Initial state simulation of cellular automata

Based on the Cellular Automata (CA) model, a MATLAB simulation was conducted. The simulation parameters were set as follows: Cell space size: n = 20, meaning the cellular space consisted of a 20 × 20 grid of cells. Evolution threshold: threshold = 0.6, which was used to determine whether an enterprise (represented by a cell) would transition to an AI innovation state. Number of evolution steps: steps = 30, indicating the number of iterative processes in the simulation. The initial state of the cells was randomly generated using the randi function in MATLAB, with values of either 0 or 1. A value of 0 represented a firm that had yet to engage in the AI innovation evolution within the manufacturing industry cluster, while a value of 1 indicated a firm actively participating in the evolution. The initial state of the cells was randomly generated (see Fig. 5). Green cells represent firms actively participating in the evolution of AI innovation within the manufacturing industry cluster, while blue cells indicate firms that have yet to engage. Figure 5 illustrates that several firms within the manufacturing industry cluster are already involved in the evolution of AI innovation.

Influence of simulation parameters on the evolution of AI in industrial clusters

In the subsequent analysis, we focus on the influence of the related parameters μ, r, and e on the evolution of AI innovation clusters within the manufacturing industry. Using Cellular Automata theory, a quantitative analysis was performed on the evolution process of AI innovation in the manufacturing cluster. Figures 6, 8, and 10 depict the state of firms in the cellular space when two parameters are held constant while varying the value of another parameter, after conducting 30 simulations. Figures 7, 9, and 11 provide the corresponding quantitative representations for Figs. 6, 8, and 10, respectively, with the horizontal axis denoting the number of simulations and the vertical axis representing the number of AI-innovative firms in the manufacturing industry cluster.

This figure illustrates the AI innovation evolution process in a manufacturing cluster under different resource ownership coefficients (μ = 0.3, 0.5, 0.7) with fixed r = 0.5 and e = 0.5. The first, second, and third images show the cellular space after 30 simulation steps for μ = 0.3, 0.5, and 0.7, respectively. Green cells represent AI-adopting firms (S = 1), and blue cells indicate non-adopting firms (S = 0).

This figure quantifies the number of AI-innovative firms in the manufacturing cluster over 30 simulation iterations for different resource ownership coefficients (μ = 0.3, 0.5, 0.7) with fixed r = 0.5 and e = 0.5. The plot shows three lines, each corresponding to a μ value, with the x-axis representing simulation steps and the y-axis indicating the cumulative number of firms with state S = 1.

This figure depicts the AI innovation evolution process in a manufacturing cluster under different knowledge-sharing coefficients (r = 0.4, 0.6, 0.8) with fixed μ = 0.5 and ε = 0.5. The first, second, and third images display the cellular space after 30 simulation steps for r = 0.4, 0.6, and 0.8, respectively. Green cells represent AI-adopting firms (S = 1), and blue cells indicate non-adopting firms (S = 0).

Employing Cellular Automata theory, a quantitative analysis was performed on the evolution process of AI innovation in the manufacturing cluster. Figures 6, 8, and 10 depict the state of firms in the cellular space when two parameters are held constant while varying the value of another parameter, after conducting 30 simulations. Figures 7, 9, and 11 provide the corresponding quantitative representations for Figs. 6, 8, and 10, respectively, with the horizontal axis denoting the number of simulations and the vertical axis representing the number of AI-innovative firms in the manufacturing industry cluster.

This figure plots the number of AI-innovative firms in the manufacturing cluster over 30 simulation iterations for different knowledge-sharing coefficients (r = 0.4, 0.6, 0.8) with fixed μ = 0.5 and e = 0.5. The plot includes three lines, each corresponding to an r value, with the x-axis representing simulation steps and the y-axis showing the cumulative number of firms with state S = 1.

Impact of cluster resources on AI-innovative manufacturing industry cluster

To examine the effect of cluster resources on the emergence and diffusion of AI-driven manufacturing innovations, a simulation analysis was performed. In this analysis, the values of r and e were fixed at 0.5, while the μ value was iterated to obtain various states and assess the occurrence of causal emergence. This approach serves as an approximate method for investigating the impact of cluster resources on the evolution of AI innovation within manufacturing industry clusters. The parameterμ represents the coefficient of firm resource ownership in the manufacturing industry cluster, which follows a normal distribution with a mean of μ. Manufacturing industry clusters typically possess an abundance of financial resources, human capital, data and technology resources, as well as AI infrastructure, alongside the research and development (R&D) capabilities necessary to leverage AI technology. If a firm fosters a corporate culture that prioritizes AI innovation, a higher μ value is anticipated. Larger μ values indicate a greater average availability of resources to firms within the cluster.

