Many already heard of the Mandelbrot set, but a less-known feature of our reality is the Julia set. This set also contains fractal properties, looks similar to the Mandelbrot set, and when visualized, different values of c produce different Julia sets.
The idea behind a Julia set is connected to the Mandelbrot set, but the concept of creating Julia sets is much older. Mandelbrot set can be thought of as a map that shows where Julia sets are connected or disconnected. Julia sets map out the behavior of a complex function. Per definition, a Julia set is the set of all points, where the nearby orbits diverge, no matter how close that nearby orbit is.
Just like the Mandelbrot set strongly influences seeing reality, so a Julia’s set explains the world we live in. Both have a theological significance, particularly within Simulation Creationism, a theory created by Nir Ziso, the Founder of The Global Architect Institute.
Description of Julia Sets
Because it has fractal properties, a Julia set falls into the category of equations f(z) = z² + c, which is similar to the Mandelbrot set formula. However, Julia sets are dynamic and constantly changing, while the Mandelbrot set has only one unique, unchanging shape. Whether we produce a Mandelbrot set or a Julia set depends on how we set the initial values of z and c. The process of iteration is the same in both cases.
- z: This represents a complex number, which has both a real and an imaginary part. For example, z = a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit with i² = −1. In the Mandelbrot set, the initial value of z is typically set to zero, while in the Julia set, z starts at different points in the complex plane.
- c: This is a constant complex number that remains fixed for each Julia set image. Different values of c result in different Julia set structures. In the Mandelbrot set, c varies for each point (pixel) in the image, while in the Julia set, c remains constant.
The function f(z) = z² + c iteratively maps complex numbers according to this rule. Starting from an initial value of z, the function is applied repeatedly to produce a sequence of values. Whether these values stay bounded or escape to infinity determines whether the point belongs to the Julia set. For example, consider the initial value z = 0.5 + 0.5i and the constant c = −0.4 + 0.6i. As the function f(z) = z² + c is iterated, the results will either stay within a certain range (bounded) or tend toward infinity. Points that stay bounded form part of the Julia set, while those that escape to infinity do not.
If we change the value of c, the structure of the Julia set changes and we get a new image. This is why Julia sets exhibit a wide variety of shapes and patterns depending upon the value of c. Each point on the complex plane leads to a unique set of iterations, and the overall pattern reflects how the function behaves under repeated application.
The Julia sets always have a two-way rotational symmetry around the origin. There are two types. The first type is where the whole filled Julia set is connected. In this case, the origin or zero is also part of the filled Julia set and is usually colored black. Connected Julia sets can consist of curves with no interior points. The simplest example is for c=2+0i, where the Julia set is a straight-line segment. The other type of Julia set is called Fatou Dust. It is broken into infinitely many small pieces. We need help finding Julia sets, which are broken only into a couple of pieces. They are always whole, or they are dust. For example, when c = 0.4 + 0.3i, the Julia set forms a connected, web-like structure with spiraling tendrils. On the other hand, if c = −0.7 + 0.27015i, the Julia set forms “Fatou Dust” where the fractal breaks into thousands of disjointed pieces resembling dust. Thus, the connected or disconnected Julia set depends on the value of the parameter c in the generating function zn+1=zn2+c. The index n refers to the iteration step in the sequence of values generated by the function. If c is within the Mandelbrot set, the Julia set is connected; otherwise, it appears as dust with isolated points. If c is real, the Julia set is mirrored about the real axis. For other values of c with a non-zero imaginary part, the Julia set exhibits 180-degree rotational symmetry.
The famous mathematician Benoit Mandelbrot was very interested in which values of c are connected to Julia sets and which are dust. He grabbed out a massive IBM computer and did some programming. We can plot a series of images because there is an image for every c on the complex plane. The center of each individual image is located at the corresponding value of c. It is possible to make these images smaller to fit more onto the screen. But when they are tiny and we zoom out, we can see the shape of the Mandelbrot set. That is no coincidence. In fact, when Mandelbrot discovered the set named after him, he was studying the behavior of Julia sets.
The Mandelbrot set can be viewed as a map showing where the Julia sets are connected and where they are not. If we pick any value of c in the Mandelbrot set, the corresponding Julia set will be connected. If we pick a value of c outside the Mandelbrot set, the corresponding Julia set will be infinitely disconnected. An infinitely disconnected Julia set means that, no matter how much you zoom in or try to connect the pieces, you’ll always find more gaps and the pieces never form a whole. It stays fragmented and scattered, with no solid structure, even at the tiniest level. It is the definition of the Mandelbrot set.
