The geometry we learn in school is relatively straightforward. A circle is a circle and a square is a square. However, rarely do we see such objects in nature. The natural world is full of twists and turns; it is complicated in structure, and it doesn’t get any easier on a small scale. There are no straight lines, no triangles, nor squares. So, how do we measure and apply it in mathematics as an expression of reality? Can we connect it to the Christian revelation in the Holy Bible and the Simulation Creationism Theory created by Nir Ziso, the founder of The Global Architect Institute?

The answer for the mathematical expression of reality is fractal geometry, which states that reality consists of complex shapes that are the same close by and far away. This truth was “found” by a French mathematician, Benoit Mandelbrot. Numbers exist in the world around us, and humans have discovered them as abstract (not concrete or visual) objects that nevertheless exist; they explain the world around us. Algebra has been helpful for all civilizations to understand what we see and experience. In modern times, mathematics can also describe the things we do not see!

## The mathematics behind fractal geometry

Mandelbrot dealt with iterative functions. It is straightforward mathematics:

F(z)=z+1 (every time we evaluate function (f), we will use it as a parameter and re-evaluate it). For instance: f(0)=0+1=1; f(1)=1+1=2; f(2)=2+1=3, etc. It is easy to see a pattern by increasing by one each time. We can use f(z)=z+2 and get other results, but it is still a pattern, or we can add a formula f(z)=z+c, where c is a constant. The mathematician took this one step forward to create Mandelbrot’s Equation.

He used the formula f(z)=z²+c. Here, c is a complex constant, and the values of c determine whether the sequence will diverge to infinity or remain bounded. The dynamics described are explicitly tied to the complex plane, explaining how different values of c affect the behavior of the sequence. Thus, the repeated iterative function will ultimately reveal the behavior of z. This is essential since the nature of iterative function where the output of one iteration becomes the input for the next is central to generating the fractal patterns observed in the Mandelbrot set.

Consider the function f(z) = z² + c with different values of c. For example, if c = 1 , we start with Z₀ = 0 and get the sequence: f(0) = 0² + 1 = 1 , f(1) = 1² + 1 = 2 , f(2) = 2² + 1 = 5 , continuing with f(5) = 5² + 1 = 26. This sequence demonstrates rapid growth, likely diverging to infinity. Alternatively, with c = -2 , starting again at Z₀= 0 , the sequence becomes f(0) = 0² – 2 = -2 , f(-2) = (-2)² – 2 = 2, and repeating with f(2) = 2² – 2 = 2 , showing a repetitive cycle between -2 and 2, indicating bounded behavior. If the absolute value of 𝑧 i.e. |z| remains finite (specifically, it does not exceed 2) over an infinite number of iterations, then c is considered part of the Mandelbrot set. If |z| exceeds 2, the sequence diverges, indicating that c is not part of the Mandelbrot set.

Mandelbrot discovered that for the real part of c, values need to be between about -2 and 1/4 for z to potentially remain bounded. This range is crucial in determining which complex numbers are part of the Mandelbrot set, as values outside this range generally lead to unbounded sequences that diverge to infinity.

To get a sense of it, Mandelbrot introduced imaginary numbers (represented by i). The Mandelbrot set involves the iteration of complex numbers (which includes both real and imaginary parts). where ( c ) is a complex number like ( c = x + yi ) (with x and y being real numbers), helps determine the set’s boundary. This process tests whether, under iteration, the values of z remain bounded or diverge to infinity. When we want to combine them visually, we get the Mandelbrot set on a complex plane of all c’s that do not escape to infinity. In studying the Mandelbrot set, the range includes imaginary parts ranging from about (-1.12i) to (1.12i) and real parts from about (-2) to (0.47). This wide range allows us to observe the complete structure of the Mandelbrot set, revealing its characteristic fractal boundary.

Two things happen when we put numbers into the Mandelbrot’s Equation. Two potential behaviors occur when iterating numbers in the Mandelbrot’s equation: the magnitude of the number may either increase indefinitely, indicating that it diverges to infinity, or it may remain within a bounded region, never exceeding a certain threshold. However, remaining bounded does not necessarily mean that the number shrinks to zero. Depending upon what happens, the computer draws a boundary line. On the computer screen, the pixel either moves and ultimately disappears from view or it moves toward the fixed point on the screen. We color that point black. The colors may be completely arbitrary, but they are not totally neglectable. They define the different areas of calculations, and the result is the absolute beauty of the Mandelbrot set.

