Bio-Modules: Mycelium-Based Composites Forming a Modular Interlocking System through a Computational Design towards Sustainable Architecture

: In a resource-constrained world, raising awareness about the development of eco-friendly alternative materials is critical for ensuring a more sustainable future. Mycelium-based composites (MBC) and their diverse applications are gaining popularity as regenerative, biodegradable, and lightweight alternatives. This research aims to broaden the design potentials of MBC in order to construct advanced systems towards a novel material culture in architecture. The proposed design method intends to explore the design and fabrication of small-scale components of MBC to be applied in modular systems. Mycelium-based modular components are being developed to fulﬁll the geometrical requirements that allow for the creation of a lightweight system without additional reinforcement. The modules are linked together using an interlocking system. Through computational design and form-ﬁnding methods, various arrangements of the modules are achieved. An initial prototype of ﬁve modules is created to demonstrate the ability of the system to form various geometrical conﬁgurations as a result of the used workﬂow. The proposed application aims to expand the scope of the use of mycelium-based composites in modular systems and to promote architectural applications using bio-based composite materials.


Relevance and Challenges
The demand for building habitats continues to rise as the population grows. The high consumption of resources and energy from the construction sector, the scarcity of natural resources, and the acknowledgment of climate change and severe environmental challenges have prompted incentives to improve material efficiency, consider the complete life cycle of buildings and their components, and search for alternative resources in place of conventional ones [1][2][3].
Bio-based materials have emerged as a popular biodegradable, regenerative, and low-cost source of using natural biological mechanisms and low-energy fabrication methods to produce composite materials [4,5]. They have numerous facets of sustainability, aiming to reduce, reuse, recycle, and recover waste and encouraging the further following of the circular economy model of closing the loop of resource use and controlling the material lifecycle.
Emerging material research and applications of bio-based composites are gaining attention as a prevalent ecological solution and a design tool capable of producing free-form are critical for growing successfully. One of the earliest large-scale examples is the Hy-Fi tower constructed from ten thousand mycelium bricks to form three intersecting cylinders, which was displayed at the 2014 MoMA PS1 Young Architects by The Living Firm and ARUP [25]. The 13 m tall structure was built using modular MBC brick elements stacked on top of each other. This project showcases MBC bricks' potential application as modular components to create large-scale structures. A successful example of MBC applications is the MycoTree by the Karlsruhe Institute of Technology, the Block Research Group at ETH Zurich, and the Future Cities Laboratory at Singapore-ETH, which was exhibited at the 2017 Seoul Biennale of Architecture and Urbanism (Figure 1a). To achieve stability and create a performative structure, the project used the 3D graphic statics method and computational tools to design the form and geometry of the components to load the material, utilizing its compressive structural capacity [26]. During the cultivation process, bamboo endplates and metal dowels were integrated into MBC components to work as joints. The advantage is that the system is easily assembled, obtaining clean connections and transferring the loads from one component to the other.
An existing work of a large-scale structure using continuous MBC is The Circular Garden by Carlo Ratti Associati (Figure 1b). To enable the growth of MBC in a continuous format, this project used the hanging chain form-finding method to create a catenary shape. This was possible by hanging a series of suspended catenary formworks while growing mycelium on it [27]. Sixty arches of four meters were cultivated in two months. The final structure pushes the boundaries of using continuous MBC for compression structures. However, large-scale components require a longer growth time, greater material quantities, special formworks, a profound design of the components, and assembly strategies at an early design stage. In architecture, various concepts of interlocking modular assemblies have been explored, where repetitive shapes are combined to form various configurations. The modular pieces have connection slots that allow them to join and lock together at different angles. The structural integrity of the interlocking system is achieved by distributing forces through the elements without the use of additional binding materials. Nguyen Khac An existing work of a large-scale structure using continuous MBC is The Circular Garden by Carlo Ratti Associati (Figure 1b). To enable the growth of MBC in a continuous format, this project used the hanging chain form-finding method to create a catenary shape. This was possible by hanging a series of suspended catenary formworks while growing mycelium on it [27]. Sixty arches of four meters were cultivated in two months. The final structure pushes the boundaries of using continuous MBC for compression structures. However, large-scale components require a longer growth time, greater material quantities, special formworks, a profound design of the components, and assembly strategies at an early design stage.
In architecture, various concepts of interlocking modular assemblies have been explored, where repetitive shapes are combined to form various configurations. The modular pieces have connection slots that allow them to join and lock together at different angles. The structural integrity of the interlocking system is achieved by distributing forces through the elements without the use of additional binding materials. Nguyen Khac Phuoc Architects and Dang + Partners created Module+, a permeable structure in rural Vietnam made up of 2000 cross-shaped modular wooden components. Each module has slots that allow the components to connect with one another [28]. This interlocking system relies on friction, without the need for additional fixtures, resulting in a self-supported system. Here, the configuration options are limited because the slots are located only along the  [29]. It consists of six plywood panels that are connected on an orthogonal spatial pattern. This concept is based on a spatial arrangement of 145 × 145 cm modular panels with integrated slots. Each slot is one-fifth the length of the panel's edge length deep. The structural performance of the global system was analyzed using finite element analysis (FEA). The resulting sculpture explores the fundamentals of interlocking modular assemblies in architectural contexts.

