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Electrical activity of fungi: Spikes detection and complexity
analysis
Mohammad Mahdi Dehshibia,b,∗,Andrew Adamatzkyb
aDepartment of Computer Science, Multimedia and Telecommunications, Universitat Oberta de Catalunya, Barcelona, Spain
bUnconventional Computing Laboratory, University of the West England, Bristol, UK
ARTICLE INFO
Keywords:
Pleurotus djamor
electrical activity
spikes
complexity
ABSTRACT
Oyster fungi Pleurotus djamor generate actin potential like spikes of electrical potential. The
trains of spikes might manifest propagation of growing mycelium in a substrate, transportation of
nutrients and metabolites and communication processes in the mycelium network. The spiking
activity of the mycelium networks is highly variable compared to neural activity and therefore
can not be analysed by standard tools from neuroscience. We propose original techniques for
detecting and classifying the spiking activity of fungi. Using these techniques, we analyse the
information-theoretic complexity of the fungal electrical activity. The results can pave ways for
future research on sensorial fusion and decision making of fungi.
1. Introduction
Excitation is an essential property of all living organisms, bacteria Masi et al. (2015), Protists Eckert and Brehm
(1979); Hansma (1979); Bingley (1966), fungi McGillviray and Gow (1987) and plants Trebacz et al. (2006); Fromm
and Lautner (2007); Zimmermann and Mithöfer (2013) to vertebrates Hodgkin and Huxley (1952); Aidley and Ashley
(1998); Nelson and Lieberman (2012); Davidenko et al. (1992). Waves of excitation could be also found in various
physical Kittel (1958); Tsoi et al. (1998); Slonczewski (1999); Gorbunov and Kirsanov (1987), chemical Belousov
(1959); Zhabotinsky (1964); Zhabotinsky (2007) and social systems Farkas et al. (2002,2003). Extracellular (EC)
action potential recordings have been widely used to record and measure neural activity in organisms with excitation.
When recorded with differential electrodes, the spike manifests a propagating wave of excitation.
In our recent studies Adamatzky (2018b,2019); Adamatzky et al. (2020), we have shown that the Pleurotus djamor
oyster fungi generate action potentials like electrical potential impulses. We observed spontaneous spike1trains with
two types of activity, i.e. high-frequency (2.6 min period) and low-frequency (14 min period). However, the proper use
of this information is subject to the accurate extraction of the EC spike waveform, separating it from the background
activity of the neighbouring cells and sorting the characteristics.
The lack of an algorithmic framework for the exhaustive characterisation of the electrical activity of the substrate
colonised by mycelium of oyster fungi Pleurotus djamor has inspired us to develop a framework to extract spike
patterns, quantify the diversity of spike events and measure the complexity of fungal electrical communication. We
evidenced the spiking activity of the mycelium (see an example in Figure 1), which will enable us to build an experi-
mental prototype of fungi-based information processing devices.
We evaluated the proposed framework in comparison with existing spike detection techniques in neuroscience Ne-
nadic and Burdick (2004); Shimazaki and Shinomoto (2010) and observed a significant improvement in the spike
activity extraction. The evaluation of the proposed method for detecting spike events compared to the specified spike
arrival time by the expert shows true-positive and false-positive rates of 76% and 16%, respectively. We found that the
average dominant duration of an action-potential-like spike is 402 sec. The amplitude of the spikes ranges from 0.5 mV
to 6 mV and depends on the location of the source of electrical activity (the position of electrodes). We have found
that the complexity of the Kolmogorov fungal spike ranges from 11 × 10−4 to 57 × 10−4. In Vicnesh and Hagiwara
(2019), the human brain’s Kolmogorov complexity is measured in normal, pre-ictal and ictal states resulting in 6.01,
5.59 and 7.12 values, respectively. Although the fungi’ complexity is considerably smaller than that of the human
∗Corresponding author
ORCID (s): 0000-0001-8112-5419 (M.M. Dehshibi); 0000-0003-1073-2662 (A. Adamatzky)
1Calling the spikes spontaneous means that the intentional external stimulus does not invoke them. Otherwise, the spikes actually reflect the
ongoing physiological and morphological processes in the mycelial networks.
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 1 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
(c) (d)
Figure 1: The electrical behaviour of the mycelium of the grey oyster fungi. (a) Example of electrical potential dynamics
recorded in seven channels of the same cluster during 409 hours. (b) Two channels are zoomed in the inserts to show the
rich combination of slow (hours) drift of base electrical potential combined with relatively fast (minutes) oscillations of the
potential. (c) DC levelling for two channels is plotted. The mismatch of DC levels indicates the resistance and different
levels of intra-communication in the substrate. (d) All ’classical’ parts of the spike, i.e. depolarisation, depolarisation
and refractory period, can be found in this sample spike. This spike has a length of 220 s, from the base-level potential
to the refractory-like phase, and a refractory period of 840 s. The depolarisation and depolarisation rates are 0.03 and
0.009 mV/s, respectively.
brain, its changes suggest a degree of intra-communication in the mycelium sub-network. In fact, different parts of the
substrate transmit different information to other parts of the mycelium network, where the more prolonged propagation
of excitation waves leads to higher levels of complexity.
The rest of this paper is structured as follows: Sect. 2presents the experimental setup. Details of the proposed spike
detection methods are explained in Sect. 3. Experimental results and complexity analyses are discussed in Sect. 4.
Finally, the discussion is given in Sect. 5.
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Electrical activity of fungi: Spikes detection and complexity analysis
2. Experimental set-up
A wood shavings substrate was colonised by the mycelium of the grey oyster fungi, Pleurotus ostreatus (Ann
Miller’s Speciality Mushrooms Ltd, UK). The substrate was placed in a hydroponic growing tent with a silver Mylar
lightproof inner lining (Green Box Tents, UK). Recordings were carried out in a stable indoor environment with the
temperature remaining stable at 22 ± 0.5°and relative humidity of air 40 ± 5%. The humidity of the substrate colonised
by fungi was kept at c. 70-80%. Figure 2shows examples of the experimental setups.
(a) (b)
(c)
Figure 2: (a) In-line placement of electrodes (1 cm distance), (b) random electrode placement, (c) the experimental setup.
