cand 4e,f). Typically, there are
low amplitude spikes detected (figure 4f), due to the reference electrodes in each differential pair being
inserted into the host wood. However, they are the fastest spiking species, with an average interval
between spikes of just above half an hour (figure 4e). We observed transitions between different types of
spiking activity from low-amplitude and very low-frequency spikes to high-amplitude high-frequency
spikes (figure 5). A dynamic change in spikes frequency in the transition is shown in figure 5b. A closer
look at the spiking discovers presence of two wave packets labelled (p
1
,p
2
) and ( p
2
,p
3
)infigure5a.
One of the wave packets is shown in figure 5c, and the key characteristics are shown in figure 6.
In experiments with S. commune, we observed synchronization of the electrical potential spikes
recorded on the neighbouring fruit bodies. This is illustrated in figure 7. The dependencies between
the spikes are shown by red (increase of potential spike) and green (decrease of potential spike) lines
in figure 7a. Time intervals between peaks of the spikes occurred on neighbouring fruit bodies are
illustrated in figure 7b. Average interval between first four spikes is 1425 s (σ= 393), next three spikes
870 s (σ= 113) and last four spikes 82 (σ= 73).
4. Towards language of fungi
Are the elaborate patterns of electrical activity used by fungi to communicate states of the mycelium and
its environment and to transmit and process information in the mycelium networks? Is there a language
of fungi? When interpreting fungal spiking patterns as a language, here we consider a number of
linguistic phenomena as have been successfully used to decode pictish symbols revealed as a written
language in [37]: (i) type of characters used to code, (ii) size of the character lexicon, (iii) grammar,
(iv) syntax (word order), and (v) standardized spelling. These phenomena, apart from grammar and
spelling, are analysed further.
To quantify types of characters used and a size of lexicon, we convert the spikes detected in
experimental laboratory recordings to binary strings s, where index iis the index of the sample taken
at ith second of recording and s
i
= 1 if there is a spike’s peak at ith second and s
0
= 0 otherwise.
Examples of the binary strings, in bar-code-like forms, extracted from the electrical activity of
C. militaris and F. velutipes are shown in figure 8.
To convert the binary sequences representing spikes into sentences of the speculative fungal
language, we must split the strings into words. We assumed that if a distance between consequent
spikes is not more than θthe spikes belong to the same word. To define θ, we adopted analogies
from English language. An average vowel duration in English (albeit subject to cultural and dialect
variations) is 300 ms, minimum 70 ms and maximum 400 ms [38], with average post-word onset of
ca 300 ms [39]. We explored two options of the separation of the spike trains into words: θ=a(s) and
potential (mV)
1.0
1.5
2.0
2.5
time (s)
1.22 × 1051.23 × 1051.24 × 1051.25 × 105
Figure 2. Example of spike detection. Temporal position of each spike is shown by red vertical line. The minor shift of the vertical
lines away from the summits is consistent all over the recording and therefore does not affect the results of the analysis.
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potential (mV)
–8
–6
–4
–2
0
2
4
6
8
10
12
4×10
56×10
58×10
510×10
512×10
514×10
516×10
518×10
5
potential (mV)
–10
–5
0
5
2×10
54×10
56×10
58×10
510×10
5
–5
–4
–3
4.0×10
54.5×10
5
potential (mV)
–1.0
–0.5
0
0.5
5×10
410×10
415×10
420×10
425 × 104
potential (mV)
0
0.05
0.10
0.15
0.20
time (s)
5×10
510×10
515×10
5
(a)
(b)
(c)
(d)
Figure 3. Examples of electrical activity of (a)C. militaris,(b)F. velutipes, insert shows zoomed in burst of high-frequency spiking,
(c)S. commune and (d)O. nidiformis. Colours reflect recordings from different channels.