Scope
Because of the nature of mycelium and its growth process, the final product will function best when fabricated in smaller fragments. In terms of growth and environment, smaller elements are easier to control, lowering the risk of contamination. The porous surface and material composition make it much more challenging to build large continuous blocks and structures. As a result, most mycelium applications focus on small-scale elements, such as thin components or combinations of small modules or blocks for forming larger structures. In architectural applications, mycelium products are expected to obtain a higher preference for modular applications.
The approach of this study focuses on the design of small-scale modular components for architectural applications. The development of mycelium-based composites involves exploring the geometry, size, thickness, interlocking strategy, and growing time of a unit. Developing a functional integrated interlocking system for connecting the modules is crucial for a successful modular system using only mycelium components. The modules are designed with finger joints for the elements to interlock beneficently to minimize contamination from the requirement of making perforations for additional fixations, formwork, and scaffolding. The concept of easy assembly and disassembly is also considered to offer geometrical flexibility and rigidity and to enable the creation of various configurations. A computational design workflow is being used to test and optimize the design and variety of connections. This type of system is characterized by the low production costs required to create fully biodegradable units, using only agricultural waste products that can be sourced regionally. This modular system is an eco-friendly solution to the commonly used conventional materials aiming to produce less waste, considering the complete life cycle of buildings and their components and fulfilling the circular economy model in the building industry.
On an architectural scale, a geometric case study is proposed and demonstrated by creating small-scale prototypes that showcase the material's feasibility in the proposed system. As an outcome, the prototypes demonstrate the design's functionality, expanding the application of MBC and promoting a novel materials culture. This paper focuses on the development of mycelium modules including the design concept of the studied geometry and its production process. The material and its properties have not been thoroughly addressed or examined but are nevertheless understood in terms of thickness, component size, interlocking techniques, and growth time.

Materials and Methods
The first challenge is to define and understand the tolerances and criteria of the shaping of these materials, with an emphasis on the geometric and joining properties of the component. In the first phase, a material study is conducted to produce mycelium modules, and the workflow is broken into four main parts: (1) identifying key factors which influence the performance of the modular components, such as the geometry, size, thickness, interlocking strategy, and growing time of the component, (2) designing the global geometry and its finger joints, (3) integrating the design process into the computational design workflow, and (4) realizing physical prototypes.
After gaining sufficient knowledge of mycelium's growing behavior, processes, and favorable conditions, the cultivation process of the organism begins. To obtain a culture, the Designs 2023, 7, 20 5 of 17 process of inoculation is required by making first-generation grain spawn and incubating it using a fungal strain. This study focuses on the design of mycelium modules, and, thus, the inoculation process was discarded because of the lack of a contained environment with proper sterility, as well as the imposed long growing period required to achieve a mature culture. One commonly used method for fabricating mycelium modules is to grow them using a mycelium growing kit, which is based on Do-it-Yourself practices and can be customized for personalized product applications ( Figure 2). Mycelium growing kits are becoming available on the market, making the material accessible to the public and allowing users to grow their products. Several companies introduced growing kits and made them easily accessible for regular users, such as the mycelium growing kit from the company Grown.bio (Heerewaarden, The Netherlands), which is used in this study to produce all the physical prototypes [23]. The kit contains 3 L of moistened hemp substrate particles of 5-15 mm inoculated with active mycelium. This growing kit grows to fill a volume of 3398 cm 3 and achieves a composite property, a density of 121.74 kg/m 3 , a compressive strength at 15% compression of 0.1246 N/mm 2 , and a flexural strength of 0.234 N/mm 2 [30]. modules is to grow them using a mycelium growing kit, which is based on Do-it-Yourself practices and can be customized for personalized product applications ( Figure 2). Mycelium growing kits are becoming available on the market, making the material accessible to the public and allowing users to grow their products. Several companies introduced growing kits and made them easily accessible for regular users, such as the mycelium growing kit from the company Grown.bio (Heerewaarden, The Netherlands), which is used in this study to produce all the physical prototypes [23]. The kit contains 3 L of moistened hemp substrate particles of 5-15 mm inoculated with active mycelium. This growing kit grows to fill a volume of 3398 cm 3 and achieves a composite property, a density of 121.74 kg/m 3 , a compressive strength at 15% compression of 0.1246 N/mm 2 , and a flexural strength of 0.234 N/mm 2 [30].
The mycelium growing kit includes a recipe and step-by-step instructions for making your own pieces at home. A fast-growing mycelium strain is included, which reduces the production time and infection risk. The growing process starts by adding 30 g of flour per 1 kg into the substrate and thoroughly mixing it until it is smooth and consistent. Then, the mixture must be kept in a clean environment to grow for four to five days at a moderate temperature and relative humidity. After the white mass has formed, the material can be removed and placed in a mixing bowl, where the bulk mass will be broken down into small particles. At this point, 30 g of additional flour will be added to the mixture. Then, it is ready to be transferred into a mold and left to grow for another four to five days. The material is then extracted from the mold and dried in an oven at 100 °C for one hour. Following these steps, a finished product can be achieved within ten days, promoting possibilities for material experimentation and hands-on practice.  The mycelium growing kit includes a recipe and step-by-step instructions for making your own pieces at home. A fast-growing mycelium strain is included, which reduces the production time and infection risk. The growing process starts by adding 30 g of flour per 1 kg into the substrate and thoroughly mixing it until it is smooth and consistent. Then, the mixture must be kept in a clean environment to grow for four to five days at a moderate temperature and relative humidity. After the white mass has formed, the material can be removed and placed in a mixing bowl, where the bulk mass will be broken down into small particles. At this point, 30 g of additional flour will be added to the mixture. Then, it is ready to be transferred into a mold and left to grow for another four to five days. The material is then extracted from the mold and dried in an oven at 100 • C for one hour. Following these steps, a finished product can be achieved within ten days, promoting possibilities for material experimentation and hands-on practice.