We inserted pairs of iridium-coated stainless steel sub-dermal needle electrodes (Spes Medica SRL, Italy) with
twisted cables into the colonised substrate for recording electrical activity. Using a high-resolution ADC-24 (Pico
Technology, UK) data logger with a 24-bit A/D converter, galvanic insulation and software-selectable sample rates
all lead to superior noise-free resolution. We recorded electrical activity one sample per second, where the minimum
and maximum logging times were 60.04 and 93.45 hours, respectively. During recording, the logger makes as many
measurements as possible (basically up to 600 per second) and saves the average value. We set the acquisition voltage
range to 156 mV with an offset accuracy of 9 𝜇V at 1 Hz to preserve a gain error of 0.1%. Each electrode pair
was considered independently with a 17-bit noise-free resolution and a 60 ms conversion time. In our experiments,
electrode pairs were placed in one of two configurations: random placement or in-line placement. The distance between
the electrodes was between 1-2 cm. In each cluster, we recorded 5–16 pairs of electrodes (channels) simultaneously.
In six trials, we also undertook recordings of the fruit body’s resistance, where electrodes were inserted in stalks of
the bodies. We measured and logged a range of resistances 1-1.6kΩusing Fluke 8846A precision multimeter, where
the test current being 1±0.0013𝜇A, once per 10 seconds, 5×104samples per trial Adamatzky et al. (2021). It should be
noted that the placement of the electrodes in two experiments was in-lines with a distance of 1 cm, in two experiments
it was in-lines with a distance of 2 cm, and in two experiments it was random with a distance of approximately 2 cm.
3. Proposed method
A spike event can be formally defined as an extracellular signal that exceeds a simple amplitude threshold and
passes through a corresponding pair of user-specific time-voltage boxes. The spike, which involves depolarisation,
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 3 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
depolarisation and refractory cycles, represents physiological and morphological processes in mycelial networks. To
extract spike events, we proposed an unsupervised approach consisting of three major steps. The pipeline of the
proposed approach is shown in Figure 3
Figure 3: The pipeline for the identification of spike events.
– Step 1: We split the entire recording duration (𝐹(𝑡)) into 𝑘chunks (𝑓𝑘(𝑡)) with respect to the signal transitions. In
order to evaluate the transitions, we determined the state level of the signal by its histogram and identified all regions
that cross the upper boundary of the low state and the lower boundary of the high state. Then, we measure scale-to-
frequency conversions of the analytic signal in each chunk using Morse wavelet basis Lilly and Olhede (2012). To
assess the existence of spike-like events, we scaled the wavelet coefficients at each frequency and obtained the sum
of the scales below the threshold specified in Algorithm 1. Finally, we selected regions of interest (ROI) enclosed
between a consecutive local minimum and a maximum of more than 30 sec.
– Step 2: We used spline interpolation to measure the analytic signal envelopes around local maximum values. To
determine the analytical signal, we first applied the discrete approximation of Laplace’s differential operator to 𝑓𝑘(𝑡)
to obtain a finite sequence of equally-spaced samples. Then, we applied discrete-time Fourier transform to this finite
sequence. From the average signal envelope, we extracted regions spanning between a consecutive local minimum and
a maximum. These regions created constraints that contributed to the identification of spike events.
– Step 3: We retained the ROIs extracted in the first step, which met the constraints of the second step. The signal
envelope could direct wavelet decomposition in an unsupervised manner in order to cluster the signal into the spike,
pseudo-spike, and background activity of the adjacent cells. In the following sub-sections, we detailed the proposed
process.
3.1. Slicing fungi electrical activity
To split the electrical activity of fungi (𝐹(𝑡)) with a duration of (𝑡) second into (𝑘) chunks (𝑓 𝑘(𝑡),1𝑘𝑡− 1),
we used the signal transitions that constitute each pulse. To determine the transitions, we estimated the state level of
𝐹(𝑡)using the histogram method IEEE (2011). Then, we identified all regions that cross the upper boundary of the
low state and the lower boundary of the high state. We followed the following steps to estimate the signal states:
1. Determine the minimum, maximum and range of amplitudes.
2. Sort the amplitude values in the histogram bins and determine the width of the bin by dividing the amplitude
range by the number of bins.
3. Identify the lowest- and highest-indexed histogram bins, ℎ𝑏𝑙𝑜𝑤,ℎ𝑏ℎ𝑖𝑔 ℎ, with non-zero counts.
4. Divide the histogram into two sub-histograms, where the indices of the lower and upper histogram bins are
ℎ𝑏𝑙𝑜𝑤 ℎ𝑏 1
2(ℎ𝑏ℎ𝑖𝑔ℎ −ℎ𝑏𝑙𝑜𝑤 )and ℎ𝑏𝑙𝑜𝑤 +1
2(ℎ𝑏ℎ𝑖𝑔ℎ −ℎ𝑏𝑙𝑜𝑤 )ℎ𝑏 ℎ𝑏ℎ𝑖𝑔ℎ , respectively.
5. Calculate the mean of the lower and upper histogram to compute the state levels.
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Electrical activity of fungi: Spikes detection and complexity analysis
Each chunk is then enclosed between the last negative-going transitions of each positive-polarity pulse and the next
positive-going transition. Figure 4shows the slicing results of two channels.
(a) (b)
Figure 4: Slicing electrical potential recordings for two channels.
3.2. Detecting time-localised events by Morse-based wavelets
The electrical activity of mycelium shows modulated behaviour with changes in amplitude and frequency over
time. This feature suggests that the signal can be analysed with analytic wavelets, which are naturally grouped into
pairs of even or cosine-like and odd or sine-like pairs, allowing them to capture phase variability. A wavelet (𝜓(𝑡))
is a finite energy function that projects 𝑓(𝑡)to a family of time-scale waveforms through translation and scaling. The
Morse wavelet (𝜓𝛽,𝛾 (𝑡)) is an analytical wavelet whose Fourier transform is supported only on a positive real axis Lilly
and Olhede (2012); Lilly (2017). This wavelet is defined in the frequency domain using Eq. 1.