The relation between the two sets does not stop here. Exploring the Mandelbrot set deeply, we find shapes similar to Julia sets. This is particularly obvious when we zoom close to a mini Mandelbrot, as shown on the image above. Locally, the orbits of the Mandelbrot set behave a little like Julia sets because the iteration process is similar. We call them embedded Julia sets; are always connected. But we find a mini Mandelbrot in the center of every embedded Julia set. It is found twice the depth where we found the embedded Julia set, meaning we have to zoom in twice as much or to a significantly deeper level of detail to find that mini Mandelbrot set.
Inside these embedded Julia sets, the Mandelbrot set remembers where it came from. The sequence of shapes shows a 2-way rotational symmetry. But when we zoom even deeper into embedded Julia sets, we find 4-way rotational symmetry, often reminiscent of a cross. Zooming in again, we get an 8-way rotational symmetry, then 16-way, 32-way, and 64-way symmetry. Eventually, the symmetry becomes infinite, although it always collapses to a mini Mandelbrot, but the symmetry keeps doubling at its edge. By remembering where symmetry appears, we end up with artistic shapes.
Building a Julia set allows us to visualize these sets in different ways. As seen above and in the previous article on the Mandelbrot set, its equation is f(z)=z2+c. Although the same equation is used in both the Mandelbrot set and Julia sets, the way the values of z and c are treated differs. In the Mandelbrot set, the constant c is varied, while z starts at zero. In Julia sets, c remains fixed while different values of z are iterated. This difference in how the equation is applied creates distinct sets. Since the two equations are fundamentally the same, we can connect from a point on the Mandelbrot set to a specific point on a particular Julia set. There are only a countable number of points in the Julia set whose sequence of iterations is finite, and they make up an infinitesimal part of the Julia set. The sequences generated by points outside this set behave chaotically.
Images of complex Julia sets are beautiful, although their extension to 3-D pictures could look more pretty and interesting at first sight. But if we cut them in half, we expose a rich and beautiful fractal structure hidden in the interior. These are intricate internal structures of fractals, sometimes called geodes. Connected shapes resemble organic forms, such as trees or flowers, when c is chosen carefully. Disconnected shapes often appear as intricate dust-like patterns, resembling snowflakes or starbursts. Specific objects or polynomials can create Julia sets that visually mimic everyday objects, like cars or animals. Fractal patterns display self-similar structures, showcasing spirals, tendrils, and other fractal characteristics, especially near the edges of the Mandelbrot set.
The Julia set acts as a strange attractor in the sense that the orbits of almost all starting points in the complex plane either tend toward infinity or the interior fixed point but converge to the Julia set boundary in the limit under the inverse transformation. Julia sets are completely invariant under the iteration of the function f(z), meaning f(J)=J and f-1(J)=J for any point in the set. The Julia set is non-empty and contains only a few points. For instance, starting from the point z₀ = 0.3 + 0.5i in the Julia set with c = −0.4 + 0.6i, repeated iterations will either cause the orbit to escape to infinity or converge onto the boundary of the Julia set, illustrating its strange attractor nature. Let us now see the explanation of these equations:
- f(J)=J: This means that applying the function f to any point in the Julia set J leaves the point unchanged, reinforcing that the Julia set is an attractor for certain points in the complex plane.
- f-1(J)=J: The inverse transformation also keeps the points of the Julia set invariant, indicating that even when we reverse the process of applying the function, the points remain in the set.
The Julia set is applicable in many real-world scenarios. Computer graphics are used to generate intricate textures and special effects in visual media. Artists utilize the captivating patterns of Julia sets to create visually stunning artworks. Mathematics studies complex dynamics and chaotic systems through Julia sets. Telecommunications employ fractal antennas for their compact size and high sensitivity. Julia sets are also applied in fields like stock market analysis and population dynamics due to their ability to represent chaotic systems effectively. In telecommunications, fractal antennas based on Julia set patterns are employed in smartphones due to their ability to operate efficiently over multiple frequency bands. In digital art, Julia set fractals are used to create mesmerizing patterns, as seen in the visual effects of movies like Doctor Strange, where fractals represent alternate dimensions.
