Mycelium as a computational medium: a framework for growth modeling towards reservoir computing

Mycelium as a computational medium: a framework for growth modeling towards reservoir computing Ioannis Tompris 1 •Ioannis K. Chatzipaschalis 1,2 •Theodoros Panagiotis Chatzinikolaou 1 • Georgios Kleitsiotis 1 •Karolos-Alexandros Tsakalos 1 •Iosif-Angelos Fyrigos 1 •Michail-Antisthenis Tsompanas 3 • Andrew Adamatzky 3 •Phil Ayres 4 •Georgios Ch. Sirakoulis 1 Accepted: 2 July 2025 ÓThe Author(s) 2025 Abstract Mycelium, the intricate vegetative network of fungi, has emerged as a promising candidate within the realm of engineered living materials (ELMs). While its intriguing structural and electrical properties highlight its potential, mycelium growth is highly sensitive to environmental conditions. To bridge this gap, a robust framework was developed to both model mycelium growth and explore its computational capabilities. This framework uses a cellular automata (CA) approach, enhanced with reaction-diffusion (RD) processes, to simulate mycelium growth under diverse environmental conditions. This configuration, combined with tunable parameters, enables the identification and validation of optimal growth patterns, supported by an algorithm designed to extract key features of hyphae–the fundamental building blocks of the mycelial network. Subsequently, the small-world properties of the modeled mycelium networks were investigated, revealing high clustering coefficients and short path lengths, characteristics that make them well-suited for reservoir computing (RC). To demonstrate their computational capabilities, mycelium-inspired RC architectures were evaluated on the MNIST dataset classification task, achieving an accuracy of up to 97.09%, highlighting the effectiveness of biologically inspired models. As a result, this framework establishes a comprehensive test-bench for mycelium modeling, growth, and computational exploration, paving the way for innovative applications in bio-inspired computing. Keywords Mycelium Reaction diffusion Cellular automata Electrical activity Small-world Reservoir computing  Neuron 1 Introduction Engineered Living Materials (ELMs) are considered as an emerging field of research, characterized by their unique ability to integrate self-healing, regenerative, and adaptive traits of biological systems within contemporary materials (Mora-Boza et al. 2023). Among various ELMs, mycelium-based materials are particularly notable (Elsacker et al. 2023;Karanaetal.2018; Adamatzky 2023) and serve as the focus of this study. This is because mycelium, the vegetative structure of fungi, is widely recognized for its growth and sustainability, offering an eco-friendly alternative to conventional materials while being abundantly available in nature (Ayres et al. 2022;Angelovaetal.2021). Furthermore, mycelium exhibits electrical activity, recently explored as a potential computing approach. More specifically, some studies (Roberts and Adamatzky 2023; Dehshibi and Adamatzky 2021; Adamatzky et al. 2019) demonstrate the distinctive electrical behavior of mycelium in response to various electrical stimuli, revealing a complex, brain-like spiking pattern that encapsulates the depolarization, repolarization, and refractory phases characteristic of biological spikes, together with low-voltage and sparse spiking activity. By integrating these electrical properties, combined with mycelium’s structural characteristics, which are indicative of small-world topologies, we enter the domain of liquid state machines (LSMs), a class of networks that utilize bio-inspired architectures and intricate dynamics (Tsakalos et al. 2021; Beiler et al. 2010;Daleetal.2021;Maass2011). LSMs belong to the broader framework of reservoir computing (RC) (Tanaka et al. 2019), which is utilized for solving pattern recognition problems and cognitive tasks. In this approach, Extended author information available on the last page of the article 123 Natural Computing https://doi.org/10.1007/s11047-025-10040-x(0123456789().,-volV)(0123456789().,-volV) input data is mapped onto a high-dimensional space representation through the reservoir dynamics, allowing for the extraction of temporal and spatial features. The reservoir, often composed of spiking neurons or non-linear dynamical units, uses recurrent connections and temporal memory to process sequential data, making it suitable for time-dependent tasks, such as pattern recognition and classification. LSMs can recognize complex patterns over time, making them useful for tasks that require