## Mandelbrot set and the Fractal Universe

Mandelbrot’s set is one of the most beautiful and remarkable discoveries in mathematics, discovered only in 1980 on a computer. It is unique, although it reminds us of the many forms and shapes in the visible world. It has infinite precision; it exists, but it is not tangible. Some call it the “thumbprint of God.” As we go deeper into the image of the Mandelbrot set, new images and patterns emerge, and it goes on and on…to infinity. Although infinitely complex, it is based on elementary mathematics (as seen above). But to make a complete set, one must multiply billions of times. It confirms that we see incomprehensible and complex things around us that straightforward mathematical formulas can explain.

The Mandelbrot set contains another simple equation: Z=z²+c, where numbers or coordinates are on the abovementioned plane. The numbers flow in both directions, constantly feeding back on themselves (iteration). The output of one operation becomes an input of another operation, and so on. That is why fractal geometry is crucial in solving Chaos Theory. One fascinating thing about the Mandelbrot set is the internal consistency of the object. It all hangs together, with perfect replicas of the whole set embedded inside. It goes on to infinity once again.

When we look deeper into the outer bits of the Mandelbrot set, at points of hair, we see that they split into two others and so on infinitely. They go in random directions quite abruptly. This mathematical entity is called the fractal. The Mandelbrot set is the most famous. It is any geometrical structure with detail on all scales of magnifications. As deep into an image we can go, new structures appear. Mandelbrot invented the name because it denotes the feeling of fragmented and fractional irregularity. It helped scientists to gain a new look at nature. They do not have any means to describe the natural forms – no straight edges, circles, or triangles. But there is a continuous pattern.

Fractals are the shapes we are entirely used to in the subconscious realm. When we look at a rather small map, we can see the coast of Portugal and say that it is pretty straight. But on a larger map, we see more details, and the coastline basically disappears. Nature does not offer smooth, continuous objects as we imagine, but fractals. We get very realistic forms when we use them to generate images on a computer. It is the same with natural things.

Biologists claim that living creatures are complicated structures produced from simple rules with a firm pattern and many details. Everything can be described in fractals, often using bits of the image we see. We can explain or even build the structures we see in nature with fractal geometry formulas. A difficulty lies in the infinite variety of forms. They all look pretty similar but diverge in terms of details. Our subconscious works in an incredible way even when we are awake.

The brain as a physical entity is also describable through the fractals. We see patterns when we close our eyes and press our fingers slightly against our eyelids. Sometimes, they echo the shapes of the Mandelbrot set. Apparently, when some illegal substances are used, one experiences visual hallucinations strikingly similar to some of the patterns of the Mandelbrot set. Obviously, these patterns resonate with the mind.

Religions are full of fractal items. In Buddhism, mandalas are symbols of fractal patterns, as is Islamic calligraphy and the shapes of Islamic tile images. In Christianity, some stained-glass windows (rose) resemble a fractal shape. Given their sacred value centuries before the Mandelbrot set was even discovered, there is a strong link between the fractals and human religiosity. These are the primordial structures we all share, constituting a background of awareness. The mind clearly finds a resonance in the Mandelbrot set.

Galaxies are fractals, and so are atoms. As the Mandelbrot set goes on infinitely, the question is: is there a limit anywhere in the universe. Cosmologists believe it is the Planck length, a million billion billion times smaller than an inch. It means there is a limit to how complex the universe can be. Nothing exists below the Planck length, but cosmologists cannot confirm it. Fractal geometry is now thoroughly embedded in modern science to describe things, and new devices based on the findings of fractal geometry that will emerge in the following centuries. The idea of The Simulation** **and Matrix arises from the use of fractal geometry. We can now simulate things in a computer with the possibility of a formula and an entity of infinite resolution.

Patterns take us to the question of determination. Newtonian science viewed the universe as a clockwork. If we know the formulas, we can predict everything because it is predetermined. Two challenges emerged, however. One is quantum mechanics, which says that there is irreducible chance built into the very fabric of the universe. The Mandelbrot set points to the reality of a predetermined Newtonian world, but in practice, we may be unable to predict the future. It can be deterministic in principle, but we cannot detect it in practice. This is how God created a system. Everything is predetermined, but we have the illusion of free will to think about the future because we cannot detect it. God does not play dice but gives us a life where we believe we play with dice.

## Fractals as designs pointing to God

Fractal patterns in nature point to determined order and complexity derived from divine intelligence. Many religions focus on the aesthetics and the beauty of nature as a sign of divine intervention. The discovery of fractals points to the infinite complexity of God, although within a finite created realm (at least if we consider Planck’s length). These patterns can be seen as God’s design or principles of creation: “For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made” (Romans 1:20).

