A journey to infinity: Fractals

January 29, 2025 - Reading time: 6 minutes

Imagine walking through a terrain that never repeats itself. It is a labyrinth of intricate patterns - mountains, branches, and valleys interwoven in endless complexity. No matter how much you zoom in, the details persist, evolving infinitely without repetition.

Such a journey compels you to ask two profound questions:

  1. What lies at the end of this road?
  2. Who or what created all of this?

The answer to the first question might appear simple at first glance. If it is proven - and you believe - that this road stretches infinitely, then every conceivable possibility must eventually arise. Shapes of all kinds will emerge along the way. You might even witness the letters of this story materializing before your eyes - or perhaps something resembling your own face. It is only a matter of time.

The second question, however, is far more intriguing: who could have crafted such an infinitely complex terrain? You might conclude that the creator must possess infinite power. This is no random collection of data; you observe intricate structures that never end. The existence of this infinite terrain suggests a creator with boundless skill and creative capacity.

But this is not entirely true.

To generate this infinite pattern, all it takes is a couple of simple mathematical equations and a computer to execute their logic. What you are observing is called a fractal - a mathematical construct. Fractals extend infinitely because they consist of endlessly complex patterns that repeat without end.

The creator of a fractal does not need to wield infinite power or control over every mountain and valley of its vast terrain. Instead, they must possess the wisdom and insight to define the abstract laws that govern its formation. Another important conclusion is that the creator must exist outside the reality of this infinite complexity.

Moreover, for any potential inhabitants of this intricate terrain, their understanding would be inherently limited. Living within the fractal, they might grasp only a tiny portion of its structure. They could never fully comprehend how it was created, as studying a fragment of the fractal cannot reveal the abstract algorithm behind its design.

One question often arises: If God exists, why would He create such a vast universe to host humans on a tiny planet? After all, 99.9999% of the universe is inhospitable to human life. Does this mean that God wasted an immense amount of space and matter if the universe was created solely for us? And why is so much of the universe hostile to human existence?

For some, these questions present a significant challenge in reconciling the concept of God's existence with the nature of the cosmos.

The answer to this question can be found by revisiting our earlier example of fractals. This universe is vast not because it had to be, but because creating such an infinite expanse can be as simple as creating a single galaxy - or even an atom.

The creator of our Universe, if He exists, does not necessarily need infinite power or direct control over every galaxy, star, planet, or atom. By conceiving abstract ideas and establishing fundamental principles through intelligent algorithms, the vast and infinitely complex universe could naturally unfold, much like intricate fractals emerge from simple mathematical rules.

This creator would need wisdom, not control over every small detail of the physical world. His role would be to conceive and design the foundational laws that bring the Universe into existence. The creator might embody the very essence of the world of abstract ideas.

From a religious perspective, the vastness of the universe reflects God's infinite power, but this example with fractals demonstrates that even a simple idea can generate an infinitely complex reality. God does not need to be infinitely powerful in a physical sense - He needs to be infinitely wise.

Such algorithms, capable of generating never-ending ordered complexity, cannot emerge randomly. They require intentional design. Infinite chaos lacks the capacity to produce such algorithms because of a fundamental limitation: the overwhelming tendency for any self-assembled order to collapse into disorder. The infinite potential for self-destruction inherent in chaotic systems makes the spontaneous formation of such ordered structures highly improbable. Remarkably, it is only in recent times that humans have discovered and developed these extraordinary algorithms.

As with fractals, a designer must possess the ability to reason logically and think abstractly when crafting a finite set of mathematical rules capable of generating the infinite complexity of our universe. These rules, the laws of nature, govern how the universe looks and functions from within.

Do we have evidence that fractal-like algorithms form the foundation of our world? Yes, we do. Across vast scales of the Universe, scientists use fractal mathematics to describe the clustering of galaxies. In the microworld, the behavior of elementary particles produced in high-energy collision experiments, such as those conducted at CERN, can also be analyzed using fractal principles.

Since the 1980s, scientists have known that the pure energy released during the annihilation of two accelerated particles, such as an electron and its antiparticle, produces complex, fractal-like patterns of observable particles. These structures made of measurable particles can be described using the same mathematical formalism that characterizes the hierarchical patterns of fractals, like those shown in this video.

There is something else you may learn about the Universe using fractals. A functioning universe cannot create the foundational laws upon which its existence depends. These laws must be intelligently established before the universe can come into being.

Comment

This is a full transcript of the YouTube video https://youtu.be/YPkzpplx0s8?si=bz27xT6FB1WUffW5  created using parts of the Chapter 9.8 of the book "The Designed World of Information: Unveiling the Incredible Realm Beyond", by Dr. Sergei V. Chekanov, 466 pages, ISBN: 9798990642836; Hardcover 9798990642843, eBook ISBN 9798990642829; Book webpage: https://ermislean.org/designed-world/

by S.V.Chekanov

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