Modular Unit Design Exploration and Analysis
Experimentation on the fabrication process, growing time, thickness, size, and interlocking strategies of the component was conducted to obtain sufficient knowledge about the growth behavior of mycelium for designing modular components.

. Geometrical Shapes and Interlocking Strategies
In the first experiment, five modules of different shapes were studied, testing the component geometry and conceptualization (Figure 3). The aim was to achieve a viable design solution of the unit's geometry that allows the modules to be connected to form a modular system without the need for additional fixations. Each sample is designed within 100 cm 2 and a density of 221 kg/m 3 , integrating one to four joints. Plastic molds were prefabricated and filled with the material, which was then left to grow for five days.

Modular Unit Design Exploration and Analysis
Experimentation on the fabrication process, growing time, thickness, size, and interlocking strategies of the component was conducted to obtain sufficient knowledge about the growth behavior of mycelium for designing modular components.

Geometrical Shapes and Interlocking Strategies
In the first experiment, five modules of different shapes were studied, testing the component geometry and conceptualization (Figure 3). The aim was to achieve a viable design solution of the unit's geometry that allows the modules to be connected to form a modular system without the need for additional fixations. Each sample is designed within 100 cm 2 and a density of 221 kg/m 3 , integrating one to four joints. Plastic molds were prefabricated and filled with the material, which was then left to grow for five days. After the samples were grown and dried, they were examined. They were evaluated based on their geometric appearance and how effectively the finger joints allowed for connection and maintained the connected modules' stability. The joint's geometry and number became a crucial design factor in inheriting the interlocking capacity without the need for additional reinforcements but relying on inheriting an existing material's characteristics, such as surface roughness, and connecting multiple parts more sustainably. By integrating three or more joints, the elements were able to form multiple compositions.
Several issues were observed in the interlocking process, which affect the stability of the overall system ( Figure 4). The manual molding process resulted in inaccuracies and deformations of the edges and groves of joints, an inadequate thickness-to-aspect ratio, and an ineffective distribution of the material. When interlocked with other samples, this resulted in most connections being unstable. Furthermore, the joint's geometric control is lacking, resulting in a weak friction force between two parts [31]. After the samples were grown and dried, they were examined. They were evaluated based on their geometric appearance and how effectively the finger joints allowed for connection and maintained the connected modules' stability. The joint's geometry and number became a crucial design factor in inheriting the interlocking capacity without the need for additional reinforcements but relying on inheriting an existing material's characteristics, such as surface roughness, and connecting multiple parts more sustainably. By integrating three or more joints, the elements were able to form multiple compositions.
Several issues were observed in the interlocking process, which affect the stability of the overall system ( Figure 4). The manual molding process resulted in inaccuracies and deformations of the edges and groves of joints, an inadequate thickness-to-aspect ratio, and an ineffective distribution of the material. When interlocked with other samples, this resulted in most connections being unstable. Furthermore, the joint's geometric control is lacking, resulting in a weak friction force between two parts [31].

Modular Unit Design Exploration and Analysis
Experimentation on the fabrication process, growing time, thickness, size, and interlocking strategies of the component was conducted to obtain sufficient knowledge about the growth behavior of mycelium for designing modular components.

Geometrical Shapes and Interlocking Strategies
In the first experiment, five modules of different shapes were studied, testing the component geometry and conceptualization (Figure 3). The aim was to achieve a viable design solution of the unit's geometry that allows the modules to be connected to form a modular system without the need for additional fixations. Each sample is designed within 100 cm 2 and a density of 221 kg/m 3 , integrating one to four joints. Plastic molds were prefabricated and filled with the material, which was then left to grow for five days. After the samples were grown and dried, they were examined. They were evaluated based on their geometric appearance and how effectively the finger joints allowed for connection and maintained the connected modules' stability. The joint's geometry and number became a crucial design factor in inheriting the interlocking capacity without the need for additional reinforcements but relying on inheriting an existing material's characteristics, such as surface roughness, and connecting multiple parts more sustainably. By integrating three or more joints, the elements were able to form multiple compositions.
Several issues were observed in the interlocking process, which affect the stability of the overall system ( Figure 4). The manual molding process resulted in inaccuracies and deformations of the edges and groves of joints, an inadequate thickness-to-aspect ratio, and an ineffective distribution of the material. When interlocked with other samples, this resulted in most connections being unstable. Furthermore, the joint's geometric control is lacking, resulting in a weak friction force between two parts [31].