The specific simulation process is as follows:

First, an evolution loop was defined, where the length of μ values is denoted as k. For each μ value, the simulation was run for a number of steps. In each step, a new matrix was created to store the next state. Each cell was traversed to calculate the number of neighboring cells entering the innovation cluster, using the Von Neumann neighborhood method, which considers 4 neighbors.

Next, the value of p₁ was calculated, following a normal distribution N(μ, σ²), using the current μ value. A uniformly distributed random number in the range [0, r] was generated as p₂. The value of P was then calculated using the formula \(\scriptstyle{p}={e}\times ({p}_{1}+{p}_{2}\times \frac{N(t)}{M})\).

The state was updated based on the value of P. If all P-values were greater than p₀ and the current cell state was 0, it was updated to 1. After updating the cell states, the final state was saved.

Through this simulation process, the final states for different μ values were obtained. The simulation results indicate that higher μ values, representing a higher average amount of resources available to firms, facilitate the acceleration of AI-driven innovation evolution within manufacturing industry clusters. Figure 6 illustrates the evolution of AI innovation across firms in the manufacturing cluster at varying resource ownership levels (μ) of 0.3, 0.5, and 0.7. The green cells indicate the firms that are actively involved in AI innovation, while the blue cells represent those that have not yet participated in the process. The findings demonstrate a clear positive relationship between the availability of cluster resources and the number of firms engaged in AI innovation. As the resource ownership coefficient (μ) increases, the number of firms adopting AI technologies within the cluster also rises.

As the resource ownership coefficient (μ) increases from 0.3 to 0.7, the number of AI-innovative firms continues to grow, reflecting the accelerating impact of resource-rich environments on AI adoption. At μ = 0.3, only a few firms engaged in AI innovation, while at μ = 0.7, a large majority of firms in the cluster had adopted AI, highlighting that higher resource availability enables widespread technological diffusion.

These results underscore the importance of resource abundance, comprising funds, skilled labor, advanced digital infrastructure, and R&D capabilities, in accelerating AI-driven innovation. Firms in resource-rich environments are more likely to leverage their technological capabilities to adopt AI, enhancing their competitive advantage. This trend illustrates that manufacturing clusters with substantial resources provide an environment conducive to rapid AI innovation, as firms are better equipped to absorb and deploy advanced technologies.

Figure 7 provides a quantitative representation of the relationship between increasing resource availability (μ values) and the number of firms participating in AI innovation within the manufacturing industry cluster. The horizontal axis represents the number of simulation iterations, while the vertical axis shows the cumulative number of firms engaging in AI-driven innovation over time.

For example, at μ = 0.3, only a limited number of firms-three-joined the AI innovation evolution, reflecting a scarcity of resources in the cluster. At μ = 0.5, around 30 additional firms participated in the process, suggesting that a moderate availability of resources facilitates broader adoption of AI. At μ = 0.7, nearly all firms in the cluster had adopted AI, highlighting that higher resource availability enables widespread technological diffusion.

This data confirms that clusters with more substantial resources, such as access to financial capital, skilled talent, and digital infrastructure, are better positioned to drive the evolution of AI technologies within manufacturing firms. The results reinforce the view that resource availability is a vital determinant in the speed and scale of AI innovation diffusion, with well-resourced clusters acting as accelerators for technological adoption and innovation diffusion across firms.

The findings from both figures highlight that cluster resources, including human capital, digital infrastructure, financial assets, and R&D capabilities, are fundamental drivers of AI innovation evolution in manufacturing clusters. The increased resource availability fosters a favorable environment for firms to invest in and adopt AI technologies, leading to broader innovation within the cluster. This aligns with the evolutionary economic geography theory, which posits that resource concentration accelerates innovation through mechanisms such as knowledge spillovers and collaborative learning. As a result, clusters with rich resources are more likely to become hubs for AI-driven innovation, reinforcing the critical importance of resource-rich environments in the growth of technological ecosystems.

