Cellular automata (CA) are mathematical models where simple rules can give rise to complex and unpredictable behavior. Cellular automata consist of a grid of cells. Each cell can exist in a finite number of states, and its development is based on the states of neighboring cells. Applications of cellular automata include chemistry, physics, and computer science. Cellular automata are used to model various physical phenomena, and some video games even mimic physical properties found in nature. In cryptography, cellular automata can serve as one-way functions—functions where it is computationally difficult to reverse the process, meaning it is hard to deduce the input (or previous state) from the output (or next state). Changes in cell states occur in discrete steps; they depend on the states of neighboring cells and predetermined rules. This property is used in the creation of cryptographic systems. Cellular automata can provoke chemical reactions, such as the Belousov–Zhabotinsky reaction.
However, CA may go beyond to the realm of theology and specific worldviews. It helps us imagine the way God created the world and how He sustains it. In that regard, Simulation Creationism, a theory developed by Nir Ziso, founder of The Global Architect Institute and The Glory of Christ Art Heritage, offers a unique approach that uses CA and its mathematical foundation to illustrate the technical details of our world’s possible creation. Specific case studies help further analyze the complexities of creation.
Foundations of Cellular Automata
John von Neumann worked on self-replicating machines in the 1940s and 1950s when he encountered cellular automata. He collaborated with Stanislaw Ulam, who suggested using a discrete system. The two scientists developed cellular automata. Von Neumann wanted to design a theoretical machine capable of self-replication, inspired by biological processes of reproduction and evolution. First, he used a kinematic model known to produce complex mechanical robots. However, the practical challenges and resource demands of this approach led Ulam to propose an alternative method using a lattice-based system.
This suggestion led von Neumann to develop a two-dimensional cellular automaton. In this model, the “universe” was represented as a grid of cells, each capable of existing in one of 29 possible states. The state of each cell was determined by its interaction with its immediate orthogonal neighbors (up, down, left, and right). Von Neumann successfully showed the possibility of self-replicating behavior. This work introduced the concept of the von Neumann universal constructor—a theoretical machine that could create copies of itself according to defined rules. In 1948, von Neumann presented his findings at the Hixon Symposium in a paper titled “The General and Logical Theory of Automata.” His work on cellular automata was later expanded and published posthumously in 1966 in the book Theory of Self-Reproducing Automata.
Stephen Wolfram’s work
Physicist and computer scientist Stephen Wolfram sees the universe as a massive computational system. In his bold theory, Wolfram suggests that the cosmos functions similarly to cellular automata—a digital framework where simple rules applied to a grid of cells evolve over time, generating complex and dynamic patterns. Wolfram suggests that there is a simple, deterministic process from which all the complexity of the universe—including the formation of galaxies and the emergence of life—arises. These processes are governed by straightforward rules that, when applied iteratively, produce the complex behaviors we see in nature. He writes in A New Kind of Science that the laws of physics may emerge from these computational rules. This means the universe is a digital entity.
Wolfram’s theory posits that reality, at its most basic level, is not continuous but composed of discrete units, akin to pixels in a digital image. These units follow fixed rules and consequently create the macroscopic world we know today. It is a bold and novel approach, quite different from the traditional space-time view of the universe, as it suggests the emergence of phenomena. This is a revolutionary idea because it challenges our concepts stemming from quantum mechanics and general relativity. Wolfram demonstrates that these deterministic rules ultimately lead to a complex universe. He has shown that cellular automata can generate patterns resembling those found in nature, such as snowflakes or spiral galaxies. The universe is complex in its origin yet grounded in straightforward foundational rules. Wolfram denies the necessity for complex equations to describe the cosmos. In the realm of physics, Wolfram’s theory introduces a radical shift. Wolfram’s discrete model provides a new way to understand the cosmos and discoveries in astrophysics.