Size and Thickness
In the second experiment, four 9 × 10 cm rectangular samples were developed, with various thicknesses ranging from 0.3 to 6 cm, to determine the most suitable ratio between the thickness and size in order to obtain a suitable friction force between two parts. There is an interdependent relationship between the thickness and the ability of the modules to successfully connect to each other. Based on the pervious experiment, the aim was to develop modules with a thickness that can provide the joints relative freedom to slide among each other with adequate friction and provide interlocking strength. An additional factor that influences the global form involves maximizing the material quantity around the edges of the joint and in the center of the component [32]. The hemp substrate consisting of 5-15 mm particles was incrementally compacted and distributed in multiple layers along the coplanar flatter side of the components to increase the density of the composite. This process allowed for arranging fiber particles horizontally along the face onto which the loads will be applied.
To test and evaluate the effect of the compacting process on the elements' strength, each sample was tested physically under different loads of 0.2, 0.5, 0.67, and 1-3.63 N/mm 2 and loaded gradually by adding the accumulation of loads onto the horizontal face to determine their maximum capacity (Table 1). The sample with a thickness of 1 cm and a density of 221 kg/m 3 could bear weights up to 3.63 N/mm 2 compared to samples with a thickness of 0.3-0.5 cm and a density of 332-407 kg/m 3 , which instantly broke under lighter loads. They also showed a light geometric transformation from a linear to a convex form as a result of shrinkage and a loss of water after being dried. The sample with a thickness of 6 cm and a density of 110 kg/m 3 did not grow successfully because of its excessive thickness in relation to its size, which limited gas exchange and prevented the organism from developing. A correlation can be observed regarding the interdependent relationship between thickness and strength. The material thickness and density contribute to the success of the interlocking system and can also affect the strength and stability of the module. Structural and mechanical strength has not yet been fully considered, as it is not the primary focus of this research. The goal of this study emphasizes the design concept for mycelium modules and its developed geometry, its thickness, the size of the component, its interlocking strategies, and its growing time. However, mechanical testing would need to be conducted in future work to assess the maximum load-bearing capacity.

Design Concept
The benefits of such material are important from an ecological perspective. However, it may also be challenging in terms of both design and production methods. The goal was to create mycelium modules while considering their fabrication characteristics and limitations such as growth time, size, and thickness, all of which must be analyzed. Because of its simplicity, a cross-shape was chosen as the fundamental form for designing the modules. Furthermore, the form's design was adjusted to satisfy the material's growth and construction criteria, resulting in mycelium modules that may organize different configurations, grow independently, and be joined to form a complete system. The geometry and design of the module have become an essential aspect of the success of the modular system's growth and functional features, as well as the material emerging as successful and suitable in giving a promising approach for construction employing modular mycelium components.
The design workflow was handled in the Rhino/Grasshopper computational design environment to facilitate the design process and obtain control over the chosen geometrical parameters. Geometrical variations of the cross-form size of 20 × 20 × 2 cm were generated and tested, with the highest number of joints, while the global geometric stability was  (Figure 5a). This is an important step for obtaining connection flexibility and generating complex compositions.
parameters, including joint geometries, thicknesses, and the sample size ratio (Figure 5b). To provide appropriate friction between two pieces, rectangular joints with an aspect ratio of 25% of the length of the longest side were designed, with a clearance range of 0.3 mm. The global geometry was then optimized, reinforcing the areas around the edges of the joint, between neighboring joints, and in the middle of the space. By incorporating these numerous parameters into the design, it becomes evident that the geometry of the module and the material are interconnected parts that complement each other in achieving a higher potential based on their inherent interdependent properties while repurposing their combined properties to achieve one component with functional capacities, allowing MBC to be used for further applications in architecture. Alternative assemblies were explored using different interlocking slots to construct various configurations of the modules. Initially, the modules were connected orthogonally. However, most of them are rigid and have limited possibilities because the slots were located only on the horizontal and vertical axes ( Figure 6). Two modules with four and six joints and 60-and 90-degree angles were introduced, allowing for the assembly of more configurations. The developed modules are easy to assemble and disassemble. The resulting systems are self-supported due to the interlocking joints, the amount of the contact surface, and the arrangement of modules that form a robust cluster. Each iteration included interlocking aspects, the number of joints, and material reinforcement criteria while maintaining the interdependent relationships between all parameters, including joint geometries, thicknesses, and the sample size ratio (Figure 5b). To provide appropriate friction between two pieces, rectangular joints with an aspect ratio of 25% of the length of the longest side were designed, with a clearance range of 0.3 mm. The global geometry was then optimized, reinforcing the areas around the edges of the joint, between neighboring joints, and in the middle of the space. By incorporating these numerous parameters into the design, it becomes evident that the geometry of the module and the material are interconnected parts that complement each other in achieving a higher potential based on their inherent interdependent properties while repurposing their combined properties to achieve one component with functional capacities, allowing MBC to be used for further applications in architecture.
Alternative assemblies were explored using different interlocking slots to construct various configurations of the modules. Initially, the modules were connected orthogonally. However, most of them are rigid and have limited possibilities because the slots were located only on the horizontal and vertical axes ( Figure 6). Two modules with four and six joints and 60-and 90-degree angles were introduced, allowing for the assembly of more configurations. The developed modules are easy to assemble and disassemble. The resulting systems are self-supported due to the interlocking joints, the amount of the contact surface, and the arrangement of modules that form a robust cluster.
Designs 2023, 7, x FOR PEER REVIEW 9 of 18 Figure 6. Assembly systems for three-dimensional configurations using 90-degree orthogonal angle slots.