The Zhongguancun area in Beijing, often referred to as the “Silicon Valley of China,” exemplifies the critical role of clustered resources in fostering the emergence and diffusion of AI-driven manufacturing innovations. As a hub for intelligent manufacturing, Zhongguancun demonstrates how financial resources, human capital, digital infrastructure, and R&D capabilities drive the evolution of AI innovation. For instance, Zhongguancun Smart Manufacturing Street spans 30,600 square meters and houses 93 enterprises across fields such as Internet of Things (IoT), AI, robotics, and 3D printing. These firms collectively generate an annual output exceeding CNY 3 billion, showcasing the transformative potential of resource-rich environments.

Zhongguancun’s success is underpinned by substantial investments in financial and human resources. By 2021, venture capital and government-supported funds had injected over CNY 150 billion into AI-related industries, significantly enhancing the R&D capacity of firms and enabling them to adopt cutting-edge AI technologies. The region’s proximity to premier academic institutions, including Tsinghua University and Peking University, further bolsters its talent pipeline. With approximately 60% of China’s AI workforce originating from these institutions, Zhongguancun ensures a steady flow of skilled professionals equipped to leverage AI technologies in manufacturing processes. The simulation analysis in this study highlights how higher μ values (representing the coefficient of firm resource ownership) accelerate the adoption and diffusion of AI innovation within manufacturing clusters. Zhongguancun exemplifies this relationship through its comprehensive digital infrastructure, which includes advanced broadband, high-speed data centers, and shared AI computing platforms, collectively enhancing firms’ capabilities to absorb and apply AI technologies. As firms with greater access to resources actively engage in innovation, they stimulate spillover effects, encouraging surrounding firms to participate in the evolution of AI innovation.

Zhongguancun’s resource richness encompasses not only financial and digital assets but also a robust culture of innovation. The region’s Smart Manufacturing Innovation Center and various smart factory initiatives, such as the ’Smart Manufacturing 100’ program, exemplify how a supportive innovation culture fosters the development of AI-driven solutions. These initiatives align with the simulation findings, where increasing μ values from 0.3 to 0.7 correspond to a significant increase in the number of firms actively engaging in AI innovation.

The real-world outcomes observed in Zhongguancun further validate the conclusions drawn from the simulation. The region’s strong cluster resources have facilitated the establishment of over 100 smart factories and intelligent manufacturing systems, significantly enhancing the adoption and diffusion of AI-driven manufacturing innovations. As a leading example of how financial capital, human talent, and digital infrastructure converge to accelerate AI innovation, Zhongguancun illustrates that resource-rich environments are crucial for promoting the evolution of AI-enabled manufacturing clusters.

Impact of cluster network on AI-innovative manufacturing industry cluster

To gain a deeper understanding of the role of knowledge sharing in the evolution of AI-driven innovations within manufacturing industry clusters, a simulation analysis was conducted. The parameters μ and e were fixed, while the range of r values was systematically explored. This approach facilitated the collection of data under varying conditions, enabling the determination of whether a causal emergence phenomenon occurred. As an approximate solution strategy, this method enhances comprehension of the intricate relationship between knowledge sharing and innovation evolution.

The results indicate that a higher degree of knowledge sharing within the cluster accelerates the evolution of AI-driven innovations. Specifically, an increased risk appetite among companies, along with collaborative knowledge sharing and strategic cooperation, correlates with a higher affinity coefficient of network contact. The parameter r represents the network contact affinity coefficient, which follows a uniform distribution. Given μ = e = 0.5, varying r values reveal that larger r values indicate a greater degree of knowledge sharing within the manufacturing industry cluster.

The specific simulation process is as follows:

First, an evolution loop was defined, where the length of r is denoted as k. For each r value, the simulation was run for a number of steps. In each step, a new matrix was created to store the next state. Each cell was traversed to calculate the number of neighboring cells entering the innovation cluster, using the Von Neumann neighborhood method, which considers 4 neighbors.

Next, the value of p₁ was calculated, following a normal distribution N(μ, σ²), using the current μ value. A uniformly distributed random number in the range [0, r] was generated as p₂. The value of P was then calculated using the formula \(\scriptstyle{p}={e}\times \left({p}_{1}+{p}_{2}\times \frac{N(t)}{M}\right)\).