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minima: 0
maxima: 6326
range: 6326
average: 116.4
median: 36
s : 312.7
% in bin
0
5
10
15
20
25
0 50 100 150 200 250
minima: 0
maxima: 3.956
range: 3.956
average: 0.2307
median: 0.1845
s : 0.2622
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5
minima: 0
maxima: 2436
range: 2436
average: 102.1
median: 44
s : 178.2
% in bin
0
5
10
15
20
25
30
0 100 200 300 400
minima: 0
maxima: 3.944
range: 3.944
average: 0.2786
median: 0.1974
s : 0.3083
0
5
10
15
0 0.2 0.4 0.6 0.8 1.0
minima: 0
maxima: 1908
range: 1908
average: 40.74
median: 12
s : 126.9
% in bin
0
10
20
30
0 50 100 150 200
minima: 0
maxima: 1.492
range: 1.492
average: 0.03177
median: 0.01368
s : 0.09428
0
5
10
15
20
25
0 0.05 0.10
minima: 0
maxima: 1448
range: 1448
average: 91.62
median: 41
s : 151.6
% in bin
0
5
10
15
20
interval (min)
0 50 100 150 200
minima: 0.003028
maxima: 0.235
range: 0.2319
average: 0.006653
median: 0.005917
s : 0.007595
0
2
4
6
8
10
12
s
p
ike am
p
litude (mV)
0.005 0.010 0.015
(a)(b)
(c)(d)
(g)(h)
(e)(f)
Figure 4. Distribution of intervals between spikes (a,c,e,g) and average spike amplitude (b,d,f,h)of(a,b)C. militaris,(c,d)
F. velutipes,(e,f)S. commune and ( g,h)O. nidiformis.
Table 1. Characteristics of electrical potential spiking: number of spikes recorded, average interval between spikes and average
amplitude of a spike.
species no. spikes interval (min) amplitude (mV)
C. militaris 881 116 0.2
F. velutipes 958 102 0.3
S. commune 530 41 0.03
O. nidiformis 1117 92 0.007
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θ=2·a(s), where a(s) is an average interval between two subsequent spikes recorded in species
s[fC:militaris,F:velutipes,S:commune,O:nidiformisg. Distributions of fungal word lengths,
measured in a number of spikes in θ-separated trains of spikes are shown in figure 9. The
distributions follow predictive values f
exp
=β· 0.73 · l
c
, where lis a length of a word, and avaries from
20 to 26, and bvaries from 0.6 to 0.8, similarly to frequencies of word lengths in English and
Swedish, figure 10 and table 2 [40]. As detailed in table 2, average word length in fungi, when spikes
grouped with θ=aare in the same range as average word lengths of human languages. For example,
average number of spikes in train of C. militaris is 4.7 and average word length in English language is
4.8. Average word length of S. commune is 4.4 and average word length in Greek language is 4.45.
p1p2p3
potential (mV)
–0.20
–0.15
–0.10
–0.05
0
0.05
time (s)
1.0×10
51.5 × 1052.0 × 105
1/w
0
0.0005
0.0010
0.0015
0.0020
spike index
0 5 10 15 20 25
p2
p1
potential (mV)
–0.15
–0.10
–0.05
time (s)
1.5×10
51.6 × 1051.7 × 1051.8×10
51.9×10
5
(b)
(a)
(c)
Figure 5. Transition to spikes outburst in S. commune.(a) There are two outbursts of spiking, first shown by arrows labelled p
1
and
p
2
and second by p
2
and p
3
.(b) Dynamical changes in frequency of spikes, as derived from (a). (c) Wave packet zoomed in, start of
the packet is shown by arrow labelled p
1
and end by p
2
.
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To uncover syntax of the fungal language, we should estimate what is most likely order of the words
in fungal sentences. We do this via characterization of global transition graphs of fungal spiking
machines. A fungal spiking machine is a finite state machine. It takes states from S∈Nand updates
its states according to probabilistic transitions: S× [0, 1] →S, being in a state s
t
∈Sat time t+ 1 the
automaton takes state s
t+1
∈Swith probability p(s
t
,s
t+1
)∈[0, 1]. The probabilities of the state
transitions are estimated from the sentences of the fungal language.
The state transition graphs of the fungal spiking machines are shown in figure 11 for full dictionary
case and in figure 12 for the filtered states sets when states over 9 are removed.
amplitude (mV)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0246810121416
width (s)
1000
2000
3000
4000
5000
spike index
0246810121416
(a)
(b)
Figure 6. Characteristics of an exemplar wave packet of electrical potential oscillation in S. commune:(a) evolution of spike
amplitude, (b) evolution of spike width. In a typical wave packet, spike width and amplitude increase till middle of the packet
and then decrease.
potential (mV)
–0.30
–0.25
–0.20
–0.15
–0.10
–0.05
0
time (s)
1.6×10
51.7×10
51.8 × 105
interval D (s)
0
500
1000
1500
2000
spike index
12345678910
(a)(b)
Figure 7. Exemplar synchronization of spikes in two neighbouring sporocarps of S. commune: channel (3–4), second sporocarp in
figure 1band channel (5–6), third sporocarp in figure 1b.(a) Spiking activity, corresponding spikes of increased voltage are linked by
red lines and decreased voltage by green line. (b) Dynamics of the interval between spikes.