𝜓𝛽,𝛾 (𝑡) = 1
2𝜋∞
−∞
Ψ𝛽,𝛾 (𝜔)𝑒𝑖𝜔𝑡 d𝜔,
Ψ𝛽,𝛾 (𝜔)
𝑎𝛽,𝛾 𝜔𝛽𝑒−𝜔𝛾𝜔 > 0
1
2𝑎𝛽,𝛾 𝜔𝛽𝑒−𝜔𝛾𝜔= 0
0𝜔 < 0
.(1)
where 𝛽0and 𝛾 > 0,𝜔is the angular frequency and 𝑎𝛽,𝛾 2𝑒𝛾
𝛽1
𝛾is the amplitude coefficient used as a real-
valued normalised constant. Here, 𝑒is Euler’s number, 𝛽characterises the low-frequency behaviour, and 𝛾defines the
high-frequency decay. We can rewrite Eq. 1in the Fourier domain, parameterised by 𝛽and 𝛾as in Eq. 2.
𝜙𝛽,𝛾 (𝜏 , 𝑠)∞
−∞
1
𝑠𝜓∗
𝛽,𝛾 (𝑡−𝜏
𝑠)𝑓(𝑡) dt = 1
2𝜋∞
−∞
ei𝜔𝜏 Ψ∗
𝛽,𝛾 (s𝜔)F(𝜔) d𝜔. (2)
where 𝐹(𝜔)is the Fourier transform of 𝑓(𝑡), and ∗denotes the complex conjugate. When Ψ∗
𝛽,𝛾 (𝜔)is real-valued, the
conjugation may be omitted. The scale variable 𝑠allows the wavelet to stretch or compress in time. In order to reflect
the energy of 𝑓(𝑡)and to normalise time-domain wavelets to preserve constant energy, 1
𝑠is typically used. However,
instead, we used 1
𝑠since we define the amplitude of the time-located signals. To recover time-domain representation,
we can use the inverse Fourier transform by 𝑓(𝑡) = 1
2𝜋∞
−∞ 𝑒𝑖𝜔𝑡 𝐹(𝜔) d𝜔and 𝜓𝛽,𝛾 (𝑡) = ∞
−∞ 𝑒𝑖𝜔𝑡 dt = 2𝜋 𝛿(𝜔), where
𝛿(𝜔)is the Dirac delta function.
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 5 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
The representation of Morse wavelets would be more oscillatory when both 𝛽and 𝛾increase, and more localised
with impulses when these parameters decrease. On the other hand, increasing 𝛽and holding 𝛾fixed expand the central
portion of the wavelet and increase the long-term rate of decay. Whereas, increasing 𝛾by keeping 𝛽constant extends
the wavelet envelope without affecting the long-term decay rate. Inspired by Lilly and Olhede (2008), we set the
symmetry parameter 𝛾to 3 and the time-bandwidth product 𝑃2=𝛽𝛾 to 60. We have used 𝐿1normalisation to provide
the same magnitude in wavelets when we have the same amplitude oscillatory components at different scales.
(a) (b)
Figure 5: Annotated spikes by the expert (black arrows) on the Morse wavelet scalogram for (a) 𝑆𝑙𝑖𝑐 𝑒1and (b) 𝑆 𝑙𝑖𝑐𝑒2.
The scalogram is plotted as a function of time and frequency, where the maximum absolute value at each frequency is
used for the normalisation of the coefficient. The frequency axis is shown on a linear scale.
Figure 5displays two randomly chosen 3000-second chunks of fungi electrical activity (namely 𝑆 𝑙𝑖𝑐𝑒1and 𝑆𝑙𝑖𝑐𝑒2)
with their Morse wavelet scalograms. We observed that the use of the maximum absolute value at each frequency
(level) to normalise coefficients may help to identify events that may involve spikes. We then used Eq. 3to normalise
coefficients and set zero entries to 1.
𝜅𝛽,𝛾 (𝜏 , 𝑠) = 𝜙𝛽,𝛾 (𝜏, 𝑠)⊺,
𝑔𝛽,𝛾 (𝜏 , 𝑠) = 𝜂×𝜅𝛽,𝛾 (𝜏, 𝑠) − min𝑠(𝜅𝛽 ,𝛾 (𝜏, 𝑠))
max𝑠(𝜅𝛽,𝛾 (𝜏 , 𝑠)) ⊺
.(3)
where ∙and (∙)⊺return the absolute value and the matrix transpose, respectively. Here, 𝜂is a scaling factor that we
empirically set to 240. We used 𝑔𝛽,𝛾 (𝜏, 𝑠)in Algorithm 1to extract the candidate ROIs shown in Figure 6. As shown
in Figure 6(c,d), some of the detected regions are either too short2or lack repolarisation and depolarisation periods
that should be removed from .
Algorithm 2is proposed to eliminate so-called pseudo-spike and inflection regions which do not reach the spike
characteristics as shown in Figure 7. Applying Algorithm 2resulted in the loss of two spikes in 𝑆𝑙𝑖𝑐𝑒1(see Figure 7(a))
and the failure to eliminate two pseudo-spike and two inflection regions in 𝑆𝑙𝑖𝑐𝑒2(see Figure 7(b)). We found that the
analysis of the analytic signal by its envelope could improve the accuracy of the spike detection.
3.3. Analytical signal envelope for locating spike pattern
We calculated the magnitude of the analytic signal to obtain the signal envelope (𝜉). The analytic signal is detected
using the discrete Fourier Transform as implemented in the Hilbert Transform. In order to highlight effective signal
peaks and neutralise inflection regions, the second numerical signal derivation (𝐿=𝜕2𝑓∕4𝜕𝑡2) was calculated. A
frequency-domain approach is proposed in Marple (1999) to approximately generate a discrete-time analytic signal.
2We observed in our previous studies Adamatzky (2018b,2019) that minimum spike length was 5 mins.
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Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
(c) (d)
Figure 6: (a,b) Identified local maxima and minima over 𝑔𝛽 ,𝛾 (𝜏, 𝑠)in (a) 𝑆 𝑙𝑖𝑐𝑒1and (b) 𝑆𝑙𝑖𝑐𝑒2. The second-row of the
plot is the inverse of the first row; therefore, the marked maximums are identical to the local minima. (c,d) Candidate
regions of interest which are alternately coloured purple and green to ease visual tracking.