Wolfram also suggests that his computational model could reconcile quantum mechanics and general relativity. These two pillars of modern physics have historically been difficult to unify, as they describe vastly different scales. Perhaps Wolfram can offer a new approach to unveiling a “theory of everything.” The implications of Wolfram’s theory extend to the possibility of simulating the universe. If the fundamental rules of reality are computational and relatively simple, future technologies might allow us to replicate various aspects of the universe in a digital environment. Wolfram has faced much criticism. His critics say that the simplicity of cellular automata might not fully capture the complexity of physical laws. Still, Wolfram’s ideas have sparked vibrant discussions across scientific disciplines. When examining simple rules encoded in DNA, we observe complex life as the end result; a similar application can be seen in artificial intelligence, making this theory plausible.
Mechanics of Cellular Automata
Cellular automata models consist of grids of cells with specific rules. These grids can be one-dimensional (1D), two-dimensional (2D), or even higher-dimensional structures. In the simplest form, each cell in the grid exists in one of two states—on (1) or off (0). The state of each cell is updated in discrete time steps according to rules that consider its current state and the states of its neighboring cells.
The cells are arranged in grids of various dimensions. A 1D grid is a simple linear array of cells. The most common type is a 2D grid. Cells interact with their neighbors using either a Von Neumann neighborhood (four orthogonal neighbors) or a Moore neighborhood (eight neighbors, including diagonals). In higher-dimensional automata, neighbor interactions become increasingly complex, making these systems less commonly explored due to their computational intensity.
Cells act according to a set of uniform and consistent rules, where each cell’s state is based on its own state and the states of its neighboring cells. The principle of locality states that a cell’s state change is influenced only by its immediate surroundings. In contrast, the principle of parallelism means all cells update simultaneously, allowing for the emergence of complex patterns from simple interactions. Each time step in a cellular automaton is referred to as a generation. The rules applied to update the cells’ states are usually the same for every cell, ensuring a uniform evolution of the system over time.
One of the most famous examples of cellular automata is The Game of Life, created by mathematician John Conway in the 1970s. It is a 2D grid where each cell can be either alive (1) or dead (0). The state of each cell in the next generation depends on the number of live neighbors it has, following these rules:
- A live cell with fewer than two live neighbors dies (underpopulation).
- A live cell with two or three live neighbors continues to the next generation.
- A live cell with more than three live neighbors dies (overpopulation).
- A dead cell with exactly three live neighbors becomes alive.
The Game of Life can produce simple patterns but also generate highly complex behaviors, such as the “glider,” a pattern that moves across the grid. Simple rules can produce unexpected complexity.
Rule 110 is a specific example of a 1D cellular automaton where the state of a cell and its neighbors determine its next state:
- If the cell and both its neighbors are on (1), the cell turns off (0).
- If the cell and both neighbors are off (0), it remains off.
- If the cell and its right neighbor are off, but its left neighbor is on, the cell turns off.
- In all other cases, the cell turns on.
Defining neighborhoods in 2D grids introduces different types of neighbor interactions:
- Moore Neighborhood: Considers all eight surrounding cells, including diagonals.
- Von Neumann Neighborhood: Considers four orthogonal neighbors (up, down, left, right).
In both types, the state of a cell evolves based on its interactions with its neighbors, following predefined rules that guide the overall behavior of the cellular automaton.
Emergence of Complexity
Complex and seemingly random structures can emerge from simple rules, such as Rule 110. However, they still follow consistent patterns. In 1994, Matthew Cook proved that Rule 110 is Turing-complete, meaning it has the computational power of a universal Turing machine and can perform any computation given enough time and resources. This finding illustrates the capacity of cellular automata to mimic complex systems and execute sophisticated computations.
Not all cellular automata have such capabilities—many follow rules that result in repetitive, predictable patterns. But exceptional cases like Rule 110 and Conway’s Game of Life can generate highly dynamic and intricate behaviors. Similar principles are also found in nature: a snowflake begins as a frozen droplet around a microscopic particle, then grows into a hexagonal shape due to the geometry of water molecules under specific humidity and temperature conditions.
Another striking example is the Belousov–Zhabotinsky (BZ) reaction, discovered by biochemist Boris Belousov. This chemical reaction oscillates between states instead of reaching a stable equilibrium, visibly changing colors in cycles. Initially seen as contradicting the Second Law of Thermodynamics, the reaction’s legitimacy was later confirmed by Anatol Zhabotinsky. It belongs to a family of oscillating reactions that show how simple chemical processes can lead to sustained complex patterns.