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The probabilistic state transition graphs shown in figure 11 are drawn using physical model spring-
based Kamada–Kawai algorithm [43]. Thus we can clearly see cores of the state space as clusters of
closely packed states. The cores act as attractive measures in the probabilistic state space. The
attractive measures are listed in table 3. The membership of the cores well matches distribution of
spike trains lengths (figure 9).
A leaf, or Garden-of-Eden, state is a state which has no predecessors. Cordyceps militaris probabilistic
fungal spiking machine has leaves ‘25’and ‘37’in the case of in grouping θ=a(figure 11a) and ‘20’,‘17’
and ‘37’in the case of in grouping θ=2·a(figure 11e). All other probabilistic fungal machines do not
have leaves apart of S. commune which has one leaf ‘11’in the case of in grouping θ=2·a(figure 11g).
An absorbing state of a finite state machine is a state in which the machine remains forever once it takes
this state. All spiking fungal machines, derived in grouping θ=a, have the only absorbing state ‘1’(figure
12a–d). They have no cycles in the state space. There are between 8 (F. velutipes (figure 12c) and O. nidiformis
(figure 12g)), and 11 leaves (S. commune (figure 12e)) in the global transition graphs. A maximal length of a
transient period, measured in a maximal number of transitionsrequired to reach the absorbing state from a
leaf state varies from 3 (F. velutipes)to11(S. commune).
State transition graphs get more complicated, as we evidence further, when grouping θ=2·ais
used (figure 12h). Fungal spiking machine O. nidiformis has one absorbing state, ‘1’(figure 12h).
Fungal spiking machines S. commune (figure 12g) and C. militaris (figure 12e) have two absorbing
states each, ‘1’and ‘2’and ‘1’and ‘8’, respectively. The highest number of absorbing states is found in
the state transition graph of the F. velutipes spiking machine (figure 12f). They are ‘1’,‘6’and ‘2’.A
number of leaves varies from 7, S. commune,to9,O. nidiformis and C. militaris, to 12, F. velutipes. Only
O. nidiformis spiking machine has cycles in each state transition graph (figure 12h). The cycles are
1 !5 and 2 !3.
To study complexity of the fungal language algorithmic complexity [44], Shannon entropy [45] and
Liv-Zempel complexity [46,47] of the fungal words (sequences of spike trains lengths) are estimated
using The Online Algorithmic Complexity Calculator
1
[44,48–50] in table 4. The complexity estimates
help us to rule out randomness of the electrical spiking events and to compare complexity of the
fungal language with that of human. Shannon entropy of the strings recorded is not shown to be
ch1
ch3
ch5
ch7
ch9
ch11
ch13
ch1
ch3
ch5
ch7
ch9
ch11
ch13
(a)
(b)
Figure 8. Bar-code-like presentation of spikes recorded in (a)C. milataris, (b)F. velutipes, 5 days of recording.
1
https://complexitycalculator.com/index.html.
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minima: 1
maxima: 87
range: 86
average: 4.726
median: 2
s: 9.018
% in bin
0
10
20
30
40
10 20 30 40 50
minima: 1
maxima: 117
range: 116
average: 8.879
median: 3
s: 16.53
0
5
10
15
20
25
30
10 20 30 40 50
minima: 1
maxima: 20
range: 19
average: 3.573
median: 2
s: 3.328
% in bin
0
10
20
30
40
5101520
minima: 1
maxima: 48
range: 47
average: 7.395
median: 3
s: 8.69
0
5
10
15
20
25
30
35
10 20 30 40 50
minima: 1
maxima: 48
range: 47
average: 4.438
median: 2
s: 6.659
% in bin
0
10
20
30
40
10 20 30 40 50
minima: 1
maxima: 74
range: 73
average: 8.456
median: 4
s: 13.26
0
5
10
15
20
25
30
10 20 30 40 50 60
minima: 1
maxima: 24
range: 23
average: 3.295
median: 2
s: 3.304
% in bin
0
10
20
30
40
no. spikes
510152025
minima: 1
maxima: 35
range: 34
average: 7.032
median: 4
s: 7.031
0
5
10
15
20
no. spikes
5 10152025303540
(a)(b)
(c)(d)
(g)(h)
(e)(f)
Figure 9. Distribution of a number of spikes in trains, i.e. of the fungal words’lengths, of (a,b)C. militaris,(c,d)F. velutipes,(e,f )
S. commune,(g,h)O. nidiformis for the train separation thresholds a(a,c,e,f) and 2 · a(b,d,f,h), where ais a species-specific average
interval between two consequent spikes, see table 1.
frequency
0
5
10
15
20
(a)(b)
word length
0
5
10
15
20
word length
246 8 10 12 14 16 2 4 6 8 10 12 14 16
Figure 10. Word length frequencies in (a) English and (b) Swedish, data are taken from table 1 in [40].