adaptability. Despite its promising topology, electrical activity, and computing potential, mycelium faces challenges as a functional material. One of the primary obstacles lies in its sensitivity to environmental conditions, which necessitates highly controlled cultivation environments. Precise regulation of temperature, humidity, and light is essential to maintain optimal growth and functionality, making largescale production and experimentation both resource-intensive and technically demanding (Omuse et al. 2022; Arya and Singh 2016; Jesse 2023; Lin et al. 2021). Additionally, the commercialization of mycelium-based materials is hindered by stringent regulatory frameworks (Aiduang et al. 2024; Molitorisova ´et al. 2021; Molitorisova ´and Monaco 2023). As a result, while mycelium holds immense potential as a sustainable and computationally active material, its practical implementation remains a challenging endeavor. In this work, we exploit the unique topology and electrical activity of mycelium to implement biologically inspired reservoir networks for RC. By utilizing the mycelium’s small-world network properties and brain-like spiking behavior, we demonstrate effective RC performance, achieving up to 97.09% accuracy on the MNIST classification task. In this direction, a proof-of-concept framework, outlined in Fig. 1, is proposed. Section 2 introduces a reaction-diffusion Mycelium Model within a Cellular Automata (CA) framework, incorporating adjustable Fitting Parameters & Environmental Conditions to simulate mycelium growth under various factors. Section 3details the Hyphae Information algorithm, which evaluates growth and extracts Small-World Metrics to assess network topology. Section 4implements Reservoir Computing utilizing this topology, with configurable Training Options and Network Evaluation methods, which include both contemporary and biologically-inspired cost functions. Finally, Section 5concludes the paper providing a thorough outline of its most important aspects. 2 Mycelium model Reaction-Diffusion (RD) processes are essential in this model as they enable accurate fungal growth simulations, including mechanisms such as hyphal extension, anastomosis, and apical and lateral branching (Fricker et al. 2017; Boswell 2008; Tompris et al. 2024). The model is developed within a CA framework, which provides a discrete, lattice-based structure that enhances parallelism and allows precise control over the diffusion dynamics of the ELM, (Tsompanas et al. 2022; Pavlidis et al. 2023; Chatzinikolaou et al. 2024; Vaxevanellis et al. 2024) ensuring seamless integration with the desired RD processes (Codd 2014;Weimar1997). In contrast, lattice-free approaches documented in the literature demonstrate promising modeling capabilities (Carver and Boswell 2008; Vidal-Diez de Ulzurrun et al. 2017), although they often incur increased computational complexity and lack the inherent parallelism offered by CA-based system. Notably, the proposed model emerges as an ideal candidate for implementation on efficient parallel hardware (Ntinas et al. 2020; Karamani et al. 2021; Chatzinikolaou et al. 2022;Chatzipaschalis et al. 2023), facilitating the development of a realtime digital twin (Chatzipaschalis et al. 2024). 2.1 Reaction-diffusion processes The mycelium model employed is grounded in RD processes (Sugimura et al. 2007; Tompris et al. 2024), as articulated in Eqs. (1)-(4). It describes the growth of Fig. 1 State machine of the proposed framework I. Tompriset al. 123 mycelium, represented by the concentration c, as the outcome of intricate interactions between the activator and the inhibitor, components uand vrespectively, with the former promoting mycelium growth, while the latter denotes it. ou ot¼r 2uþfðjuþu2kuvÞn;u2Xcð1Þ ov ot¼dr2vþfðlu3vÞ;v2Xð2Þ dc dt ¼fmcðaðuÞcÞðc1Þ;c2Xð3Þ aðuÞ¼ n;if uthreshold nhðuthresholdÞ;otherwise ð4Þ A critical aspect to consider is the initial segment of Eqs. (1) and (2), which relates to the diffusion term. This segment employs the Laplacian operator rto precisely describe the spatial propagation of these components, with the parameter dgoverning the rate at which the inhibitor expands relative to the activator. The second term in the corresponding equations, a polynomial of uand vis called the reaction term and denotes the interaction between the two components and their respective effects on each other. Herein, the term flinearly scales the values of uand vto desirable ranges, while the adjustable terms d,j,kand l are treated as fitting parameters and allow for various growth