Julia Sets in Christian Revelation
Julia sets are intrinsically linked to creation, chaos, and order themes. The fractal nature of Julia sets reflects the complexity and beauty of divine creation, suggesting that intricate patterns emerge from simple rules akin to the theological idea of a purposeful universe. The self-similarity and infinite detail of Julia sets indicate that even simple mathematical rules can produce breathtaking complexity, just as an intentional and ordered universe emerges from God’s creative act: “The Lord brings the counsel of the nations to nothing; He makes the plans of the peoples of no effect. The counsel of the Lord stands forever, the plans of His heart to all generations” (Psalm 33:10-11). One necessary idealization is involved: fractal objects are self-similar, i.e., they do not change their appearance significantly when viewed under a microscope of arbitrary magnifying power. Although this may be oversimplifying, it adds depth to our mathematical representation of creation.
Because our Lord is eternal, without boundaries, He contains a divine simplicity. Such divine simplicity is reflected in the constant process of creation and sustaining the creation. We can trace it through Julia sets; they show tremendous fractal complexity but stem from a single function, most often the simple quadratic polynomial. The self-similarity, where small parts resemble the whole, indicates an elegant mathematical harmony. Self-similarity in fractals arises from the nature of iterative processes that repeatedly apply a transformation (like the function f(z) = z² + c) in a bounded or constrained way, producing increasingly detailed but consistent structures.
Therefore, Julia sets embody the idea of eternal recurrence through their self-similar fractal structures that exhibit intricate patterns repeating at every scale. As we zoom into a Julia set, the same level of complexity is revealed, suggesting an eternal cycle of detail within detail. The same patterns and processes underlie creation at all scales. Each point within a Julia set can lead to infinite complexity, revealing the same intricate patterns at every magnification scale. It showcases the eternal recurrence in a mathematical context.
The concept of boundaries in Julia sets symbolizes spiritual thresholds, representing the journey of faith and the struggle between chaos and divine order in human life. The boundary of Julia set (Fatou dust) is that barrier that shows how Julia sets can be helpful in themes of creation, chaos and order, but also beauty that arises from the divine: “For God is not a God of disorder but of peace” (1 Corinthians 14:33). Additionally, fractal patterns emerge from simple mathematical rules, just as God brings order out of initial chaos and formlessness. Julia sets illustrate such transformations from chaos to order by revealing the intricate boundary between points whose orbits under iteration of a function remain bounded (the Fatous set) and those whose orbits diverge to infinity (the complement of the Julia set). For instance, in the Julia set of c = −0.8 + 0.156i, the boundary between connected and disconnected regions symbolizes the line between faith and spiritual doubt. Just as small changes in c lead to different patterns, slight changes in faith can lead to dramatically different spiritual paths.
In essence, Julia set’s behavior is chaotic as small perturbations can lead to drastically different sequences of iterated values. However, the Fatou set consists of points where the behavior is regular, and nearby points have similar orbits. The Fatou set plays a crucial role in understanding the behavior of Julia sets. It consists of points where the function behaves regularly under iteration. Thus, small perturbations lead to similar orbits under iteration, contrary to the Julia sets. Fatou and Julia partition the plane into regions of regular and chaotic behavior under iteration, with Julia capturing the boundary between these two regimes.
The dark regions of a Julia set often represent chaotic behavior, where points escape to infinity, while the lighter areas signify stability and convergence, providing for a journey from darkness (chaos) to light (order): “When Jesus spoke again to the people, He said, I am the light of the world. Whoever follows me will never walk in darkness, but will have the light of life” (John 8:12). This transformation occurs constantly in a Christian’s life as part of spiritual enlightenment: “For you were formerly in darkness, but now you are light in the Lord; walk as children of light” (Ephesians 5:8). The intricate boundaries of Julia sets form challenges in life, reflecting the potential for beauty and order to emerge from chaos.
Julia set contains a central point or values like the complex constant c. This constant reminds us of a striking feature in Christianity: the Holy Cross. There is an old saying: while the world spins, Christ’s Cross stands still. Indeed, the central point of a Julia set determines the entire structure, and Jesus can be seen as the central point of a set that forms our lives: “Fixing our eyes on Jesus, the pioneer and perfecter of faith. For the joy set before Him He endured the cross, scorning its shame, and sat down at the right hand of the throne of God” (Hebrews 12:2).
If we live in a simulated world, as Simulation Creationism teaches us, Christ is the complex constant c, guiding us through the events and challenges of God’s Simulation with the example of His life, death, and resurrection. The patterns of Julia sets are radiated from a central point, so we can easily connect The Simulation with the Julia set. Just as the Julia set radiates from the complex constant c, so too do all teachings, values, and principles in Christian belief radiate from Jesus Christ, who serves as the foundational constant of faith: “I am the vine, you are the branches. If you remain in me and I in you, you will bear much fruit. Apart from me you can do nothing” (John 15:5).