The state was updated based on the value of P. If all P-values were greater than p₀ and the current cell state was 0, it was updated to 1. After updating the cell states, the final state was saved.

Through this simulation process, the final states for different r values were obtained. The simulation results indicate that higher r values, representing a higher degree of knowledge sharing, facilitate the acceleration of AI-driven innovation evolution within manufacturing industry clusters.

Figure 8 illustrates the evolution of firms in the cellular space under varying levels of the knowledge-sharing coefficient (r), set at 0.4, 0.6, and 0.8. The green cells highlight firms actively engaged in AI innovation, while the blue cells represent those that have yet to take part in the process. The simulation results demonstrate a clear positive relationship between knowledge sharing and the acceleration of AI innovation within manufacturing industry clusters. At r = 0.4, only a small number of firms engaged in AI innovation, reflecting the limited diffusion potential in environments with weak inter-firm knowledge-sharing mechanisms. As the knowledge-sharing coefficient increases to 0.6, the diffusion process is moderately enhanced, with a greater number of firms adopting AI technologies. At r = 0.8, the majority of firms within the cluster actively engage in AI innovation, showing that strong knowledge-sharing networks significantly enhance the speed and scale of AI adoption. These results emphasize the pivotal role of collaborative knowledge-sharing ecosystems in driving AI innovation evolution within manufacturing clusters.

To further illustrate this relationship, Fig. 9 provides a quantitative representation of the cumulative number of firms involved in AI innovation as a function of knowledge-sharing intensity. The findings show a steady increase in AI adoption as r rises, with a notable surge in firm participation when r reaches 0.8. Specifically, at r = 0.4, approximately 20 additional firms participated in the AI innovation cluster, whereas at r = 0.8, this number exceeded 30, reflecting the exponential effect of enhanced inter-firm knowledge exchange.

This aligns with the evolutionary economic geography theory, which posits that well-connected clusters facilitate knowledge diffusion, reduce technological learning curves, and enable firms to improve their innovation capabilities collectively. The presence of strong collaborative networks accelerates AI technology diffusion and enhances the overall resilience and adaptability of manufacturing clusters in an ever-evolving technological landscape.

These findings have several important implications. First, manufacturing clusters should actively develop structured platforms for knowledge exchange, such as AI research alliances, joint R&D centers, and digital innovation hubs, to foster collaborative learning and maximize technological spillovers. Second, informal knowledge-sharing mechanisms, such as professional networking events, open-source AI collaborations, and mentorship initiatives, should be encouraged to facilitate the organic diffusion of AI innovation.

Finally, cluster networks act as a multiplier effect, meaning that firms embedded in highly interconnected clusters experience faster AI adoption compared to those in isolated environments. Therefore, fostering strong inter-firm connections and enhancing collaborative knowledge-sharing mechanisms is crucial for accelerating the evolution of AI-driven innovation within manufacturing clusters.

Shenzhen, a leading hub for AI-driven manufacturing in China, exemplifies the vital role of cluster networks in promoting knowledge sharing and expediting the evolution of AI-driven innovations. With over 2200 AI enterprises operating within its ecosystem, Shenzhen illustrates how collaborative networks enable the diffusion of innovation through strategic cooperation and knowledge exchange. Industry leaders such as Huawei and Tencent serve as pivotal hubs, connecting smaller firms and research institutions, thereby enhancing the overall connectivity of the cluster network.

The success of Shenzhen’s AI-enabled manufacturing cluster is evidenced by initiatives such as the Open AI Innovation Center, which provides shared resources, including computing power, datasets, and simulation tools. These resources enable firms to pool their expertise and collaborate on joint R&D projects, effectively increasing the affinity coefficient of network contact (r). For instance, partnerships between Huawei and Tencent, as well as Huawei’s collaboration with UBTech Robotics, illustrate how strategic alliances enhance innovation capabilities across the cluster. In particular, the joint development of AI-powered robotic assembly lines for automotive manufacturing by Huawei and UBTech exemplifies how knowledge sharing and collaborative efforts can lead to significant efficiency gains, validating simulation findings that higher r-values correspond to more rapid innovation diffusion.