In this approach, the negative frequency in half of each spectral period is set to 0, resulting in a periodic one-sided
spectrum. The procedure for generating a complex-valued 𝑁-point (𝑁is even) discrete-time analytic signal (𝐹(𝜔))
from a real-valued 𝑁-point discrete time signal (𝐿[𝑛]) is as follows:
1. Calculate the 𝑁-point discrete-time Fourier transform using 𝐹(𝜔) = 𝑇𝑁−1
𝑛=0 𝐿[𝑛]𝑒−𝑖2𝜋𝜔𝑇 𝑛 , where 𝜔
1∕2𝑇Hz. 𝐿[𝑛],0𝑛𝑁− 1 is obtained by sampling the band-limited real-valued continuous-time sig-
nal 𝐿(𝑛𝑇 ) = 𝐿[𝑛]at periodic time intervals of 𝑇seconds to prevent aliasing.
2. Calculate the 𝑁-point one-sided discrete-time analytic signal transform:
𝑍[𝑚] =
𝐹[0],for 𝑚= 0
2𝐹[𝑚],for 1𝑚𝑁
2− 1
𝐹[𝑁
2],for 𝑚=𝑁
2
0,for 𝑁
2+ 1 𝑚𝑁− 1.
(4)
3. Calculate the 𝑁-point inverse discrete-time Fourier transform to obtain the complex discrete-time analytic signal
of same sample rate as the original 𝐿[𝑛]
𝑧[𝑛] = 1
𝑁𝑇
𝑁−1
𝑚=0
𝑍[𝑚]𝑒
𝑖2𝜋𝑚𝑛
𝑁(5)
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Electrical activity of fungi: Spikes detection and complexity analysis
Algorithm 1: Detecting candidate regions for time-localised events.
Input : 𝑔𝛽 ,𝛾 (𝜏, 𝑠)– Scaled wavelets coefficients.
Output: – set of candidate regions.
1begin
2𝜖= 0.05 × (max(𝑔𝛽,𝛾 (𝜏 , 𝑠)) − min(𝑔𝛽,𝛾 (𝜏, 𝑠)));
3𝑚𝑎𝑥𝑔←set of all LocalMaximum(𝑔𝛽,𝛾 (𝜏 , 𝑠), 𝜖);
// LocalMaximum() returns 𝜏∗if ∀𝜏∈ (𝜏∗±𝜖), 𝑔𝛽,𝛾 (𝜏∗, 𝑠)𝑔𝛽 ,𝛾 (𝜏, 𝑠).
4𝑚𝑖𝑛𝑔←set of all LocalMinimum(𝑔𝛽,𝛾 (𝜏 , 𝑠), 𝜖);
5←𝐬𝐨𝐫𝐭 (𝑚𝑖𝑛𝑔𝑚𝑎𝑥𝑔);
6𝑛=𝐜𝐚𝐫𝐝();
// 𝐜𝐚𝐫𝐝(𝐴)returns number of entries in 𝐴.
7if 𝑛1 (mod 2) then
8slack ←𝐦𝐞𝐚𝐧(difference of two consecutive entries);
9Add 𝐦𝐢𝐧(𝑛+ slack, 𝜏)to ;
10 𝑛=𝑛+ 1;
11 end
12 ←(𝑖,𝑖+1),∀𝑖∈ {1,3,⋯, 𝑛 − 1}
13 end
14 return
Algorithm 2: Excluding pseudo-spike and inflation regions form candidate ROI.
Input : — set of ROI, i.e., Algorithm 1output,
𝑓— Electrical potential.
Output: — set of wavelet-based ROIs,
— set of pseudo-spike and inflection regions.
1begin
2for 𝑖= 1 to 𝐜𝐚𝐫𝐝()do
3𝑙𝑏 ←(𝑖, 1);
4𝑢𝑏 ←(𝑖, 2);
5if (𝑢𝑏 −𝑙𝑏)>30 then
6𝑐ℎ𝑢𝑛𝑘 =𝑓[𝑙𝑏 ⋯𝑢𝑏];
7𝑚𝑖𝑛𝑖𝑚𝑎 =𝐦𝐢𝐧(isLocalMinimum(chunk));
// isLocalMinimum() and isLocalMaximum() use spline interpolation in
locating local extreme Hall and Meyer (1976).
8𝑚𝑎𝑥𝑖𝑚𝑎 =𝐦𝐚𝐱(isLocalMaximum(chunk));
9if 𝑓(𝑚𝑖𝑛𝑖𝑚𝑎)<𝐦𝐢𝐧(𝑓(𝑙𝑏), 𝑓 (𝑢𝑏)) 𝐨𝐫 𝑓(𝑚𝑎𝑥𝑖𝑚𝑎)>𝐦𝐚𝐱(𝑓(𝑙𝑏), 𝑓 (𝑢𝑏)) then
10 ←[𝑙𝑏, 𝑢𝑏];
11 else
12 ←[𝑙𝑏, 𝑢𝑏];
13 end
14 end
15 end
16 end
17 return ,
Obtaining an analytic signal in this way satisfies two properties: (1) The real part is equivalent to the original discrete-
time sequence; (2) the real and imaginary components are orthogonal. Calculating the magnitude of the analytic signal
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Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
Figure 7: Results of applying Algorithm 2to (a) 𝑆𝑙𝑖𝑐𝑒1and (b) 𝑆 𝑙𝑖𝑐 𝑒2. Two spike events are missed in 𝑆𝑙𝑖𝑐𝑒1. Two
pseudo-spike and two inflection regions still remain in 𝑆𝑙𝑖𝑐𝑒2.
using Eq. 6results in the signal envelope (𝜉[𝑛]) containing the upper (𝜉𝐻[𝑛]) and lower (𝜉𝐿[𝑛]) envelopes of 𝐿[𝑛].
𝜉[𝑛] = 𝑧[𝑛](6)
Envelopes are calculated using spline interpolation over a local maximum separated by at least 𝑛𝑝= 60 samples.
We considered 𝑛𝑝= 60 because, in our previous studies Adamatzky (2018b,2019), we did not observe any electrical
potential of spikes shorter than 60 seconds. Algorithm 3was proposed to locate candidate regions using a signal
envelope.