Thus, the Mandelbrot set was called the “Thumbprint of God”; it has been seen for centuries in Christian art without knowing the internal logic of such patterns. Dwelling deeper into fractal geometry helps us grow spiritually since it leads to the infinite complexity of God’s mind as found in animal coloration, patterns on skins and shells, blood and pulmonary vessels (also connected to river systems), coastlines, craters, trees (and their branching), snowflakes, DNA, mountain ranges, and lightning bolts that are basically everywhere: “The heavens declare the glory of God, and the sky above proclaims his handiwork” (Psalm 19:1). These are mathematical models that allow us to model infinity.

Planck’s length, the smallest possible point in the fractal geometry, is the moment of creation. If we consult the Bible, we read: “Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light” (Genesis 1:2-3). The movement happened before there was light, albeit motion is impossible in the void, according to physics. Once the Holy Spirit created the point in space, it could move to the edge of its awareness and expand consciousness, thus creating it. Despite the chaos, the Spirit of God was present in a superior way and continues to build our world and our personal lives even when we only see trouble and unsolved issues: “He saved us through the washing of rebirth and renewal by the Holy Spirit, whom he poured out on us generously through Jesus Christ our Savior” (Titus 3:5-6).

The argument from design has been part of Christian apologetics for centuries. Looking at the stars and the natural world, we ask how all this exists without God. In the 19^{th} century, the answer was found in science. After a period of the atheistic or agnostic scientific explanation of the world, we come full circle to new scientific discoveries pointing to the Creator. God’s light breaches the darkness since it discovers and corrects things. It is a path through life revealed to us as Christ’s light: “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).

Fractal geometry can be approached in many ways. For some Christian theologians, looking at the fractals with faith is the only way these beautiful aspects of creation become evidence of God’s work and its infinite development. It can be interpreted as the Kingdom of God, which never stops rising, as Jesus explains: “This is what the kingdom of God is like. A man scatters seed on the ground. Night and day, whether he sleeps or gets up, the seed sprouts and grows, though he does not know how. All by itself the soil produces grain—first the stalk, then the head, then the full kernel in the head” (Mark 4:26-28).

This answer does not amuse us. The universe would be meaningless and purposeless if everything hung on chance. Instead, there should be a clear connection between fractal geometry and divine creation. One of the leading issues in cosmology is the vast number of initial adjustments required for a universe like ours to work. Theology has a standing answer: it is designed as such from the beginning by God, who created everything to function** **well. From the beginning, God gave humanity the roof over their heads: “The Lord wraps himself in light as with a garment; he stretches out the heavens like a tent” (Psalm 104:2). What is meant for the world, in general, can also be used as an encouragement for our personal world. In this relation between the big and the small, we can recognize the spiritual segment of the fractal geometry.

The patterns of such design are now being discovered in the fractals and other fine-tuning mechanisms of our cosmos, where everything seems constant. The same anywhere we look: “And see that you make them after the pattern for them, which is being shown you on the mountain” (Exodus 25:40). Another question astrophysicists want to avoid is why is there a universe at all, bringing us to the issue of causation. Instead, they dwell on the multiverse theory, which is not scientific but mere speculation and wishful thinking.

God relates to the world so that we can relate to God. He does it in many simple ways and images, which we now find in fractals: “My hand laid the foundation of the earth, and my right hand spread out the heavens; when I call to them, they stand forth together” (Isaiah 48:13). Some standard images bear a much more profound significance. One is light. God cannot be light without actually enlightening the world. Another is a blessing. God blesses the world (in Hebrew, Barak), but people also bless God (using the same Hebrew word in the Bible). God gives unreservedly. Our task is to receive, but by receiving correctly, we also give back to God through recognition and thankfulness.

There is no worldly reality where God is not present in a saturated way that fills everything. He is not a God who sits and watches us, nor is He someone just doing a job for us. He intimately and imminently connects to the creation: “The God who made the world and everything in it is the Lord of heaven and earth and does not live in temples built by human hands. And he is not served by human hands, as if he needed anything. Rather, he himself gives everyone life and breath and everything else. From one man he made all the nations, that they should inhabit the whole earth, and he marked out their appointed times in history and the boundaries of their lands. God did this so that they would seek him and perhaps reach out for and find him, although he is not far from any one of us. For in him we live and move and have our being. As some of your own poets have said, “We are his offspring” (Acts 17:24-28).