patterns, explained thoroughly in Section 3.1. The variable spaces of Xand Xcand the differences between them should also be noted. While Xrepresents growth of a component throughout the whole grid, Xc, tied to the activator, defines a growth that is restricted within a specified radius relative to c, effectively replicating the plasma membrane of a biological organism and maintaining biological fidelity. Finally, moving on to Eqs. (3) and (4), it is evident that the activator uindirectly regulates the growth of mycelium cthrough the function a(u), indicating that growth occurs only when the activator reaches or exceeds a specific threshold value. Lastly, in Eq. (4), the values of the parameters nand h, depend on the defined threshold and enable cto assume both positive and negative values, through a(u). 2.2 Environmental conditions Mycelial growth can be affected by environmental factors such as temperature, humidity, and light. In the model, the influence of these environmental conditions on mycelial growth is computed on the factor nof Eq. (1), which affects the reaction term of the activator, encapsulating the aggregated environmental effects, as shown in Eq. (5), thereby dynamically modifying growth behaviors and environmental interactions. n¼nmin þnspan SF ðTF _HF _LFÞð5Þ TF ¼aTðTTminÞðTmax TÞ;Tmin\T\Tmax ð6Þ HF ¼0:00232 H20:326 Hþ11:4;H[Hmin ð7Þ LF ¼ 81011 LW4 104þffiffiffiffiffiffiffi LI4 p;if LF 2 2;otherwise 8 < :ð8Þ The environmental effects are mathematically represented in Eqs. (5)-(8), where TF denotes the influence of temperature, HF represents the effect of relative humidity, and LF captures the impact of light. These factors can assume values within the interval [0, 2]. Values below 1 restrict growth by directly limiting the concentration of the activator, while values above 1 promote growth. The parameters nmin and nspan are adjusted to align with the properties of the simulated mycelium, and only one environmental condition is examined at a time. Additionally, the substrate factor SF is introduced, to apply a small deviation of approximately 5%in the matrix n, ensuring a non-uniform and biologically plausible substrate. Furthermore, it has been observed that mycelium grows best in a particular temperature range representing a normal distribution (Omuse et al. 2022), while outside of this range, growth rates are slowed down by thermal stress (at high temperatures) or enzymatic inefficiency (at low temperatures). The optimal temperature values for optimal growth seem to be between 10 C(Tmin) and 35 C(Tmax) with a peak around 25 C, as illustrated in Fig. 2a. In order to model this non-linear correlation between fungal growth and temperature, the Van Der Heide model has been used (Van der Heide et al. 2006), due to its simplicity and biological relevance in modeling the nonlinear relationship between temperature and fungal growth. This is described in Eq. (6), where TF represents the temperature’s influence on mycelial growth rate due to a specific temperature (T), while ais a multiplier to limit TF on the specified range [0, 2]. Considering the humidity factor, it has been noted that the mycelium can grow vigorously as humidity rises. The reason is that the better hydration conditions allow nutrients to be transported and enzymatic reactions that are necessary for mycelial growth to occur. The Time of Wetness (TOW) model, which links mycelium growth rates to the duration of high relative humidity (e.g., above 80%), explains this phenomenon (Arya and Singh 2016). It has been observed that an area is not seen as prosperous and, hence, growth is hindered when the humidity level falls below 75%. In accordance with the findings from Arya and Singh (2016), which suggest a positive association of relative humidity to mycelial growth, the Mycelium as a computational medium: a framework... 123 mathematical model relating humidity and growth is presented in Eq. (7). Herein, Hrepresents relative humidity in the span of [0, 100], while HF represents mycelial growth rate due to a specific humidity. The relationship between humidity and mycelial growth is depicted in Fig. 2b. Light exerts a complex and wavelength-dependent influence on fungal mycelium growth. According to Lin et al. (2021), the growth and reproduction of Aspergillus oryzae were found to be highly sensitive to blue light (around 475 nm) under specific conditions, whereas green light (around 520 nm) and red light (around 630 nm) had minimal impact on the growth of mycelium. The inhibitory effects of light depend not only on the wavelength