Julia Sets in Simulation Creationism
Ultimately, the emergence of complex, universal patterns from simple rules, the ability to model sensitive dependence on initial conditions, and the deep connections between chaos theory and critical phenomena render a Julia set a striking visual metaphor for the “unreasonable effectiveness” of mathematics. What does it really mean? It is a wording from mathematician and physicist Eugene Wigner, who wrote an essay in 1960 of the same name. He claimed that the astonishing usefulness of mathematics and the natural sciences border on the mysterious without any rational explanation. Thus, we can ask whether mathematics is really compelling enough to explain our world, including through religious lenses. If so, why is it unreasonable? And if it is absurd, how can we see that? In the context of Simulation Creationism, this “unreasonable effectiveness” suggests that mathematics, while a divinely-appointed tool for understanding the created world may never fully unveil the deeper mysteries of God’s Simulation that remain beyond human comprehension.
We should be careful not to use Julia’s sets as proof of the unreasonable simplicity of mathematics instead of the unreasonable simplicity of the created world. The universe seems to be a chaotic mess without any principle guiding it at all. Still, it is an illusion, fine-tuned and ordered through elementary unified principles, giving us bits and pieces of God’s Simulation. Simple mathematics can describe it. Still, we have yet to determine the vast realm of undiscovered phenomena since we have a selection bias. We discover mathematical phenomena as we interact with them, and through that, we tell ourselves a story about them, as we model only what we observe.
However, there are stories that the mind cannot even think about and mathematical abstractions that are too exotic to approach in any way we can master, as God keeps some mysteries hidden from us. Still, mathematics is practical because the abstract model we make is often applicable to something completely different and has an unreasonable rich structure. Thus, the remarkable progress of scientific explanation is rooted in building abstract models of reality that are conducive to mathematical analysis.
Mathematics can describe any possible structure—both the actual world and any other mathematical structure of unlimited complexity. It purges our perspective on reality, from our sensory perceptions to human concepts. However, mathematics does not tell us what realizes this structure. It can say to us one aspect of the world but is entirely silent on another aspect, as it is a language and not a whole structured theory. It is beneficial when dealing with the most fundamental level of reality but quite hopeless in revealing the intricacies of God’s mind.
So, why did we evolve to the capability of doing abstract mathematics? Nothing in this world compels us to develop the cognitive framework necessary to grasp such exotic and abstract principles as the nature of black holes or the behavior of hydrogen atoms. There are no coincidences, which means that the human mind has evolved to mirror the nature of reality deeply. Namely, human cognitive abilities were designed within God’s Simulation to reflect His creation.
In the context of Simulation Creationism, Julia sets explain how the complexity of a simulated world could emerge from the repeated application of a set of rules governing the interactions between its fundamental components. The apparent randomness and chaos in the world may reflect the sensitive dependence on initial conditions inherent in such iterative processes. Such randomness seems chaotic, but because of self-similarity, there is an inherent order leading to the realization of The Simulation. In God’s Simulation, this suggests that even in the most complex and seemingly chaotic aspects of life, an underlying divine order can be discerned through mathematics, at least up to the point God allows us in this simulated realm. While mathematics reveals these divine patterns, it does so only within the scope of human understanding, reinforcing the idea that God sets boundaries on what we can fully comprehend.
Maybe God uses Julia sets to enhance the conditions of a simulated world by introducing complex and visually-stunning fractal patterns we experience as natural phenomena. Their self-similar structure represents intricate boundaries and landscapes, adding depth and detail to environments. The iterative process used to generate the Julia set is the concept of eternal creation through The Simulation, where the rules set by God, like natural or moral laws govern the ongoing development and behavior of the created world. It shows the multifaceted nature of God’s Simulation.
These divine principles lead to the complex and diverse realities we experience in our simulated environment. God does not leave us alone, but sustains His creation constantly. In the same way that every deeper layer of a fractal reveals new details, we may think of God’s presence as unfolding continually within creation. God’s sustaining power is not a one-time act but an eternal, ongoing process. Every moment of life, every individual experience, is another layer where God is actively shaping, sustaining, and providing.