Computational Design
An integrative computational design workflow was adopted to optimize the developed geometry and to test various assembly possibilities (Figure 7) by incorporating a Figure 6. Assembly systems for three-dimensional configurations using 90-degree orthogonal angle slots.

Computational Design
An integrative computational design workflow was adopted to optimize the developed geometry and to test various assembly possibilities (Figure 7) by incorporating a formfinding method, an assembly strategy of the modular components, and an optimization process [33]. After experimenting with numerous geometrical modifications of the basic module, an optimal shape was chosen and transferred to the digital model to be used as the primary input for the assembly strategy process. Various assembly logics and constraints for connections were developed, guiding the modules to interlock with each other by defining the slots and specifying the center points of the interlocking modules. To conduct the simulation, all the constraints were gathered and added to the aggregate setup. A catenary arch was modeled to optimize the aggregation process and arrange elements based on a target. An arch-shape global geometry was chosen to evaluate the capabilities of the components' assembly in a proposed architectural case study. The arch is an inverted catenary shape, an optimized form determined by its weight which works under compression.

Defining the Assembly Strategy
To design the assembly strategy for the elements, the Grasshopper plug-in Wasp was used inside the Rhino/Grasshopper environment [35]. The setup involves defining the rules and guidelines for connections by specifying which modules can interlock with each other via which slots (Figures 8a and 9a). First, the center points of the interlocking slots need to be located. An octagonal prism of the modules' boundaries was used as the reference geometry to simplify the geometric shape (Figure 8b). The center points of the slots' faces were then located. Interlocking aggregation can be accomplished in several ways. The first method is to use a "rule generator," which automatically generates all possible connection outcomes based on the defined center points of interlocking slots for random aggregation. A different method involves the use of a text string, which allows for the direct conversion of text into rules for generating controlled aggregation. Finally, all parameters are put into the aggregation setup, which is then executed to build aggregation (Figure 9b). A catenary structure was explored to achieve equilibrium. The physics simulation plugin Kangaroo3d in Rhino/Grasshopper was used to simulate a form of a 2.4 m height arch [34]. The form-finding process was initially defining the length of a curve-here, 3.7 m. The curve was then subdivided and assigned with anchors and boundaries for the simulation to start. Subsequently, the engine built a relaxed state of the system and resolved the form until an equilibrium state was achieved. A catenary curve was obtained as a result of this setup, and it could be then used for testing arrangements of modules along its thrust line.

Defining the Assembly Strategy
To design the assembly strategy for the elements, the Grasshopper plug-in Wasp was used inside the Rhino/Grasshopper environment [35]. The setup involves defining the rules and guidelines for connections by specifying which modules can interlock with each other via which slots (Figures 8a and 9a). First, the center points of the interlocking slots need to be located. An octagonal prism of the modules' boundaries was used as the reference geometry to simplify the geometric shape (Figure 8b). The center points of the slots' faces were then located. Interlocking aggregation can be accomplished in several ways. The first method is to use a "rule generator," which automatically generates all possible connection outcomes based on the defined center points of interlocking slots for random aggregation. A different method involves the use of a text string, which allows for the direct conversion of text into rules for generating controlled aggregation. Finally, all parameters are put into the aggregation setup, which is then executed to build aggregation (Figure 9b).

Defining the Assembly Strategy
To design the assembly strategy for the elements, the Grasshopper plug-in Wasp was used inside the Rhino/Grasshopper environment [35]. The setup involves defining the rules and guidelines for connections by specifying which modules can interlock with each other via which slots (Figures 8a and 9a). First, the center points of the interlocking slots need to be located. An octagonal prism of the modules' boundaries was used as the reference geometry to simplify the geometric shape (Figure 8b). The center points of the slots' faces were then located. Interlocking aggregation can be accomplished in several ways. The first method is to use a "rule generator," which automatically generates all possible connection outcomes based on the defined center points of interlocking slots for random aggregation. A different method involves the use of a text string, which allows for the direct conversion of text into rules for generating controlled aggregation. Finally, all parameters are put into the aggregation setup, which is then executed to build aggregation (Figure 9b).

Generating Aggregation
A parametric workflow was adopted to optimize the aggregation process by placing parts based on an objective, given a suitable form and rules of assembly ( Figure 10). Any geometry can be transformed into a field of points, allowing the modules to be positioned accordingly. The optimized catenary form was converted into a high-resolution boundary filled with points. The position and coordinates (x,y,z) of all points were extracted ( Figure  10b). These points were then referenced with a numeric value between 0 and 1, indicating their distance from the geometry.
Points with lower values (numeric value closer to zero) were closer to the arch, which means there was a high probability of placing parts, and points with higher values (numeric value closer to one) were found further away, meaning less portability. As a result of this process, a list of numeric values referring to the three coordinates (x,y,z) could be extracted and fed into the aggregation component, along with the defined assembly rules, the geometry of the modules, and the number of parts for controlling placing parts iteratively without collisions.