but also on its intensity, which is measured in lmol photons m2s1. For instance, blue light at intensities of 60 and 80 lmol photons m2s1significantly suppressed mycelium growth, reducing colony diameters compared to darkness. In contrast, red and green light consistently showed negligible inhibition, with growth rates comparable to those observed in complete darkness. This wavelength-intensity interplay reflects the selective activation of fungal photoreceptors, which are sensitive to specific light spectra. Blue light receptors, for example, are known to trigger inhibitory responses that reduce hyphal elongation and suppress conidium production. In the study, the number of conidia produced under blue light irradiation with and intensity of 80 lmol photons m2s1was 57:4% lower than that in the darkness group. This stark reduction underscores the potential for blue light to regulate fungal reproduction in controlled environments. On the other hand, red light receptors appeared inactive under the tested conditions, aligning with the insensitivity observed in colony diameter and conidium yield. To capture this relationship, seen in Fig. 2c, the formula presented in Eq. (8) was employed, with LW to represent the light wavelength on the visible area [380, 780] and LI to represent the intensity on the range [0, 100]. 2.3 Cellular automata implementation Herein, the algorithm underlying the mycelium model is presented and thoroughly illustrated in Fig. 3and described in Algorithm 1. To begin with, given that the concentrations of uand vmust be determined prior to c, and the activator uis constrained to values within a specific spatial range from c, the first step involves defining the matrix Xc.Thismatrixis constructed by conditionally updating its values, specifically in cases where cexceeds 0.5, with a 5 5 inverse-square distance-weighted kernel (L2), centered at the source (where c[0:5) (line 3 of Algorithm 1). This simulates the propagation of the central ‘‘fired‘‘ cell’s influence to its neighbors, with the effect diminishing as a function of distance from the source. Adjacent cells that are activated through this process are marked with Xc¼1, enabling the activator uin these regions and facilitating its spread. Algorithm 1 Mycelium model pseudo-code (iterative process) Fig. 2 Normalized effect of environmental factors integrated on the proposed model, namely (a) temperature, (b) humidity, and (c) light intensity and wavelength I. Tompriset al. 123 After the variable space Xcis determined and moving on to the calculation of the activator and inhibitor, the Laplacian operator, which models diffusion across space (O’Reilly and Beck 2006), is applied to uand v, by convolving the system with a 3 3 Laplacian kernel (L1Þ (lines 4 and 5). This approach allows for the parallel update of the concentrations of both the activator uand the inhibitor v, along with the calculation of the corresponding reaction terms of uand v. Also, in this state of the CA, the growth matrix nis integrated with the reaction terms of the activator u, allowing the model to simulate growth under distinct environmental influences. It is noteworthy that the calculation of the concentration of each RD component involves the time derivative, and consequently a relative time unit dt ¼105was applied to both the reaction and diffusion terms. Following this, the function aðuÞis defined. Depending on whether the activator’s concentration meets the required threshold, set to 1, cis subsequently updated (lines 6-11). Finally, the concentrations of u,v, and care evaluated to ensure they remain within their limits (lines 12-16). If any concentration falls outside the allowable range, it is bounded properly. In cases where the concentration cis negative, a scenario that, while biologically implausible, can arise due to the dynamics of aðuÞin discrete time and space, the concentration is not immediately clamped to 0 or 1. Instead, a small negative or positive noise term is introduced, respectively, to ensure continued growth under the constraints of discrete time and space. This approach maintains the system’s stability while accommodating the inherent limitations of the modeling framework. 