Today, cellular automata are valuable tools in diverse scientific fields for modeling phenomena such as natural formations, biological colonies, and pattern growth. By following simple, local rules, they demonstrate how complexity can emerge unexpectedly from simplicity.
Biblical Perspectives on Creation through Cellular Automata
God commands in the Book of Genesis, “Let there be light” (Genesis 1:3). This marks the initiation of order, structure, and illumination in the void—a moment of initialization seen in cellular automata, where a chaotic or empty grid begins to evolve under specific rules. Before God’s command, the earth is described as “formless and empty, with darkness over the surface of the deep” (Genesis 1:2). A cellular automaton also begins with a formless grid that transforms as simple rules introduce order and structure. The Bible opens with a world in chaos—empty, dark, and silent. Then comes a turning point: a voice says, “Let there be light.” It is a short command, but it changes everything. That moment is reminiscent of how a simple rule in a cellular automaton can suddenly bring a lifeless grid to life. One small change, and patterns begin to form. In 1 Corinthians 14:33, it is written that God is not a God of disorder but of peace. Creation is not merely about making things—it is about shaping them into something meaningful. Similarly, as the automaton updates step by step, what begins as randomness gradually organizes itself.
Light is the first element created, used to separate day from night in a binary fashion. Cellular automata also begin with a binary state, as the grid can be either on or off, alive or dead. This is a deterministic feature, just as God establishes physical laws to govern His creation: “If I have not established my covenant with day and night, and the fixed laws of heaven and earth…” (Jeremiah 33:25). Genesis explains how creation initiates a series of interconnected events bringing everything we know and see into existence. The moment of creation is the initialization stage for emergent patterns and behaviors. These are often unpredictable yet inherently beautiful and complex.
Observation plays a crucial role in both divine creation and cellular automata. God observes and judges the light as good, separating it from darkness (Genesis 1:4). In cellular automata, observing the grid’s evolution helps in understanding its behavior and emergent complexity. The beauty of this evolution reflects the sentiment in Ecclesiastes 3:11: “He has made everything beautiful in its time.” In the separation of light and darkness, structure emerges. This depends on partitions, as seen in cellular automata, which serve as the framework for pattern formation. Once again, from a simple initial state—or chaos—a complex system emerges.
Light symbolizes knowledge, presence, and divine revelation: “God is light; in Him there is no darkness at all” (1 John 1:5). Jesus, as the “Light of the World” (John 8:12), embodies the transformative power of light. This creative force continues to operate, just as the initial configuration of cellular automata can develop complex patterns. This can be understood as the underlying transformative power of Jesus Christ, as noted in 2 Corinthians 4:6: “Let light shine out of darkness.”
In Simulation Creationism, as proposed by The Global Architect Institute, Divine Light is viewed as a fundamental energy permeating our simulated world, embodying knowledge, spiritual enlightenment, and God’s presence, as seen in Genesis 1:3 and John 8:12. Within the simulated framework, Divine Light acts as the initial energy transforming a static universe into a dynamic Simulation, guiding human consciousness toward spiritual truths and differentiating between divine and lesser lights, reflecting moral and spiritual dichotomies.
Genesis states that God’s structured creation over six days is a progressive sequence, with each day building upon the last. In cellular automata, generations build upon the previous ones, with emergent potential; similarly, the six days of creation can be understood as a development of subsequent states.
The Nature of Divine Law
God determines every event in the universe’s history, including all human actions, through His sovereignty and omniscience. All occurrences are preordained by divine decree. Since God knows everything, any event that happens must be determined by Him, as He alone existed prior to creation: “For what can be known about God is plain to them, because God has shown it to them” (Romans 1:19).
The laws of nature are expressions of God’s creative will, a perspective known as decretalism. Regularities in nature are not only descriptive but rooted in divine decrees of creation. We know them as the laws of physics. They form the constraints within which structure emerges, according to God’s wishes or decrees. How God accomplishes this remains a mystery. If fundamental physics is deterministic, God may operate within these laws without violating them—or intervene through indeterministic gaps such as quantum events: “I, the Lord, do not change” (Malachi 3:6). Simulation Creationism suggests the concept of God’s Singularity—a setting of fundamental laws for our simulated world—where rare violations of these laws are known as miracles. It is a singular and harmonious system of God’s order. Creation reflects a contingent rationality, expressing divine order while allowing complexity and variability within predetermined boundaries.