Generating Aggregation
A parametric workflow was adopted to optimize the aggregation process by placing parts based on an objective, given a suitable form and rules of assembly ( Figure 10). Any geometry can be transformed into a field of points, allowing the modules to be positioned accordingly. The optimized catenary form was converted into a high-resolution boundary filled with points. The position and coordinates (x,y,z) of all points were extracted (Figure 10b). These points were then referenced with a numeric value between 0 and 1, indicating their distance from the geometry.
Points with lower values (numeric value closer to zero) were closer to the arch, which means there was a high probability of placing parts, and points with higher values (numeric value closer to one) were found further away, meaning less portability. As a result of this process, a list of numeric values referring to the three coordinates (x,y,z) could be extracted and fed into the aggregation component, along with the defined assembly rules, the geometry of the modules, and the number of parts for controlling placing parts iteratively without collisions. means there was a high probability of placing parts, and points with higher values (numeric value closer to one) were found further away, meaning less portability. As a result of this process, a list of numeric values referring to the three coordinates (x,y,z) could be extracted and fed into the aggregation component, along with the defined assembly rules, the geometry of the modules, and the number of parts for controlling placing parts iteratively without collisions. Complex geometries were possible using this parametric workflow. Due to the computational complexity of the aggregation process, the model was broken up into smaller sections to maximize the placement of parts within a pre-defined boundary along a geometry thrust line ( Figure 11). First, the curve was divided into eight segments, with a tangent line generated at each resulting point. These tangent segments were then extruded into surfaces to form boundaries, allowing the modules to be placed where they intended to be. The planes were subdivided into grids to guide the placement of the modules in space. The grid was used to maintain a distance of 10 × 10 cm to distribute the points sufficiently within the rectangular boundary and ensure that the gaps between parts could overlap once all modules were oriented onto the tangent planes ( Figure 12). It could also serve as a geometric reference for the parts placement and keep track of the distance between interlocking sections. Complex geometries were possible using this parametric workflow. Due to the computational complexity of the aggregation process, the model was broken up into smaller sections to maximize the placement of parts within a pre-defined boundary along a geometry thrust line ( Figure 11). First, the curve was divided into eight segments, with a tangent line generated at each resulting point. These tangent segments were then extruded into surfaces to form boundaries, allowing the modules to be placed where they intended to be. The planes were subdivided into grids to guide the placement of the modules in space. The grid was used to maintain a distance of 10 × 10 cm to distribute the points sufficiently within the rectangular boundary and ensure that the gaps between parts could overlap once all modules were oriented onto the tangent planes ( Figure 12). It could also serve as a geometric reference for the parts placement and keep track of the distance between interlocking sections.
A numeric list was extracted, which included the points of the tangent planes, along with the geometry of the modules and their orientation. The list was then fed into the aggregation component to control the parts' placement, following the workflow discussed in the previous section. The algorithm of the aggregation component could then generate the configurations while maintaining the planarity of the modules. The gaps and the discontinuity of the parts from each iteration were compensated by overlapping layers of modules over each other to create a continuous system. Furthermore, redundant elements were removed, ensuring that there were no loosely linked modules. The resulting final aggregation was a compact self-supported system.    A numeric list was extracted, which included the points of the tangent planes, along with the geometry of the modules and their orientation. The list was then fed into the aggregation component to control the parts' placement, following the workflow discussed in the previous section. The algorithm of the aggregation component could then generate the configurations while maintaining the planarity of the modules. The gaps and the discontinuity of the parts from each iteration were compensated by overlapping layers of modules over each other to create a continuous system. Furthermore, redundant elements were removed, ensuring that there were no loosely linked modules. The resulting final aggregation was a compact self-supported system.

Forming an Arch
Seventy-three modules of 20 × 20 × 2 cm were joined in equilibrium along a catenary curve to form the final articulation of an arch structure: 2.4 m high, 3.7 m long, and 1 m wide (Figure 13a). This initial design showcases the potential of the developed system in a full-scale architectural application. Two support anchors, each made up of 28 modules, were designed to support the structure, acting as buttresses for transferring loads and ensuring overall stability. In two triangular arrangements, 14 modules were joined to form

Forming an Arch
Seventy-three modules of 20 × 20 × 2 cm were joined in equilibrium along a catenary curve to form the final articulation of an arch structure: 2.4 m high, 3.7 m long, and 1 m wide (Figure 13a). This initial design showcases the potential of the developed system in a full-scale architectural application. Two support anchors, each made up of 28 modules, were designed to support the structure, acting as buttresses for transferring loads and ensuring overall stability. In two triangular arrangements, 14 modules were joined to form a cluster (Figure 13b). Two customized modules with a flat base were built for this layout to provide the foundation with extra strength. As a result of this configuration, loads could be transferred from one element to another, achieving equilibrium in the system. Similarly, large-scale applications can also be achieved by connecting multiple arches, using additional lateral horizontal modules as supports to form a vault ( Figure 14).
Designs 2023, 7, x FOR PEER REVIEW 13 of 18 a cluster (Figure 13b). Two customized modules with a flat base were built for this layout to provide the foundation with extra strength. As a result of this configuration, loads could be transferred from one element to another, achieving equilibrium in the system. Similarly, large-scale applications can also be achieved by connecting multiple arches, using additional lateral horizontal modules as supports to form a vault ( Figure 14).