2.4 CA response under different conditions The response of the employed CA model to different environmental conditions is evaluated in this Section. The precise calculations allow the simulation of mycelial behavior under varied conditions, making the model a robust tool for predictive analysis and optimization. In Fig. 4a-b, the influence of varying temperatures on mycelium growth is illustrated. Optimal growth is observed at T¼25C, while minor deviations from this temperature, such as T¼29C, do not significantly impede growth and can still support favorable development. In contrast, substantial deviations lead to reduced growth rates, primarily due to enzymatic inefficiency or thermal stress, as evidenced in the case of T¼15C. Following, Fig. 4c-d present the mycelium growth under different relative humidity levels. A very high relative humidity ensures mycelium development, like in the case of H¼97%, where a proper growth can be observed. On the other hand, insufficient humidity can inhibit growth, as observed in the case of H¼84%. Finally, the influence of light on mycelium growth is depicted in Fig. 4e-f. Light affects mycelial development primarily through its wavelength (LW) and intensity (LI). Short wavelengths, such as blue light, particularly at high intensity, are demonstrated to inhibit growth (480 nm at an intensity of 80 lmol photons m2s1), whereas red light, especially at low intensity, exhibits minimal inhibitory effects (630 nm at an intensity of 0). This is clearly demonstrated by the limited growth observed under blue light compared to the red light scenario. Fig. 3 Representation of the RD algorithm utilized in the proposed CA Mycelium Model. Begins with initialization of u,v,c. Following, Xcis generated based on the concentration of c. Should it be sufficient, apart from vnew,unew is also generated promoting growth and aðunewÞis calculated. Finally, cnew is defined based on aðunewÞand each of the components fu;v;cgnew are bounded to their corresponding ranges Mycelium as a computational medium: a framework... 123 (a) Temperature’s impact for T=15C (b) Temperature’s impact for T=29C (c) Humidity’s impact for H=84% (d) Humidity’s impact for H=97% (e) Light’s impact for LW =480nm and LI =80µmol photons m−2s−1 ( f ) Light’s impact for LW =630nm and LI =0µmol photons m−2s−1 Fig. 4 Impact of diverse environmental conditions on mycelium growth every 15,000 timesteps, in a 200 200 lattice I. Tompriset al. 123 3 Evaluating model as a reservoir network Modeling itself can reproduce plausible results. However, it is difficult to accurately simulate mycelium growth because of the complex and dynamic interactions between hyphae, the fundamental structural units of mycelium (namely the tips), and their surroundings. In most fungi, hyphae serve as the primary mechanism for vegetative growth and are collectively referred to as mycelium. Being able to identify which parameters can be adjusted accordingly to match realistic fungi behavior can lead to an accurate reservoir network with proper computational properties based on its small-world properties. 3.1 Hyphae information extraction Given the model’s emphasis is on generalization, its capacity to represent a variety of mycelium structures, greater attention should be directed towards the parameters d,j,k, and l, which critically influence the topological characteristics of the hyphae, particularly the count, width, and length of the hyphal tips and ultimately serve as tuning parameters. To quantify the specified characteristics, an algorithm has been developed to generate the necessary metrics for adjusting the model to the corresponding real mycelium as it calculates the discussed hyphal features of an experimental mycelium image. In such a way, it is possible to infer the fungal network’s efficiency, flexibility, and general health under different circumstances, leading to modeling simulations that closely resemble actual observations of fungal growth. Initially, the mycelium core must be determined, as it is the central hub from which the hyphal strands occur. This process is achieved by applying a convolutional kernel to detect regions within the matrix c, which represents the mycelium concentration. This process identifies areas characterized by eight high-concentration neighbors that signify the core of the structure. Subsequently, a specified concentration threshold is applied to these regions to validate the true core and not other densely connected regions. This threshold is dynamically determined based on the concentration range, the predefined number of growth iterations in the model, and the initial conditions, which influence the rate at which the maximum concentration within the range is achieved over the specified iterations. In order to detect the first characteristic (the hyphal count), the algorithm must locate the hyphal tips by employing neighbor count analysis. They are represented as