Figure 8(a,d) shows the candidate regions in before applying Step 13. At this step, while includes regions
that do not align with the spike definition (pointed by arrow in the plot), the correctly identified spikes are consistent
with our findings in Adamatzky (2018a,b). Steps 13 and 14 were used to remove non-spike regions marked in red
in Figure 8(b,e). However, the output of Algorithm 3(see Figure 8(c,f)) still includes regions belonging to either
pseudo-spike/inflection regions or refractory periods attached to pseudo-spike regions.
To fix mis-identified ROIs in Algorithms 2and 3, we proposed Algorithm 4in which regions in (∪)are used
to update . Indeed, if the ROI in is a subset of (∪), we add it to the spike event set (𝑠) and update the spike
length. If the ROI in (∪)is a subset of , we add it to the pseudo-spike set (𝑝). In the case of an intersection that
does not meet the subset requirement, we concatenate ROIs and divide the new region from the intersection point into
two segments. Then, we add the segment with the minimum length to 𝑝. Finally, regions with a length of less than
60 seconds are excluded from both 𝑠and 𝑝. The results are shown in Figure 9.
4. Experimental results
This section consists of objective and complexity analyses. In the objective analysis, we demonstrated the effective-
ness of the spike event detection method compared to conventional spike detection techniques in neuroscience Nenadic
and Burdick (2004); Shimazaki and Shinomoto (2010). We also compared the proposed method with the expert opinion
on the location of spikes. In the complexity analysis, we selected the complexity measures used in previous studies Mi-
noofam et al. (2012,2014); Parsa et al. (2017); Taghipour et al. (2016); Dehshibi et al. (2015,2020); Gholami et al.
(2020) to quantify spatio-temporal activity patterns.
4.1. Objective analysis
Various methods have been proposed for detecting and sorting spike events in EC recordings Quiroga et al. (2004);
Nenadic and Burdick (2004); Obeid and Wolf (2004); Wilson and Emerson (2002); Gotman and Wang (1991); Wilson
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 9 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
Algorithm 3: Detecting candidate spike region from signal envelope.
Input : 𝜉[𝑛]— Envelope of signal 𝐿[𝑡],
𝑛𝑝= 60 — Minimum distance between two consecutive local extreme.
Output: — set of envelope-based ROIs.
1begin
2𝜉𝑀[𝑛] = 𝜉𝐻[𝑛] + 𝜉𝐿[𝑛]∕2;
3[𝑣𝑎𝑙𝑚𝑖𝑛, 𝑖𝑛𝑑𝑚𝑖𝑛 ] = isLocalMinimum(𝜉𝑀[𝑛], 𝑛𝑝);
4[𝑣𝑎𝑙𝑚𝑎𝑥, 𝑖𝑛𝑑𝑚𝑎𝑥 ] = isLocalMaximum(𝜉𝑀[𝑛], 𝑛𝑝);
// isLocalMinimum() and isLocalMaximum() locate local minimum and maximum,
respectively.
5𝑗←index of the first local maximum whose value is greater than the value of the first local minimum;
6for 𝑖= 1 to 𝐜𝐚𝐫𝐝(𝑖𝑛𝑑𝑚𝑖𝑛 )do
7if 𝑗𝐜𝐚𝐫𝐝(𝑖𝑛𝑑𝑚𝑎𝑥 )then
8Δ←𝑣𝑎𝑙𝑚𝑎𝑥(𝑗) − 𝑣𝑎𝑙𝑚𝑖𝑛 (𝑖);
9Add 𝑖𝑛𝑑𝑚𝑖𝑛(𝑖), 𝑖𝑛𝑑𝑚𝑎𝑥 (𝑗),Δto ;
10 𝑗←𝑗+ 1;
11 end
12 end
// has 𝑗rows and 3columns, as 1,2, and 3.
13 𝜌=𝐦𝐞𝐚𝐧(3) − 𝐬𝐭𝐝(3);
// 𝐦𝐞𝐚𝐧() and 𝐬𝐭𝐝() calculate the mean and standard deviation, respectively.
14 Remove the 𝑘𝑡ℎ entry from where 3(𝑘)< 𝜌 – see Figure 8(b);
15 end
16 return
et al. (1999); Franke et al. (2010); Rácz et al. (2020); Wang et al. (2020); Sablok et al. (2020); Liu et al. (2020). However,
only a few of these methods do not require additional details, such as template construction and the supervised setting
of thresholds for detecting and sorting spike events Nenadic and Burdick (2004); Shimazaki and Shinomoto (2010).
Nenadic and Burdick Nenadic and Burdick (2004) have developed an unsupervised method for detecting and locating
spikes in noisy neural recordings. This approach benefits from the continuous transformation of the wavelet. They
applied multi-scale signal decomposition using the ‘bior1.3,’ ‘bior1.5,’ ‘Haar,’ or ‘db2’ wavelet basis. To determine
the presence of spikes, they separated the signal and noise at each scale and performed Bayesian hypothesis testing.
Finally, they combined decisions on different scales to estimate the arrival times of individual spikes.
Shimazaki and Shinomoto Shimazaki and Shinomoto (2010) proposed an optimisation technique for the timing-
histogram bin width selection. This optimisation minimised the mean integrated square in the kernel density estima-
tion. This method benefits from variable kernel width, which allowed grasping non-stationary phenomena. Also, this
method used stiffness constant to avoid possible overfitting due to excessive freedom in the bandwidth variability. The
calculated bandwidth was then used as a proxy for filtering spike event regions. Figure 10 shows the results of applying
these methods to two chunks with a length of 3000 seconds.
Both compete methods could not correctly detect all spike events that were located by the expert. The wavelet-based
method could locate three spikes in Figure 10(b) without detecting any spike in Figure 10(a). The adaptive bandwidth
kernel-based method could detect one spike in Figure 10(b) and one pseudo-spike in Figures 10(a, b). While our
proposed method misidentified one spike event in Figure 9(a) and three spikes in Figure 9(b).
We also compared the proposed method with the expert opinion on a randomly selected 36,000-second chunk,
i.e., 10 hours of electrical activity recordings. In this quantitative comparison, the proposed approach could correctly
locate 21 spikes and four pseudo-spike events. Our method also overestimated two refractory periods, resulting in the
true-positive and false-positive rates of 76% and 16%, respectively. Figure 11(a) shows located spikes by the expert,
and Figure 11(b) demonstrates the results of the proposed spike detection method.