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10

species specific, it is 2.3 for most species but 2.4 for C. militaris in the case of θ=agrouping and 2.5 for
most species but 2.6 for O. nidiformis in the case of θ=2·a. The same can be said about second-order
entropy (table 4). Omphalotus nidiformis shows highest values of algorithmic complexity for both cases
of spike trains separation (table 4a,b) and filtered sentences (where only words with up to nine spikes
are left) (table 4c). In order of decreasing algorithmic complexity, we then have C. militaris,F. velutipes
and S. commune.
The hierarchy of algorithmic complexity changes when we normalize the complexity values dividing
them by the string lengths. For the case θ=a, the hierarchy of descending complexity will be S. commune
(7.55), C. militaris (6.51), F. velutipes (3.94) and O. nidiformis (3.67) (table 4a). Note that in this case a
Table 2. Average word lengths in fungal and human languages. l
1
is an average word length in the spike grouping using θ=a
and l
2
using θ=2·a,mis an average word length of 1950+ Russian and English language approximated from the
evolutionary plots in [41] and average word length in Greek language approximated from Hellenic National Corpus [42].
l
1
l
2
C. militaris 4.7 8.9
F. velutipes 3.6 7.4
S. commune 4.4 8.5
O. nidiformis 3.3 7
m
English language 4.8
Russian language 6
Greek language 4.45
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(h)
Figure 11. State transition graphs of fungal spiking machines, where spikes have been grouped using θ=a(a–d) and θ=2·
a(e–h). (a,e)C. militaris,(b,f )F. velutipes,(c,g)S. commune and (d,h)O. nidiformis.
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normalized algorithmic complexity of S. commune is nearly twice higher than that of O. nidiformis. For the
case θ=2·a, S. commune still has the highest normalized algorithmic complexity among the four species
studied (table 4b). Complexities of C. militaris and F. velutipes are almost the same, and the complexity of
O. nidiformis is the lowest. When we consider filtered sentences of fungal electrical activity, where words
with over nine spikes are removed, we get nearly equal values of the algorithmic complexity, ranging
from 3.96 to 4.05 (table 4c). LZ complexity hierarchy is the same for all three cases—θ=a(table 4a),
θ=2·a(table 4b) and filtered sentences (table 4c): S. commune,C. militaris,F. velutipes and O.
nidiformis. To summarize, in most conditions, S. commune is an uncontested champion in complexity
of the sentences generated followed by C. militaris.
5. Discussion
We recorded extracellular electrical activity of four species of fungi. We found evidences of the spike
trains propagating along the mycelium network. We speculated that fungal electrical activity is a
2
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28 44
37
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35
(h)
Figure 12. Filtered state transition graphs of fungal spiking machines, where spikes have been grouped using θ=a(a–d) and
θ=2·a(e–h). (a,e)C. militaris,(b,f)F. velutipes,(c,g)S. commune and (d,h)O. nidiformis. The transitions were filtered in such
manner that for each state iwe select state jsuch that the weight w(i,j) is maximal over w(i,z), where z∈S,Sis a set of states.
Table 3. Attractive cores in the probabilistic state spaces of fungal spiking machines. The attractive cores, or limit cycle, are such
subgraphs of the global transition graph that when a machine enters the subgraph it will stay there forever.
θ=aθ=2·a
C. militaris 1, …,8 1,…,3,
F. velutipes 1, …, 8, 9 1, 2, 4, 15, 16
S. commune 1, …,4,8 1,…,4,7
O. nidiformis 1, …,5 1,…, 5, 10, 12
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manifestation of the information communicated between distant parts of the fungal colonies. We adopted
a framework of information encoding into spikes in neural system [51–54] and assumed that the
information in electrical communication of fungi are encoded into trains of spikes. We therefore
attempted to uncover key linguistic phenomena of the proposed fungal language. We found that
distributions of lengths of spike trains, measured in a number of spikes, follow the distribution of
word lengths in human languages. We found that size of fungal lexicon can be up to 50 words;
however, the core lexicon of most frequently used words does not exceed 15–20 words. Species
Table 4. Block decomposition method (BDM) algorithmic complexity estimation, BDM logical depth estimation, Shannon entropy,
second-order entropy, LZ complexity. The measures are estimated using The Online Algorithmic Complexity Calculator (https://
complexitycalculator.com/index.html) block size 12, alphabet size 256. Spike trains are extracted with (a)θ=aand (b)θ=
2·a, where ais an average interval between two consequent spikes, see table 1. We also provide values of the LZ complexity
and algorithmic complexity normalized by input string lengths. In table (c), we provide data on the strings of train powers (in
number of spikes) calculated with θ=aand then filtered so values over 9 are removed and the complexity is estimated in
alphabet of nine symbols.