the array cells of cwith a limited number of neighbors (three or fewer) having less than a specific concentration. This concentration is relative to the concentration of cnear its edges. To compute the width of each tip, which reflects the robustness and vitality of fungal growth, a kernel based on the inverse square of the distance from the core is convolved with the tip locations of c. This convolution measures the intensity distribution around each tip, serving as a proxy for width. Finally, to determine the length of each tip that gives information about the magnitude and direction of fungal growth, a breadth-first search (BFS) algorithm is utilized. Starting from each identified tip, the BFS investigates the shortest route from the tip to the mycelium core, tracing the hyphae backwards to the core. The search terminates when a core cell is detected, and the path length is then measured to indicate how far the hyphal tip extends from the core. In Fig. 5the metrics are visualized on a 2D plane, taking into account the default values for the tuning parameters. In Fig. 5b the mycelium core has been identified, while in Fig. 5c-d each cell represents the tip width and tip length, respectively. The visualized metrics in Fig. 6illustrate how variations in the four key parameters (d,j,k, and l)by5%affect hyphal growth characteristics, including tip count, average width, and average length. These parameters align with their roles in Eqs. (1)-(4), demonstrating their influence on hyphal morphology. The parameter d, representing the ratio between the inhibitor’s and activator’s diffusion rates, enhances inhibitor diffusion, allowing it to spread more extensively across the grid. This forces the activator into narrower pathways, leading to increased branching and tip count while reducing hyphal width. The parameter j amplifies activator concentration, promoting both wider and longer hyphal tips. In contrast, kreduces width and length by lowering activator concentration while simultaneously decreasing tip count by diminishing the inhibitor’s influence in the reaction terms. Lastly, lsuppresses all three characteristics, tip width, length, and count, by directly increasing inhibitor concentration, thereby limiting overall growth and structural expansion. 3.2 Small-world properties With the mycelium model and feature extraction established, this work explores how the unique characteristics of mycelium’s structure can serve as a basis for unconventional computing that is resource-, cost-, and power-efficient. Its intricate structure, which is marked with high and random connectivity, showcases a small-world topology, mainly high connectivity at its core sparsity connections near its edges, which is a useful attribute for building reservoir networks, as it has been shown to improve the echo-state property (Kawai et al. 2019). Additionally, it has been shown that the echo-state property in reservoir computing is improved by small-world characteristics, which are characterized by high node clustering and short Mycelium as a computational medium: a framework... 123 path lengths between nodes (Tsakalos et al. 2021; Manneschi et al. 2021; Bassett and Bullmore 2017). In order to evaluate the mycelium model’s feasibility as a reservoir, the average path length (APL) and average clustering coefficient (Ci), two important metrics representative of small-world characteristics, were computed. The results were shown for 30 different runs, as presented in Table 1, to ensure fidelity and account for the small randomness inherent in the model. First, an adjacency matrix A, derived from the mycelium’s concentration matrix c, has been created in order to obtain these metrics. In addition, the model was treated as an unweighted graph, with each cell of the matrix chaving a significant concentration (greater than 0.5) being considered as a node. The APL (Average Path Length) is a critical metric for evaluating the efficiency of information propagation within a network. It is defined as the mean of the shortest paths between all pairs of nodes and is computed using Eq. (9), where d(i,j) represents the shortest path distance between nodes iand j, and Ndenotes the total number of nodes. A low APL (greater than but close to 1) signifies rapid information transmission across the network, a fundamental characteristic for enabling the responsive dynamics required in reservoir computing (Nakajima and Fischer 2021). APL ¼1 NðN1ÞX i6¼j dði;jÞð9Þ The clustering coefficient quantifies the propensity of nodes to form densely interconnected