Determinism posits that all events, including human actions, are determined by prior causes, suggesting that free will is an illusion. Every choice appears inevitable due to preceding factors. The Bible supports this view of predetermination, indicating that God, in His sovereignty, predestines individuals in all aspects, including salvation or condemnation: “He predestined us for adoption to sonship through Jesus Christ, in accordance with His pleasure and will… In Him, we were also chosen, having been predestined according to the plan of Him who works out everything in conformity with the purpose of His will” (Ephesians 1:5-11). While humans seem to make free choices, these are ultimately bound by divine decree. The Global Architect Institute aligns with this theological stance, refuting compatibilism, which suggests that free will exists within a deterministic framework. Instead, Simulation Creationism proposes that God orchestrates every move within The Simulation, with souls as conscious observers who interpret—or misinterpret—the Creator’s message.
Cellular automata provide a useful analogy for discussing determinism. Stephen Wolfram’s work introduces computational irreducibility, meaning the future states of these systems cannot be predicted without replicating each step. He defines it as a rule where no shortcut or simplified mathematical model can predict the outcome of a system faster than just model every step. While initial rules and conditions determine outcomes, the system’s evolution appears unpredictable and complex. In this way, cellular automata reflect a deterministic framework in which the Creator, God, exists in an eternal present—simultaneously knowing all events, past, present, and future. God predetermines events through His Singularity, yet is not subject to unpredictability.
Probabilistic cellular automata may help in reconciling free will with determinism, but as all prior states ultimately predetermine choices, free will is merely an illusion. Even quantum indeterminacy has hidden variables, strengthening determinism.
Simulation Creationism and Cellular Automata
Returning to Conway’s Game of Life, Simulation Creationism offers a framework for exploring the creation of life and the universe through simple deterministic rules. The evolution of a cellular automaton is entirely determined by its initial configuration and the rules applied, resembling how simulated processes might evolve life as we know it.
Some cellular automata configurations—such as Langton’s replicator—make copies of themselves, exemplifying how specific arrangements can autonomously encode instructions to generate new structures. Such configurations can help explain the simulated origins of life arising from chaos by adjusting rules and initial conditions. In this way, cellular automata may serve as a blueprint for a simulated world in which God establishes fundamental rules. These rules govern the evolution of simple states into complex patterns, akin to divine laws. Should God alter these rules—such as changing gravitational forces—the entire structure of reality would shift accordingly. This could reflect the concept of “a new heaven and a new earth,” where everything differs from our current simulated world. Hence, God’s design is intentional, allowing for predictable outcomes based on initial conditions and rules.
Under the right conditions, cellular automata can replicate life-like behaviors, where life emerges from a designed framework. The Bible teaches that God designs life and also creates souls, endowing us with consciousness, awareness, and purpose. We now consider how this might work, as machine consciousness remains a topic of ongoing debate. Hans Moravec proposed that a cellular automaton could recognize its own status and seek its creator in much the same way that people seek God. Our souls likewise strive to find their place within God’s creative work.
Once a cellular automaton reaches a stable end state, nothing further occurs. This offers a useful comparison with Christian eschatology: once creation fulfills its purpose, it no longer develops. The remaining transformation is redemption, restoring the personal soul to its original, perfect state. In cellular automata, a similar restoration can occur through reversibility, where systems return to their previous states. This analogy is meaningful, as it strengthens faith in renewal and restoration.
Through our ability to understand and develop cellular automata, we reflect our far lesser creative capacity as creatures made in the image of God (Genesis 1:26–27). We mimic aspects of simulated reality, and cellular automata serve as a microcosm of life, purpose, and creation.
Limits of Cellular Automata vs. the Infinite Nature of God’s Creation
The computational capacity of cellular automata is limited by their design. For example, certain classes of cellular automata can only mimic specific behaviors or patterns. Recent research on affine cellular automata—CAs that apply affine/linear transformations over finite fields—demonstrates that they reproduce configurations confined to those fields, underscoring their inherent limitations. While cellular automata can model complexity, they are ultimately bounded by these constraints.