Shenzhen’s cluster also highlights the importance of risk appetite and cooperative competition in driving innovation. Smaller firms, supported by shared infrastructure and mentorship from larger enterprises, actively engage in self-innovation, further enriching the cluster’s knowledge pool. For example, Orbbec Inc.’s advancements in AI vision technologies and the integration of voice-controlled robotic arms were achieved through collaboration with both startups and established players, demonstrating the self-reinforcing nature of the cluster network.

The impact of Shenzhen’s collaborative networks on innovation is further substantiated by measurable outcomes. Recent data indicates that Shenzhen’s AI industry achieved a revenue of CNY 248.8 billion in 2022, reflecting a year-on-year growth of 32.1%. A significant percentage of surveyed firms reported enhancements in production efficiency and product quality directly linked to shared AI solutions within the cluster. These findings are consistent with simulation results, where increasing the r-value (network contact affinity) from 0.4 to 0.8 resulted in a notable increase in the number of firms actively engaged in AI innovation processes.

Supporting the simulation’s conclusions, Shenzhen’s cluster illustrates that higher levels of knowledge sharing and collaborative networks expedite the evolution of AI-driven innovations. By fostering an environment conducive to strategic cooperation, resource sharing, and risk-taking, Shenzhen’s AI-enabled manufacturing cluster provides tangible evidence of the theoretical framework’s predictions. This ecosystem not only cultivates innovation within individual firms but also enhances the overall adaptability and competitiveness of the manufacturing cluster.

Impact of cluster environment on AI-innovative manufacturing industry cluster

To investigate the impact of the cluster environment on the evolution of AI-driven innovations within manufacturing industry clusters, a simulation analysis was conducted. The values of μ and r were fixed, while the range of e values was systematically traversed. This approach facilitated the collection of data under varying conditions, enabling the subsequent determination of causal occurrences. As an approximate solution strategy, this method enhances our understanding of the complex relationships between the cluster environment and innovation evolution.

Given that μ = r = 0.5, we varied e. When the environmental conditions of manufacturing industry clusters, such as economic factors, political influences, industry standards, and market demand, are all favorable, the value of e tends to increase. Larger e values indicate stronger policy support and improved economic conditions.

The specific simulation process is as follows: First, an evolution loop was defined, where the length of e values is denoted as k. For each e value, the simulation was run for a number of steps. In each step, a new matrix was created to store the next state. Each cell was traversed to calculate the number of neighboring cells entering the innovation cluster, using the Von Neumann neighborhood method, which considers 4 neighbors.

Next, the value of p₁ was calculated, following a normal distribution N(μ, σ²), using the current μ value. A uniformly distributed random number in the range [0, r] was generated as p₂. The value of P was then calculated using the formula \(p=e\times \left({p}_{1}+{p}_{2}\times \frac{N(t)}{M}\right)\).

The state was updated based on the value of P. If all P-values were greater than p₀ and the current cell state was 0, it was updated to 1. After updating the cell states, the final state was saved.

Through this simulation process, the final states for different e values were obtained. The simulation results indicate that higher e values, representing stronger policy support and better economic conditions, facilitate the acceleration of AI-driven innovation evolution within manufacturing industry clusters.

Figure 10 illustrates the evolution of AI innovation across firms in the manufacturing cluster under varying environmental support coefficients (e) set at 0.4, 0.6, and 0.8, with resource ownership (μ) and knowledge sharing (r) held constant at 0.5. The green cells represent firms that are actively participating in the evolution of AI innovation, while the blue cells indicate firms that have yet to engage in the process. As e increases, the number of firms adopting AI innovation grows, showing a positive relationship between environmental support and innovation participation. At e = 0.4, there is limited engagement due to unfavorable environmental factors. At e = 0.8, the majority of firms participate, demonstrating how supportive economic conditions and policy environments encourage widespread AI adoption.

This figure shows the AI innovation evolution process in a manufacturing cluster under different environmental support coefficients (e = 0.4, 0.6, 0.8) with fixed μ = 0.5 and r = 0.5. The first, second, and third images illustrate the cellular space after 30 simulation steps for e = 0.4, 0.6, and 0.8, respectively. Green cells denote AI-adopting firms (S = 1), and blue cells represent non-adopting firms (S = 0).