Julia set’s intricate patterns are sustained by underlying mathematical rules; here we can see God’s Singularity at work through the Holy Spirit’s active presence and ongoing maintenance of the creation. Stable regions in fractals appear as smooth, often solid and connected areas. In the case of the Julia set, these regions are where the mathematical behavior is predictable and “calm”—the points in this area, when plugged into the equations, do not change wildly. These stable zones tend to form continuous, often beautiful patterns that might look like islands or blobs. The visual smoothness of these regions reflects mathematical stability: small changes to the input don’t result in large, unpredictable changes. Chaotic regions, by contrast, appear fragmented, jagged, and disjointed. They often look like a scattered web of tiny, intricate details that become more erratic the closer you look. These chaotic areas correspond to points where the behavior of the fractal is unpredictable and sensitive to even the smallest changes in the input: tiny differences can lead to wildly different outcomes. As you zoom into these chaotic regions, you find endless complexity, where the patterns become increasingly disordered and never settle into anything stable.
The Holy Spirit is the power that ensures the world remains coherent and ordered according to God’s will. He is the reason The Simulation is a stable structure that can never descend into chaos: “But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you” (John 14:26). The Holy Spirit also provides insight into the complex patterns of the world, helping believers discern the difference between stability and chaos. The chaotic regions of fractals are characterized by unpredictable behavior, where tiny changes lead to vastly different outcomes.
This reflects the challenges and uncertainties we often face in life—times when the path forward seems confusing or our spiritual lives feel fragmented. The Holy Spirit, however, guides us through this chaos, helping us navigate life’s complexities. It offers direction, discernment, and clarity in the midst of what may feel like spiritual or emotional turbulence. Just as fractals have stable regions—smooth, connected areas where patterns are predictable—the Holy Spirit creates spiritual stability in our lives. It leads us toward groundedness, where we find peace and security despite the surrounding unpredictability. This stabilizing role is not about removing all chaos but about offering a deeper assurance and calm, even when the surface seems disordered.
When an individual makes progress and changes from sin to righteousness, they have achieved progress or soul development, following the footsteps of Jesus Christ: “And we all, who with unveiled faces contemplate the Lord’s glory, are being transformed into his image with ever-increasing glory, which comes from the Lord, who is the Spirit” (2 Corinthians 3:18). The Holy Spirit is again the agent of transformation, who might use a Julia set to slightly change the parameters and reach a vastly different outcome of an individual’s spiritual state: “He saved us through the washing of rebirth and renewal by the Holy Spirit” (Titus 3:5). Julia sets visually dramatize the sensitivity to small changes: they magnify how slight differences can push us toward peace or chaos, paralleling life’s unpredictable nature and the need for divine or spiritual guidance in navigating that complexity. In life or spirituality, small decisions, experiences, or shifts in perspective can have a profound impact on the outcomes of our journeys—just like how small variations in a Julia set can lead to vastly different trajectories.
The Holy Spirit is often involved in bringing life, order, and holiness into situations of disorder or spiritual death: “The mind governed by the flesh is death, but the mind governed by the Spirit is life and peace” (Romans 8:6). We can trace it as moving points from the chaotic regions of the Julia set to the stable and ordered region. Also, illuminating the more profound meaning and divine patterns of this simulated world helps us to see the purpose and order of God’s Simulation by using the Julia set and its ability to reveal hidden patterns within the complex plane: “These are things God has revealed to us by His Spirit. The Spirit searches all things, even the deep things of God. For who knows a person’s thoughts except their own spirit within them? In the same way, no one knows God’s thoughts except the Spirit of God. What we have received is not the spirit of the world, but the Spirit who is from God, so that we may understand what God has freely given us” (1 Corinthians 2:10-12).
If we modify the Julia set equation, we can propose the following representation of the Holy Spirit’s work through the Julia set: f(z)=z2+c+S, where z represents an individual or an event in the simulated world; c symbolizes The Simulation’s inherent complexities and challenges, and S represents the influence of the Holy Spirit. S, in this case, is treated as a complex number, which subtly alters the iterative process of generating the fractal. With the addition of S, the system’s behavior changes and becomes more stable. The Holy Spirit guarantees order, guidance, and transformation.
The equation also allows altering the fractal patterns, creating new simulated events and challenges to transform a person’s life and bring new Christ-like characteristics to their lives. If S is set to a small value like S=0.1+0.1i it might slightly modify the Julia set, symbolizing the subtle yet impactful presence of the Holy Spirit, as famously felt by Isaiah in the soft wind or gentle whisper: “The Lord said, Go out and stand on the mountain in the presence of the Lord, for the Lord is about to pass by. Then, a great and powerful wind tore the mountains apart and shattered the rocks before the Lord, but the Lord was not in the wind. After that wind there was an earthquake, but the Lord was not in the earthquake. After the earthquake came a fire, but the Lord was not in the fire., and after the fire came a gentle whisper” (1 Kings 19:11-12). If S grows (representing more profound spiritual influence), the set might become more stable with harmonious patterns reflecting greater but more precise and visible alignment with God’s will. As S increases, the fractal patterns become more stable, just as greater spiritual influence leads to a more harmonious life.