C. militaris F. velutipes S. commune O. nidiformis
(a)
algorithmic complexity, bits 1211 1052 981 1243
algorithmic complexity normalized 6.51 3.94 7.55 3.67
logical depth, steps 4321 4957 3702 5425
logical depth normalized 23 19 28 16
Shannon entropy, bits 2.4 2.3 2.3 2.3
second-order entropy, bits 3.8 3.7 3.7 3.7
LZ complexity, bits 1153 1495 910 1763
LZ complexity (normalized), bits 6.2 5.6 7 5.2
input string length 186 267 130 339
C. militaris F. velutipes S. commune O. nidiformis
(b)
algorithmic complexity, bits 1047 1295 980 1393
algorithmic complexity normalized 10.57 10.04 14.4 8.82
logical depth, steps 2860 4147 3046 4731
logical depth normalized 29 32 45 30
Shannon entropy, bits 2.5 2.5 2.5 2.6
second-order entropy, bits 4 4.2 4.2 4.3
LZ complexity, bits 594 993 666 1232
LZ complexity normalized 6 7.7 9.8 7.8
input string length 99 129 68 158
C. militaris F. velutipes S. commune O. nidiformis
(c)
algorithmic complexity, bits 679 976 466 1276
algorithmic complexity normalized 3.96 3.97 4.05 4
Shannon entropy, bits 2.5 2.6 2.5 2.5
second-order entropy, bits 4.7 5 4.5 4.9
LZ complexity, bits 735 1009 563 1208
LZ complexity normalized 4.3 4.1 4.9 3.8
input string length 171 246 115 319
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S. commune and O. nidiformis have largest lexicon while species C. militaris and F. velutipes have less
extensive one. Depending on the threshold of spikes grouping into words, average word length varies
from 3.3 (O. nidiformis) to 8.9 (C. militaris). A fungal word length averaged over four species and two
methods of spike grouping is 5.97 which is of the same range as an average word length in some
human languages, e.g. 4.8 in English and 6 in Russian.
To characterize a syntax of the fungal language, we analysed state transition graphs of the probabilistic
fungal spiking machines. We found that attractive measures, or communication cores, of the fungal
machines are composed of the words up to 10 spikes long with longer words appearing less often.
We analysed complexity of the fungal language and found that species S. commune generates most
complex, among four species studied, sentences. The species C. militaris is slightly below S. commune in
the hierarchy of complexity and F. velutipes and O. nidiformis occupy lower levels of the hierarchy. We
found that Shannon entropy poorly, if at all, discriminate between the species. That could be due to
sentences in the fungal language possessing the same amount of information about physiological state of
fungi and environment. LZ complexity, algorithmic complexity and logical depth give us substantial
differentiation between species. The algorithmic complexity is the most ‘species-sensitive’measure. This
could be due to the fact, while conveying the same amount of information, dialects of different species
are different.
Future research should go in three directions: study of inter-species variations, interpretation of a
fungal grammar and reconsideration of the coding type. First, we should increase the number of fungi
species studied to uncover if there is a significant variation in the language syntax among the species.
Second, we should try to uncover grammatical constructions, if any, in the fungal language, and to
attempt to semantically interpret syntax of the fungal sentences. Third, and probably the most
important direction of future research, would to be make a thorough and detailed classification of
fungal words, derived from the train of spikes. Right now, we classified the word based solely on a
number of spikes in the corresponding trains. This is indeed quite a primitive classification akin to
interpreting binary words only by sums of their bits and not exact configurations of 1s and 0s. That
said, we should not expect quick results: we are yet to decipher language of cats and dogs despite
living with them for centuries, and research into electrical communication of fungi is in its pure infant
stage. And last but not least, there may be alternative interpretations of spiking electrical activity as a
language. For example, one can adopt the technique of signals integration over time trace, as has been
done in experiments with chemical Turing machine [55]. Another option could be to characterize each
peak by determining its fuzzy entropy by the algorithm presented in [56].
Data accessibility. Data can be accessed as [57].
Competing interests. I declare I have no competing interests.
Funding. This project has received funding from the European Union’s Horizon 2020 research and innovation
programme FET OPEN ‘Challenging current thinking’under grant agreement no. 858132.
Acknowledgements. Author is grateful to reviewers for their extensive comments which helped to substantially improve
the paper.
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