We applied the proposed method to six experiments where the statistical results are shown in Figures 12 and 13 and
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 10 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b) (c)
(d) (e) (f)
Figure 8: Results of Algorithm 3applied to 𝑆𝑙𝑖𝑐𝑒1(first row) and 𝑆 𝑙𝑖𝑐𝑒2(second row). (a,d) Candidate regions by finding
local minima and maxima in the analytic signal envelope. The pointed regions are also highlighted in the bar chart in
red. (b,e) The absolute difference in prominence between the successive local minima and maxima. Regions that do
not satisfy 3(𝑘)< 𝜌 are coloured in red. (c,f ) Regions of Interest in . The grey dashed rectangle shows the correct
spike, including repolarisation, depolarisation, and refractory periods. The purple dashed rectangle shows the region whose
refractory period attached to the pseudo-spike region.
(a) (b)
Figure 9: Results of applying Algorithm 4to (a) 𝑆𝑙𝑖𝑐 𝑒1and (b) 𝑆 𝑙𝑖𝑐𝑒2. We alternatively used red/purple for colouring
spike events and blue/cyan for colouring pseudo-spike events.
summarised in Table 1. It should be noted that the placement of the electrodes in two experiments was in lines with
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 11 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
Algorithm 4: Extracting fungi spike and pseudo-spike events.
Input : ,,— Regions of interest.
Output: 𝑠,𝑝— Fungi spike and pseudo-spike events, respectively.
1begin
2foreach 𝑟𝑒∈do
3𝑐ℎ𝑢𝑛𝑘𝑒←[𝑟1
𝑒⋯𝑟2
𝑒];
4foreach 𝑟𝑤∈ (∪)do
5𝑐ℎ𝑢𝑛𝑘𝑤←[𝑟1
𝑤⋯𝑟2
𝑤];
6switch 𝑐ℎ𝑢𝑛𝑘𝑤, 𝑐ℎ𝑢𝑛𝑘𝑒do
7case 𝑐ℎ𝑢𝑛𝑘𝑒⊂ 𝑐ℎ𝑢𝑛𝑘𝑤do
8𝑐ℎ𝑢𝑛𝑘𝑤(𝑒𝑛𝑑 ) = 𝑐ℎ𝑢𝑛𝑘𝑒(𝑒𝑛𝑑);
9𝑠←𝑐ℎ𝑢𝑛𝑘𝑤;
10 end
11 case 𝑐ℎ𝑢𝑛𝑘𝑤⊂ 𝑐ℎ𝑢𝑛𝑘𝑒do
12 𝑝←𝑐ℎ𝑢𝑛𝑘𝑤;
13 end
14 case intersect(𝑐ℎ𝑢𝑛𝑘𝑤, 𝑐 ℎ𝑢𝑛𝑘𝑒)do
// intersect() checks if two chunks have an intersection point.
15 Split the concatenation of 𝑐ℎ𝑢𝑛𝑘𝑤and 𝑐ℎ𝑢𝑛𝑘𝑒from intersection point into two
sub-Chunks;
16 𝑝←sub-Chunks;
17 end
18 end
19 end
20 end
21 foreach 𝑟∈ (𝑠∪𝑝)do
22 Remove 𝑟if 𝑟<60;
23 end
24 end
25 return 𝑠,𝑝
a distance of 1 cm, in two experiments it was in lines with a distance of 2 cm, and in two experiments it was random
with a distance of approximately 2 cm. The proposed method is implemented in MATLAB R2020a, where the code
and details of the experiments can be found in Dehshibi and Adamatzky (2020).
These results are consistent with the experiments carried out on the electrical activity of Physarum polycephalum
Adamatzky (2013,2018a) where it has been reported that the length of the Physarum spike is between 60 and 120
seconds. Physarum is faster than fungi in terms of growth. Now, with further observations, we can hypothesise that
the length of the fungal spikes cannot be less than 60 seconds.
4.2. Complexity Analysis
To quantify the complexity of the electrical signalling recorded, we used the following measurements:
1. The Shannon entropy (𝐻) is calculated as 𝐻= − 𝑤∈𝑊(𝜈(𝑤)∕𝜂⋅𝑙𝑛(𝜈(𝑤)∕𝜂)), where 𝜈(𝑤)is a number of
times the neighbourhood configuration 𝑤is found in configuration 𝑊, and 𝜂is the total number of spike events
found in all channels of the experiment.
2. Simpson’s diversity (𝑆) is calculated as 𝑆=𝑤∈𝑊(𝜈(𝑤)∕𝜂)2. It linearly correlates with Shannon entropy for
𝐻 < 3and the relationship becomes logarithmic for higher values of 𝐻. The value of 𝑆ranges between 0 and
1, where 1 represents infinite diversity and 0, no diversity.
3. Space filling (𝐷) is the ratio of non-zero entries in 𝑊to the total length of string.
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 12 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
Figure 10: Results of applying proposed algorithms in Nenadic and Burdick (2004); Shimazaki and Shinomoto (2010) to
(a) 𝑆𝑙𝑖𝑐𝑒1and (b) 𝑆 𝑙𝑖𝑐𝑒2. Note that the wavelet-based method can only locate spike arrival time. The kernel bandwidth
optimisation can, however, extract the spike region.
(a) (b)
Figure 11: (a) Spike arrival time located by the expert. Here we used augmented pink arrow to point to these spikes.
(b) Spike regions extracted by the proposed method. Spike regions are alternatively coloured in orange and violet. The
green areas point to pseudo-spike regions that are mistaken for spikes. Blue rectangles with dash edge show overestimated
refractory periods. We used black arrows to point to the missed spikes.
4. Expressiveness (𝐸) is calculated as the Shannon entropy 𝐻divided by space-filling ratio 𝐷, where it reflects
the ‘economy of diversity’.
5. Lempel–Ziv complexity (𝐿𝑍) is used to assess temporal signal diversity, i.e., compressibility. Here, we repre-
sented the spiking activity of mycelium with a binary string where ‘1s’ indicates the presence of a spike and ‘0s’
otherwise. Formally, as both the barcode and the channels’ electrical activity are stored as PNG images, LZ is
the ratio of the barcode image size to the size of the electrical activity image (see Figure 14 and 15).