Figure 11 presents a quantitative representation of the number of firms adopting AI innovation in the cluster as a function of varying environmental support coefficients (e) at values of 0.4, 0.6, and 0.8, while μ and r remain fixed at 0.5. The graph clearly shows that as e increases, so does the number of AI-innovative firms within the cluster. At e = 0.4, the low level of external support restricts the diffusion of AI technologies, and only a few firms participate. However, as e increases to 0.6 and 0.8, a marked increase in the number of AI-innovative firms is observed. This highlights the impact of a supportive economic and policy environment in fostering the adoption of AI technologies across a broader range of firms. The findings align with the understanding that government support, policy incentives, and favorable economic conditions are pivotal in driving technological innovation within industrial clusters.

This figure quantifies the number of AI-innovative firms in the manufacturing cluster over 30 simulation iterations for different environmental support coefficients (e = 0.4, 0.6, 0.8) with fixed μ = 0.5 and r = 0.5. The plot displays three lines, each corresponding to an e value, with the x-axis representing simulation steps and the y-axis indicating the cumulative number of firms with state S = 1.

The results indicate that a favorable cluster environment can facilitate the evolution of AI innovation within the cluster, whereas an unfavorable cluster environment can significantly impede it. The industrial cluster environment encompasses factors such as the economy, policy, industry standards, and market demand, all of which positively influence talent development within clusters. Consequently, it is crucial to establish a conducive cluster environment to foster the evolution of AI-driven innovations in manufacturing industry clusters.

Bangalore, often referred to as the ’Silicon Valley of India,’ serves as a compelling example of how a favorable cluster environment promotes the evolution of AI-enabled manufacturing clusters. As a global hub for intelligent manufacturing and semiconductor industries, the city exemplifies the transformative impact of policy support, economic strength, and market demand in driving AI-driven innovations. Leading companies such as Hindustan Aeronautics Limited, Bosch, IBM, and Intel have integrated AI technologies into their manufacturing processes, utilizing advanced techniques like selective laser sintering and fused deposition modeling to significantly reduce production times and enhance efficiency. These advancements underscore the importance of a resourceful and supportive environment in enabling firms to adopt and scale AI technologies.

Strong policy support is a cornerstone of Bangalore’s AI-enabled manufacturing ecosystem. Government initiatives such as the Karnataka Artificial Intelligence Policy (2019) and the Startup India program provide tax incentives, subsidies, and funding partnerships that promote the adoption of AI in manufacturing. Additionally, innovation hubs like the Center of Excellence for Artificial Intelligence have facilitated over 150 AI-driven manufacturing projects, focusing on Industry 4.0 applications such as predictive maintenance and process automation. These policies align with simulation findings indicating that higher e-values, which represent favorable cluster environments, significantly accelerate the adoption and diffusion of AI technologies. For example, simulation results show that at e = 0.8, all firms within a cluster engage in the AI innovation evolution, highlighting the transformative potential of a robust policy-driven cluster environment.

Bangalore’s economic foundation further strengthens its position as a leader in AI-enabled manufacturing. The city contributes over $77 billion annually to India’s GDP, equipping companies with the financial resources necessary to invest in cutting-edge AI technologies. These economic advantages create fertile ground for the integration of AI technologies into manufacturing clusters, enabling firms to maintain competitiveness in a rapidly evolving global landscape. Simulation analyses reveal that strong economic conditions (high e-values) significantly enhance firm participation in innovative evolution, as evidenced by Bangalore’s ability to attract major investments and foster large-scale AI-driven manufacturing initiatives.

Bangalore’s success also reflects the influence of market demand and adherence to global standards. Leading manufacturing firms, such as Bosch and Toyota, collaborate with local startups and research institutions to develop advanced AI solutions for robotics and quality control. For instance, the partnership between Toyota Kirloskar Motors and IISc to create AI-driven quality assurance algorithms illustrates how strategic cooperation can accelerate innovation. Furthermore, the city’s burgeoning semiconductor industry, exemplified by Intel’s Very Large-Scale Integration (VLSI) design hub, highlights how advanced R&D capabilities contribute to the ecosystem’s success. These real-world developments validate simulation findings that favorable cluster environments foster the widespread adoption and diffusion of AI technologies, with Bangalore serving as a model for AI-driven innovation in manufacturing clusters worldwide.