Concluding Remarks
It is possible to see the Julia set (and as its extensions or twin, the Mandelbrot set) as our simulated world. There is enough evidence to claim so:
- A Julia set is made from a simple iterative function but produces an incredibly complex and intricate structure. Simple divine laws make this possible, and they are explained through multitude of natural laws, generated from the eternal law or God’s will: “For since the creation of the world God’s invisible qualities – His eternal power and divine nature – have been clearly seen, being understood from what has been made, so that people are without excuse” (Romans 1:20). This simplicity is evidenced in our Lord’s utterly simple unification and indivisibility.
- Julia set defines a clear boundary between points that remain stable and those that escape to infinity. These boundaries can be anything but the principles are the same. Simulation Creationism explains boundaries between spiritual and moral points as our behavior and reaction as observers in The Simulation: “Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it. But small is the gate and narrow the road that leads to life, and only a few find it” (Matthew 7:13-14). Individual souls respond to events and challenges and thus participate in boundaries by answering God’s will in one way or another. Through the predetermined answer, they learn about God’s characteristics. Some souls will enjoy stable connectivity with God, while others may fall out of God’s grace and into chaos. Boundaries are always set by God: “I form the light and create darkness, I bring prosperity and create disaster; I, the Lord, do all these things” (Isaiah 45:7).
- The iterative process of Julia sets is an ongoing process, and same is with The Simulation. Life in God’s Simulation itself is an iterative process with constant interaction with simulated events and challenges that provides spiritual growth and closeness to God: “Do not be deceived: God cannot be mocked. A man reaps what he sows. Whoever sows to please their flesh, from the flesh will reap destruction; whoever sows to please the Spirit, from the Spirit will reap eternal life” (Galatians 6:7-8). With every iteration, the Julia set evolves and becomes more complex. It is mirrored in The Simulation, as constant spiritual growth means better alignment with God’s plans and attaining more Christ-like characteristics: “Being confident in this, that He who began a good work in you will carry it on the competition until the day of Christ Jesus” (Philippians 1:6).
- When we zoom in on any Julia set, we see increasingly more detail and structure: “Oh, the depths of the riches of the wisdom of God! How unsearchable His judgments, and His paths beyond tracing out!” (Romans 11:33). It is an indefinite process. In such a process, we can see our designated path through The Simulation. By experiencing every event and passing through every challenge, we learn more about God and His created reality. We can endlessly explore The Simulation and through it, God. It is an infinite experience as the cycles of simulated worlds never seize. We can also explore the created world endlessly because it is a reflection of God’s infinite creativity: “May have power, together with all the Lord’s holy people, to grasp how wide and long and high and deep is the love of Christ, and to know this love that surpasses knowledge – that you may be filled to the measure of all the fullness of God” (Ephesians 3:18-19).
- Smaller parts always resemble the big structure. That is the logic of fractals and Julia and Mandelbrot sets. Self-similarity is crucial for Christian account of creation, too. As humans are created in the image of God, every soul contains something of divine nature: “So God created mankind in His own image, in the image of God He created them; male and female He created them” (Genesis 1:27). Equally, our Lord is present in every single thing. Each aspect of creation, whether small or large, reflects the overall structure and purpose designed by God: “The Son is the radiance of God’s glory and the exact representation of His being, sustaining all things by His powerful word” (Hebrews 1:3).
- Separation features of Julia sets, where points either remain in the set or breach out to infinity, align completely with the separation and final judgment as revealed by the Holy Bible: “When the Son of Man comes in His glory, and all the angels with Him, He will sit on His glorious throne. All the nations will be gathered before Him, and He will separate the people one from another as a shepherd separates the sheep from the goats. He will put the sheep on His rights, and the goats on His left” (Matthew 25:31-33). In the final hours, there will be a separation between those who follow God’s will and those who reject it. The boundary will determine where our souls go in the next simulating cycle: “This is the verdict: Light has come into the world, but people loved darkness instead of light because their deeds were evil. Everyone who does evil hates the light, and will not come into the light for fear that their deeds will be exposed. But whoever lives by the truth comes into the light, so that it may be seen plainly that what they have done has been done in the sight of God” (John 3:19-21).