Many properties of cellular automata, such as determining whether a configuration will reach a particular state after an infinite number of iterations, are undecidable. These questions do not admit answers within the finite framework of the automaton. Such systems simply cannot capture the full complexity of dynamic phenomena. Alan Turing proved the related Halting Problem: no algorithm can decide, for every program, whether it will eventually stop or run forever. Cellular automata illustrate these broader limits of undecidability, and we can find echoes here of the long-term behavior of God’s Simulation—questions that cannot be resolved within a finite framework.
Comparing these constraints to God’s Simulation reveals a stark contrast—God’s creative power is not algorithmically bound, unlike CA—and also aids in understanding the divine framework. Theology places God outside time and space, granting our Creator unbounded creative potential. Cellular automata are incapable of such transcendence. This infinite nature suggests that God’s creation encompasses possibilities beyond human comprehension: “For my thoughts are not your thoughts, neither are your ways my ways,” declares the Lord. “As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts” (Isaiah 55:8–9). The infinite nature of God’s creation implies a vast and infinitely complex reality, whereas cellular automata can explore only a limited set of configurations based on predetermined rules. By contrast, God’s creation is unrestricted. There are neither fixed initial conditions nor finite rules, for God acts freely within His dynamic reality.
God’s Simulation is filled with purpose and meaning, reflecting divine intention in every aspect of existence: “The Lord has made everything for its purpose, even the wicked for the day of trouble” (Proverbs 16:4). This purposeful design stands in stark contrast to the mechanical nature of human.
Role of Observation
The observer in cellular automata reconstructs or interprets the system’s state based on available outputs. Observability is the ability to infer a system’s internal state from its external outputs. This often involves reconstructing system states from sensor data to explain dynamic behavior. Sensors must be placed strategically, and algorithms must be capable of interpreting the data; without these conditions, observation will not be effective.
In extended or interactive versions of cellular automata—such as those incorporating agent behavior or feedback loops—an observer can influence the system’s dynamics. Similarly, in quantum mechanics, measurement can affect a system; observing a particle can alter its state.
Cellular automata can exhibit unpredictable behaviors arising from simple rules. Observers must account for this complexity when interpreting results. The inherent unpredictability requires more than observation alone: it requires analysis and contextual understanding—and, in a theological sense, divine insight. This leads us to consider the role of the observer in God’s Simulation.
In theological discourse, God is often viewed as both the creator and observer of creation. Just as an observer in a cellular automaton seeks to understand the system’s state and dynamics, God perceives and understands all aspects of creation—its present states and futures—since God acts outside of time: “Great is our Lord and abundant in power; his understanding is beyond measure” (Psalm 147:5).
As humans, we are limited both in our understanding of cellular automata and in comprehending God’s Simulation. Our efforts to observe and interpret reality confront God’s infinite wisdom: “Oh, the depth of the riches of the wisdom and knowledge of God! How unsearchable his judgments, and his paths beyond tracing out!” (Romans 11:33). Christianity calls for humility in understanding divine acts and in recognizing our finite nature. We learn about nature and reality through experience, simulated events, and challenges—interpreting them as observers of cellular automata must interpret data meaningfully. In this process, we encounter uncertainty, complexity, and unpredictability—but also faith, divine purpose, and meaning.
Research suggests that observers construct knowledge in ways similar to participants within God’s Simulation. Observers learn and derive meaning from experience, much as individuals in a simulated environment interact with their surroundings.
As active participants in God’s creation, humans also engage with the world. Our thoughts and consciousness help us comprehend reality, as Klee Irwin emphasizes. Thus, observers can influence outcomes within God’s Simulation through their perceptions and intentions, suggesting that consciousness may also shape reality.
Conway’s Game of Life as a Metaphor for Creation
Conway’s Game of Life is a metaphor for modeling of creation, where simple rules lead to complex outcomes. God’s creative acts establish foundational principles that guide the unfolding of reality. The Game of Life illustrates the balance between chaos (birth) and order (stability). Viewed this way, we can see how God might work through chaotic events and established laws to fulfill divine purposes.