groups, facilitating Fig. 5 Basic mycelium characteristics produced by the hyphae extraction algorithm, namely: aconcentration, bcore, ctip width, and dtip length Fig. 6 Change in: ahyphal tip count, baverage tip width and caverage length (log scale) by adjusting the model’s tuning parameters to 5%of their default values, being d¼29, j¼0:8, k¼0:8 and l¼3:5 Table 1 Small-World characteristics for 30 runs of the model Average path length Clustering coefficient 11.65 161.72 10.19 160.21 21.58 171.69 20.18 170.20 31.71 181.63 30.20 180.19 41.67 191.74 40.21 190.18 51.82 201.68 50.19 200.22 61.73 211.77 60.20 210.21 71.79 221.75 70.18 220.19 81.66 231.71 80.22 230.20 91.74 241.69 90.19 240.18 101.81 251.72 100.21 250.20 111.83 261.70 110.20 260.19 121.68 271.76 120.18 270.21 131.85 281.73 130.19 280.20 141.72 291.78 140.21 290.18 151.77 301.74 150.20 300.19 Avg - 1.729 Avg - 0.198 I. Tompriset al. 123 localized and intricate dynamics within the network. For a given node i,Ciis determined by Eq. (10), where degðiÞ represents the degree of node i. A high clustering coefficient (less than but close to 1) is a hallmark of small-world networks and enhances the network’s capacity to generate diverse, context-dependent responses, which are crucial for applications in reservoir computing (Gallicchio et al. 2018). Ci¼Pj;kAijAjkAki degðiÞðdegðiÞ1Þð10Þ The APL values demonstrate an average of 1:729 across all configurations, with a range extending from 1:58 to 1:85, while the Civalues exhibit an average of 0:198, ranging from 0:18 to 0:22. To assess these metrics and determine whether the resulting topology exhibits small-world characteristics, the small-world coefficient must be computed. If this coefficient, derived from Eq. (11), exceeds one (S[1), results in the topology being classified as smallworld (Hung and Wang 2010). S¼Cgraph Crandom Lrandom Lgraph ð11Þ Herein, Lgraph and Cgraph represent the average path length and average clustering coefficient of the graph, respectively, while Lrandom and Crandom denote the corresponding metrics for a random graph with an equivalent number of nodes and edges. These metrics were computed using the NetworkX Python package (Hagberg et al. 2008), which supported the efficient generation of a sufficiently large sample (up to 30 instances) of random graph metrics. The results not only yielded a small-world coefficient significantly greater than one but also revealed values consistently ranging between 30 and 1000, highlighting the mycelium network’s strong potential as a small-world topology. These results indicate the network’s capacity for rapid data propagation and structural adaptability. The high clustering coefficient and optimal average path length confirm its suitability for dynamic, nonlinear applications. 4 Reservoir computing with mycelium CAbased networks The biological mycelium has been the subject of research regarding its electrical activity (Adamatzky 2022,2018b), which has demonstrated its ability to propagate information and electrical signals across its network. In particular, studies have revealed that mycelial networks are capable of performing basic computational operations, such as implementing Boolean logic gates (Adamatzky et al. 2022). When combined with its inherent small-world properties, marked by high clustering coefficients and short path lengths, these properties suggest mycelium could be an effective substrate for reservoir computing. To evaluate this potential, two different mycelium-based reservoir networks, illustrated in Fig. 7, have been defined and their performance was evaluated on the classification of the MNIST dataset, thereby constituting a comprehensive testbed. Both networks start with a fully connected input layer, followed by a mycelium-based reservoir layer. The construction of the reservoir layer utilizes the adjacency matrix Aanalyzed in Section 2as its weight matrix. The response of the reservoir layer to each image, for a time window of 6 ms, is captured and, along with the corresponding labels, is used to train the output weights (WO) of the networks. 4.1 Reservoir layer neuron The electrical activity observed in mycelium exhibits striking similarities to biological neuronal spiking behavior, characterized by distinct phases of depolarization, repolarization, and a refractory period (Adamatzky 2018a). Thus, a biological neuron model is selected in the reservoir (a) Contemporary (b) Biological Fig. 7 The two Reservoir network architectures employed, differing in their output Mycelium as a computational medium: a framework... 123