6. Perturbation complexity index 𝑃 𝐶𝐼 =𝐿𝑍 ∕𝐻.
To calculate Lempel–Ziv complexity, we saved each signal as a PNG image (see two examples in Figure 15), where
the ‘deflation’ algorithm used in PNG lossless compression Deutsch and Gailly (1996); Howard (1993); Roelofs and
Koman (1999) is a variation of the classical LZ77 algorithm Ziv and Lempel (1977). We employed this approach as
the recorded signal is a non-binary string. We take the largest PNG file size to normalise this measurement.
In order to assess signal diversity across all channels and observations, each experiment was represented by a binary
matrix with a row for each channel and a column for each observation. This binary matrix is then concatenated by
observation to form a single binary string. We used Kolmogorov complexity algorithm Kaspar and Schuster (1987)
to measure the Lempel—-Ziv complexity (𝐿𝑍𝑐) across channels. 𝐿𝑍 𝑐 captures both temporal diversity on a single
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 13 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b) (c)
(d) (e) (f)
Figure 12: Distribution of spike event lengths with superimposed Gaussian and Adaptive bandwidth kernels Shimazaki and
Shinomoto (2010). (a,b) In-line electrode arrangements with a distance of 1 cm. (c,d) In-line electrode arrangements with
a distance of 2 cm. (e,f ) Random electrode arrangements with an approximate distance of 2 cm.
Table 1
The dominant value and bandwidth for the length and amplitude of the spike in each experiment across all recording
channels. Duration and amplitude of spikes are estimated by the probability density function (PDF) and the adaptive
bandwidth kernel (ABK) Shimazaki and Shinomoto (2010). The bold-faced blue and red entries show the absolute
minimum and maximum values, respectively. As we have bi-directional potential changes, we have considered absolute
value.
#Channels #Spikes
Length (sec) Amplitude (V)
PDF ABK PDF ABK
Dominant Bandwidth Dominant Bandwidth Dominant Bandwidth Dominant Bandwidth
#1 8 565 84.00 75.61 84.00 60.22 0.00003 0.00048 -0.00117 0.00576
#2 5 447 366.80 154.31 625.60 126.47 0.00642 0.00544 0.00642 0.00667
#3 4 124 84.00 75.61 84.00 60.22 0.00003 0.00048 -0.00117 0.00576
#4 5 951 534.12 80.09 534.12 84.80 -0.00239 0.00301 -0.00239 0.00508
#5 5 573 334.25 74.52 334.25 80.9 -0.01536 0.00218 -0.01462 0.00357
#6 15 862 1014.72 99.53 1014.72 92.67 -0.00172 0.00381 -0.01277 0.00591
channel and spatial diversity across channels. We also normalised 𝐿𝑍 𝑐 by dividing the raw value by the randomly
shuffled value obtained for the same binary input sequence. Since the value of 𝐿𝑍 for a fixed-length binary sequence
is maximum if the sequence is absolutely random, the normalised values represent the degree of signal diversity on a
scale from 0 to 1. The results of the calculation of these complexity measurements for all six configurations are shown
in Figure 16 and summarised in Table 2.
We calculated the aforementioned complexity criteria for three forms of writing to illustrate the communication
complexity of the mycelium substrate, including (1) news items3, (2) random alphanumeric sequences4and (3) periodic
3https://www.sciencemag.org/news/2020/07/meet-lizard-man-reptile-loving-biologist-tackling-some-biggest-questions-evolution
4We used available service at https://www.random.org/
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 14 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b) (c)
(d) (e) (f)
Figure 13: Distribution of spike maximum amplitudes with superimposed Gaussian and Adaptive bandwidth kernels Shi-
mazaki and Shinomoto (2010) for (a,b) in lines electrode placement with a distance of 1 cm. (c,d) in lines electrode
placement with a distance of 2 cm. (e,f ) random electrode placement with an approximate distance of 2 cm.
Table 2
The mean of complexity measurements for six experiments.
#Channel #Spike Lempel–Ziv
complexity
Shannon
entropy
Simpson’s
diversity
Space
filling Kolmogorov PCI Expressiveness
#1 8 565 0.79 45.81 0.76 30.68×10−5 30.36×10−4 0.365 20.8×104
#2 5 447 0.91 63.27 0.98 35.20×10−5 35.78×10−4 0.021 18.6×104
#3 4 124 0.75 22.57 0.61 48.10×10−5 10.94×10−4 0.333 29.71
#4 5 951 0.93 123.11 0.89 57.30×10−5 56.05×10−4 0.072 23.8×104
#5 5 573 0.88 75.75 0.79 53.02×10−5 52.80×10−4 0.077 16.4×104
#6 15 862 0.69 39.96 0.71 24.20×10−5 25.06×10−4 0.207 20.4×104
alphanumeric sequences encoded with Huffman code Huffman (1952), see barcode in Figure 17. Table 3presents the
results of the comparison. We also considered two podcasts in English (387 seconds) and Chinese (385 seconds)
to compare the complexity of fungal spiking with human speech. Both podcasts were in MP3 format at a sampling
rate of 44100 Hz. We randomly selected two chunks from two electrical activity channels with a duration of 388
and 342 seconds to compare with the English and Chinese podcasts, respectively. We observed that, in both cases, the
Kolmogorov complexity of the fungal is lower than the human speech, implying the fact that the amount of information
transmitted by the fungi is less than the human voice. From a technical point of view, we computed the DC level of
each signal and binarised the signal with respect to that level Huang and Lin (2009). To binaries the signal, we set the
inputs with values less than or equal to the DC level to 0 and the rest of the inputs to 1. The findings are shown in
Figure 18.
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Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
(c) (d)
(e) (f)
Figure 14: Barcode-like representation of spike events in various channels for (a,b) in-line electrode arrangements at a
distance of 1 cm, (c,d) in-line electrode arrangements at a distance of 2 cm, and (e,f) random electrode arrangements at
an approximate distance of 2 cm.
5. Discussion
We developed algorithmic framework for exhaustive characterisation of electrical activity of a substrate colonised
by mycelium of oyster fungi Pleurotus djamor. We evidenced spiking activity of the mycelium. We found that average
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 16 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
Figure 15: Two samples from input channels, which are saved in black and white PNG format without axes and annotations.