In the Game of Life, a dead cell becomes alive if it has exactly three live neighbors. The emergence of new life from existing conditions is a desirable result, as it shows life arising from existing creation rather than “creation ex nihilo,” as Christianity suggests. A divine act utilizes existing elements and brings forth life. Conversely, a live cell dies from underpopulation (fewer than two neighbors) or overpopulation (more than three neighbors), highlighting the interplay between life’s fragility and the balance required for sustainability. Death in the Game of Life can represent the natural cycle of life, where existence is contingent upon conditions, including mortality and divine providence.
Specific configurations in the Game of Life become stable or oscillate between states. For example, still lives do not change over generations, while oscillators return to their initial state after a finite number of generations. This reveals that there is order within creation, as well as purpose. We might think life is dynamic and unpredictable, yet there is an underlying stability that the Creator ordains.
Patterns such as gliders and spaceships illustrate how simple rules can give rise to complex, moving behaviors across the grid. Gliders can represent the continuity of life through space and time. Without such movement or pulsing, there would be no growth or evolution within God’s Simulation. The R-pentomino pattern is notable for chaotic initial behavior before stabilizing after 1,103 generations, while producing gliders that escape to infinity. In the same vein, God brings order from chaos or creates purpose from seemingly random events. The Gosper glider gun produces gliders indefinitely—an image of continuous creation and growth, an ongoing creative process in God’s universe.
Simulating Biblical Events
Biblical events and miracles can be interpreted as simulated phenomena. Cellular automata can model such events and offer insights into their dynamics and outcomes. Focusing on the Book of Exodus, we can explore how these events might be reconstructed within a structured framework.
The plagues in Exodus are a series of ten calamities inflicted upon Egypt to compel Pharaoh to release the enslaved Israelites. These plagues—ranging from the plague of blood to the death of the firstborn—demonstrate God’s power and judgment against Egyptian rulers determined to resist the liberation of the Israelites. The narrative reveals God’s intention to harden Pharaoh’s heart, ensuring a prolonged display of divine power: “But I will harden Pharaoh’s heart, and though I multiply my signs and wonders in Egypt, he will not listen to you” (Exodus 7:3–4).
Cellular automata can mimic these plagues by defining cell states such as healthy (unaffected areas), affected (areas experiencing a specific plague), and dead (areas devastated by the plagues). Here’s how cellular automata might emulate specific plagues:
- Plague of Blood: “Moses and Aaron did just as the Lord had commanded… and all the water was changed into blood” (Exodus 7:20–21). In this situation, cells representing water sources transition from healthy (clear) to affected (blood). A rule could specify that if a water cell is adjacent to an affected cell, it becomes affected in the next iteration, spreading the state of blood throughout the water system.
- Plague of Frogs: “Stretch out your hand… and make frogs come up on the land of Egypt” (Exodus 8:5). This plague can be modeled as a chain reaction: cells representing water bodies become populated with frogs, which then cause adjacent land cells to become populated as frogs move inland. Over successive iterations, this process reproduces the expanding presence of frogs across the land.
- Death of the Firstborn: “Every firstborn son in Egypt will die…” (Exodus 11:5). This scenario could be modeled as a sudden state transition in which cells representing households are marked as dead based on specific conditions (e.g., presence of a firstborn male and absence of lamb’s blood on the door), demonstrating the selective nature of this plague.
The parting of the Red Sea, traditionally viewed as a miraculous event, has also been explored with models that apply fluid-dynamics principles: “Then Moses stretched out his hand over the sea, and the Lord drove the sea back by a strong east wind all night and made the sea dry land, and the waters were divided” (Exodus 14:21). The parting is presented here as an emergent phenomenon arising from interactions of fundamental physical laws within a simulated reality. A temporary modification of the simulated world’s parameters—through divine intervention—would momentarily alter the underlying physics to achieve a specific outcome.
Divine actions in God’s Simulation can be viewed as adjustments to the rules governing the simulated reality. The miracles of Exodus are not random occurrences but intentional manipulations of a designed system, reflecting a structured and purposeful divine plan.