As a Danish theologian, Niels Henrik Gregersen, states, “If God is not to be traced in the details of scientific exploration of nature, God cannot be present in the tissues and texture of the world.” God’s constituting of the fundamental laws of nature is a core tenet in the inherited notion of design. Thus, the idea that we need to find proof of design outside the naturalistic explanations may prove very wrong. Precisely, the findings we have quickly point to God’s design, and fractals are such a thing. Namely, if scientists can explain fractal geometry (there are certainly abilities and hypotheses), it does not mean that we cannot find God in a particular design. It is even more plausible as such: “The more creative nature is, the more benevolent and the more beautiful is the grandeur of God’s creativity,” says Gregersen when pointing to the descriptions of natural beauty in the Bible.

## Fractal geometry as sacred geometry

Self-similarity in scale, a cornerstone of fractal geometry, is a parable of reality, just as Jesus was telling parables to His disciples to show what the Kingdom of God is like. The two kinds of parables correspond. The art of telling parables is an ancient human art that works well to convey a more profound message. On the other hand, fractal beauty can be seen only with the help of a computer. In modern times, we can make fractal Christian art in a new manner but it is still based on metaphysics, which involves sacred geometry and fractal mathematics.

Sacred geometry is another ancient tradition in noted architectural wonders, such as the Cathedral of Milan and many other sacred buildings. The geometry is sacred because it copies God’s creative work: “When he established the heavens, I was there; when he drew a circle on the face of the deep” (Proverbs 8:27). It relies on the objective shapes in nature that allow us to understand creation, such as honeycombs, seashells, pine cones, etc. God’s natural order has been revealed to humankind, and people have built on that order. The Bible gives us many accounts of creating sacred spaces, such as the Tabernacle or the Temple of Solomon. Sacred space is related to sacred geometry, which is used to find balance and sacred ratios.

Following the activities of the Holy Spirit through the cycles of creation, the movement of its awareness forms two cycles called the Vesica Piscis:

Expanding to the third circle forms the shape of the Holy Trinity:

After six days of creation, a new pattern emerged called the Seed of Life because it contains all the necessary preconditions for life when followed in Genesis 1:

The second dimension of circles creates a three-dimensional shape. This cluster of spheres was known in the ancient times as the Egg of Life:

This structure exists in everything around us. When the third rotation occurs, the nineteen circles emerge into the Flower of Life:

This shape has been found in all human civilizations. It was thought that information hidden in the Flower of Life was so important and sacred that our ancient ancestors had to keep it secret. When the Flower of Life extends, and all the circles are completed, the Fruit of Life is revealed:

In ancient traditions, it was the feminine shape. Curved lines represent formlessness and emotion. Once we add masculine energy or lines, the formless begins to take the shape of Metatron’s Cube, containing the fabric of reality. Out of this shape, we get Platonic solids or objects of the same size with edges of the same length and angles of the same degree. There are five Platonic solids: cube, tetrahedron, octahedron, dodecahedron, and icosahedron. The ancient mathematicians studied these shapes and forms. Interestingly, every element in the periodic table has a shape similar to one of these Platonic solids. It all starts with the Holy Spirit.

## Fractal Geometry and Simulation Creationism

An explanation of fractal geometry’s connection to the biblical revelation is possible through Simulation Creationism. Fractal geometry tells us that shapes form our world in a self-similarity category, where they remain the same at every level, from the maximized whole to the minutest details. It contains a plausible idea that everything is generated through a complex simulation, i.e, a product of God’s Singularity.

Scientists working with fractal geometry use computer algorithms to create fractal patterns. The Mandelbrot Set itself was discovered by using a computer. The level of mathematical and computing operations is on such a scale that humans would need thousands of years to calculate it. Thus, fractal patterns in nature and their replication through sacred geometry in the human realm resemble simulating processes. They correspond to underlying computational and simulation processes that contain the basic rules from which complexity emerges.

If everything is fractal, then our minds may be fractal as well. We may have evolved to be skilled discoverers of the fractals that surround us in nature. God gave us a genuine intuition and the possibility of understanding what is happening in The Simulation and the simulation process itself. We may even subconsciously be drawn into the patterns. As free will is basically an illusion, we are predetermined to focus on fractals insofar as they show us the truth of Simulation Creationism. In essence, fractal geometry strongly confirms a Simulation process**.** We see it everywhere in the universe, from the shapes of galaxies to atoms. This means an out-of-universe creator of such a Simulation corresponds to the Christian God described in Simulation Creationism. Using fractals and basic rules, the Holy Spirit works through its energy to simulate what we perceive as reality. Simulation Creationism, coupled with sound Christian theology, points to fractal geometry as a solid argument for its truth.