Table 3
The complexity measurements for pieces of news, a random sequence of alphanumeric, a periodic sequence of alphanumeric
along with three chunks randomly selected from our experiments.
Length Lempel–Ziv
complexity
Shannon
entropy
Simpson’s
diversity
Space
filling Kolmogorov PCI Expressiveness
News 36187 0.127919 4.421728 0.999941 0.465996 0.765382 0.173096 9.49
Random sequence 36002 0.125465 5.770331 0.999941 0.469835 1.001850 0.173621 12.28
Periodic sequence 36006 0.127090 3.882058 0.999937 0.442426 0.076508 0.019708 8.77
Chunk 1 36000 0.067611 16.194914 0.947368 0.000556 0.006307 0.000389 29150.84
Chunk 2 36000 0.007250 15.478087 0.944444 0.000528 0.006727 0.000435 29326.90
Chunk 3 36000 0.068417 31.680374 0.976190 0.001194 0.012613 0.000398 26523.10
dominant duration of an action-potential like spike is 402 sec. The spikes amplitudes’ depends on the location of the
source of electrical activity related to the position of electrodes, thus the amplitudes provide less useful information.
The amplitudes vary from 0.5 mV to 6 mV. This is indeed low compared to 50-60 mV of intracellular recording,
nevertheless understandable due to the fact the electrodes are inserted not even in mycelium strands but in the substrate
colonised by mycelium. The shift of the distribution to higher values of spike amplitude in experiments with a distance
of 2 cm between the electrodes might indicate that the width of the propagation of the excitation wave front exceeds
1 cm and might even be close to 2 cm.
The spiking events have been characterised with several complexity measures. Most measures, apart of Kol-
mogorov complexity shown a low degree of variability between channels (different sites of the recordings). The Kol-
mogorov complexity of fungal spiking varies from 11×10−4 to 57×10−4. This might indicated mycelium sub-networks
in different parts of the substrate have been transmitting different information to other parts of the mycelium network.
This is somehow echoes experimental results on communication between ants analysed with Kolmogorov complexity:
longer paths communicated ants corresponds to higher values of complexity Ryabko and Reznikova (1996).
LZ complexity of fungal language (Tab. 2) is much higher than of news, random or periodic sequences (Tab. 3).
The same can be observed for Shannon entropy. Kolmogorov complexity of the fungal language is much lower than
that of news sampler or random or periodic sequences. Complexity of European languages based on their compress-
ibility Sadeniemi et al. (2008) is shown in Figure 19, French having lowest LZ complexity 0.66 and Finnish highest
LZ complexity 0.79. Fungal language of electrical activity has minimum LZ complexity 0.61 and maximum 0.91
(media 0.85, average 0.83). Thus, we can speculate that a complexity of fungal language is higher than that of human
languages (at least for European languages).
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 17 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b)
(c) (d)
(e) (f)
Figure 16: (a) Shannon entropy, (b) Simpson’s diversity, (c) Space filling, (d) Expressiveness, (e) Lempel–Ziv complexity,
and (f) Perturbation complexity index. All measurements are scaled to the range of [0,1].
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 18 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
(a) (b) (c)
Figure 17: Binary representation of (a) pieces of news,(b) random sequence of alphanumeric, and (c) periodic sequence
of alphanumeric after applying Huffman coding.
(a) DC level = −6.49× 10−5, sampling rate = 44 kHz, samples
= 17100912, Kolmogorov = 0.739866
(b) DC level = −27.23× 10−5 , sampling rate = 1 Hz, samples
= 388, Kolmogorov = 0.598645
(c) DC level = −20.05 × 10−5, sampling rate = 44 kHz, sam-
ples = 15057264, Kolmogorov = 0.753261
(d) DC level = −9.31 × 10−5, sampling rate = 1 Hz, samples
= 342, Kolmogorov = 0.574892
Figure 18: Comparison of the human voice in (a-c) English/Chinese with the electrical activity of fungi with the duration
of (b-d) 388/342 seconds.
Acknowledgement
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.
Declaration of competing interest
There is no conflict of interest with this paper.
Credit Author Statement
All authors are responsible for the experiments and writing of the paper.
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 19 of 22
Electrical activity of fungi: Spikes detection and complexity analysis
LZ complexity
0.60
0.65
0.70
0.75
0.80
0.85
Language
fr es pt ga it en sl nl mt da el sv lv de pl lt sk et fi fu
Figure 19: Lempel-Ziv complexity of European languages (data from Sadeniemi et al. (2008)) with average complexity of
fungal (‘fu’) electrical activity language added.
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Mohammad Mahdi Dehshibi received his PhD in Computer Science from Islamic Azad University, Tehran, Iran in 2017.
He is currently a postdoctoral research fellow at Universitat Oberta de Catalunya (UOC). He was a visiting researcher in
Unconventional Computing Lab, UWE, Bristol, U.K. He has contributed to over 50 papers published in scientific Journals
or International Conferences. His research interests include Unconventional Computing, Affective Computing, and Cellular
Automata.
Andrew Adamatzky is Professor of Unconventional Computing and Director of the Unconventional Computing Labora-
tory, Department of Computer Science, University of the West of England, Bristol, UK. He does research in molecular
computing, reaction-diffusion computing, collision-based computing, cellular automata, slime mould computing, massive
parallel computation, applied mathematics, complexity, nature-inspired optimisation, collective intelligence and robotics,
bionics, computational psychology, non-linear science, novel hardware, and future and emergent computation. He authored
seven books, mostly notable are ‘Reaction-Diffusion Computing’, ‘Dynamics of Crow Minds’, ‘Physarum Machines’, and
edited twenty-two books in computing, most notable are ‘Collision Based Computing’, ‘Game of Life Cellular Automata’,
‘Memristor Networks’; he also produced a series of influential artworks published in the atlas ‘Silence of Slime Mould’.
He is founding editor-in-chief of ‘J of Cellular Automata’ and ‘J of Unconventional Computing’ and editor-in-chief of ‘J
Parallel, Emergent, Distributed Systems’ and ‘Parallel Processing Letters’.
Dehshibi and Adamatzky.: Preprint submitted to Elsevier Page 22 of 22