Fabrication
To demonstrate the applicability of the developed system, five modules of 20 × 20 × 2 cm were produced as a small-scale demonstrator to further understand the physical limits, properties, and potential of the system as an initial design phase. To prepare for the manufacturing, the 3D model was converted into 2D drawings. Prefabricated plastic molds were CNC-cut from recyclable plastic sheets and used to assemble the walls of the mold in order to obtain clean edges after demolding. Based on the results of the experiments, this fabrication procedure was chosen to achieve a clearance range of 0.2-0.6 mm, thereby increasing the friction between the parts and improving the system stability.

Fabrication
To demonstrate the applicability of the developed system, five modules of 20 × 20 × 2 cm were produced as a small-scale demonstrator to further understand the physical limits, properties, and potential of the system as an initial design phase. To prepare for the manufacturing, the 3D model was converted into 2D drawings. Prefabricated plastic molds were CNC-cut from recyclable plastic sheets and used to assemble the walls of the mold in order to obtain clean edges after demolding. Based on the results of the experiments, this fabrication procedure was chosen to achieve a clearance range of 0.2-0.6 mm, thereby increasing the friction between the parts and improving the system stability. Additionally, the vertical plastic walls were CNC-cut as a continuous strip, glued, and dried in place before the material filling process began for additional support. Three 3L growing kits of mycelium material were used to produce the modules ( Figure 15). The molds were assembled and filled with the material using an incremental compacting process to ensure even distribution [17,26]. Following the growth procedure, which was previously explained, the growing process was accomplished.
Designs 2023, 7, x FOR PEER REVIEW 14 of 18 Additionally, the vertical plastic walls were CNC-cut as a continuous strip, glued, and dried in place before the material filling process began for additional support. Three 3L growing kits of mycelium material were used to produce the modules ( Figure 15). The molds were assembled and filled with the material using an incremental compacting process to ensure even distribution [17,26]. Following the growth procedure, which was previously explained, the growing process was accomplished.

Physical Prototypes
The design and fabrication process were materialized on a prototypical scale. The final prototype consisted of five modules which were able to form different geometrical configurations, resulting in the utilized workflow ( Figure 16). Each module weighted 0.39 N and had a density of 50 kg/m 3 , including two modules with four and six joints, as well as a density of 100 kg/m 3 for the special module with a flat base; thus, it could support a weight more than two thousand times higher than its self-weight. These initial prototypes were then capable of holding the weight of an average adult (80 kg), resulting in a deflection of 0.2 cm The fabrication process and the adequate distribution of the material resulted in lightweight modules which could be assembled in various configurations ( Figure 17). The finger joints were fabricated with clean edges and enough of a contact

Physical Prototypes
The design and fabrication process were materialized on a prototypical scale. The final prototype consisted of five modules which were able to form different geometrical configurations, resulting in the utilized workflow ( Figure 16). Each module weighted 0.39 N and had a density of 50 kg/m 3 , including two modules with four and six joints, as well as a density of 100 kg/m 3 for the special module with a flat base; thus, it could support a weight more than two thousand times higher than its self-weight. These initial prototypes were then capable of holding the weight of an average adult (80 kg), resulting in a deflection of 0.2 cm The fabrication process and the adequate distribution of the material resulted in lightweight modules which could be assembled in various configurations ( Figure 17). The finger joints were fabricated with clean edges and enough of a contact surface, which provided the joints relative freedom to slide among each other with adequate friction, resulting in a sufficient interlocking mechanism. Alternative assemblies using different interlocking slots of the modules could be possible, and various scenarios were tested for assembling vertical, horizontal, and diagonal configurations. The developed modules are also easy to assemble and disassemble.

Physical Prototypes
The design and fabrication process were materialized on a prototypical scale. The final prototype consisted of five modules which were able to form different geometrical configurations, resulting in the utilized workflow ( Figure 16). Each module weighted 0.39 N and had a density of 50 kg/m 3 , including two modules with four and six joints, as well as a density of 100 kg/m 3 for the special module with a flat base; thus, it could support a weight more than two thousand times higher than its self-weight. These initial prototypes were then capable of holding the weight of an average adult (80 kg), resulting in a deflection of 0.2 cm The fabrication process and the adequate distribution of the material resulted in lightweight modules which could be assembled in various configurations ( Figure 17). The finger joints were fabricated with clean edges and enough of a contact surface, which provided the joints relative freedom to slide among each other with adequate friction, resulting in a sufficient interlocking mechanism. Alternative assemblies using different interlocking slots of the modules could be possible, and various scenarios were tested for assembling vertical, horizontal, and diagonal configurations. The developed modules are also easy to assemble and disassemble.

Conclusions
The purpose of this research was growing materials experimentation by demonstrating the development of MBC in the form of modular components which could result in multiple geometrical configurations that do not require the use of extra pieces for fastening. This was accomplished by including numerous criteria into the design, ensuring proper material distribution via the molding and compacting processes, and applying computational design to optimize the geometries. Hemp substrate was chosen and found to be compatible with mycelium, achieving greater stiffness [9,17]. The compacting and material distribution that was used for the cultivation process increased the density of the composite and arranged fiber particles horizontally, thereby improving the modules' stability.
Five prototype modules were created and assembled in various configurations to demonstrate and validate the system's geometrical feasibility, interconnecting possibilities, and applications. The embedded finger joints allowed the mycelium modules to interconnect and form a biodegradable modular system. These developed prototypes can be respectively scaled up for larger architectural applications. The main limitation is the need for excessive control over the growing and cultivation time,

Conclusions
The purpose of this research was growing materials experimentation by demonstrating the development of MBC in the form of modular components which could result in multiple geometrical configurations that do not require the use of extra pieces for fastening. This was accomplished by including numerous criteria into the design, ensuring proper material distribution via the molding and compacting processes, and applying computational design to optimize the geometries. Hemp substrate was chosen and found to be compatible with mycelium, achieving greater stiffness [9,17]. The compacting and material distribution that was used for the cultivation process increased the density of the composite and arranged fiber particles horizontally, thereby improving the modules' stability.
Five prototype modules were created and assembled in various configurations to demonstrate and validate the system's geometrical feasibility, interconnecting possibilities, and applications. The embedded finger joints allowed the mycelium modules to interconnect and form a biodegradable modular system. These developed prototypes can be respectively scaled up for larger architectural applications. The main limitation is the need for excessive control over the growing and cultivation time, molding, and production process. The main goal of the prototypes was to test the interlocking system while considering upscaling in an architectural context for future studies. The physical prototypes demonstrated the interlocking and the system capacities needed to build a modular system in various configurations. However, more research on the structural capabilities of the joints and reinforcement strategies is required.
In the future development of this work, it is intended to perform mechanical tests to explore the strength and stability of the interlocking joints in different loading scenarios by applying a gradual compressive loading in a set-up of two or more connected modules, as well as to understand the material properties and the structural behavior. The integration of different materials, such as wood, into the molding process is also considered. Wood could bind with mycelium and act as a reinforcement, increasing the compressive strength and flexural properties. This could speed up the fabrication process while also increasing the strength of the composite and making the molding process more resource-efficient. It is important for structural analysis simulation to be integrated into the computational design workflow to provide optimum shapes based on force flows and loads distribution. Furthermore, bio-based coatings need to be studied and considered to be integrated into the composite to increase the rigidity and water resistance by lowering water absorption. This can enhance the mechanical properties and create opportunities for the use of MBC in external applications ( Figure 18). In future work, producing the complete structure will demonstrate the full potential of the system's capabilities. The process itself promotes further material experimentation and design explorations. It highlights the importance of understanding and identifying the characteristics and properties of the materials, studying potential growing methods, and supporting the use of computational design in developing complex geometries in an architectural context. This research has presented methods for expanding the scope of the use of mycelium-based composites in modular systems and promoting architectural applications using bio-based composite materials.
(a) (b) Figure 18. Concept for the self-supported interlocking system in (a) an interior application and (b) an external environment.
Author Contributions: The conceptualization, design, methods, presentation, prototyping, and testing, as well as the writing of this paper, were carried out by O.A. This paper was supervised and reviewed by H.D. and E.S., and both gave prerequisite knowledge, support, and guidance to the author in the field of biocomposites and sustainable architectural building elements. All authors have read and agreed to the published version of the manuscript.  In future work, producing the complete structure will demonstrate the full potential of the system's capabilities. The process itself promotes further material experimentation and design explorations. It highlights the importance of understanding and identifying the characteristics and properties of the materials, studying potential growing methods, and supporting the use of computational design in developing complex geometries in an architectural context. This research has presented methods for expanding the scope of the use of mycelium-based composites in modular systems and promoting architectural applications using bio-based composite materials.
Author Contributions: The conceptualization, design, methods, presentation, prototyping, and testing, as well as the writing of this paper, were carried out by O.A. This paper was supervised and reviewed by H.D. and E.S., and both gave prerequisite knowledge, support, and guidance to the author in the field of biocomposites and sustainable architectural building elements. All authors have read and agreed to the published version of the manuscript.
Funding: This research was partially funded by the Fachagentur Nachwachsende Rohstoffe e. V. (FNR, Agency for Renewable Resources) under Bundesministeriums für Ernährung und Landwirtschaft (BMEL, Federal Ministry of Food and Agriculture) throughout the research project Leicht-Pro: Pultruded load-bearing lightweight profiles from natural fiber composites (FKZ:22027018), managed by Hanaa Dahy, director of the BioMat Department at ITKE, University of Stuttgart. The work was also partially supported by Krown-Design BV, Hogewaard 21D, 6624 KP Heerewaarden, Netherlands, the company from which the mycelium growing kits were purchased. Data Availability Statement: Not applicable.