[Knowledge Transfer] The Mandelbrot Collection - "Fingerprint of God"

Human beings always have various myths about the universe. Throughout the ages, countless wise men have meditated on the deep night sky, hoping to find answers from it. From asking how human beings were born to asking how the universe was born, they are constantly exploring the unknown.

In this process, many wise men have also "doubted life". For example, Einstein muttered to himself in his later years, thinking that everything in the universe was "arranged" .

So, is the universe really designed ? What is the magical pattern "God's fingerprint" discovered by scientists ?

man looking up at the starry sky

What is "God's Fingerprint"?

What does God look like in your imagination? I'm afraid most people will first think of an old man with a white beard. Although we have no chance to see God's true face in this life, after all, we are not religious, but we can take a look at what God's fingerprints look like.

The so-called fingerprint of God refers to the Mandelbrot set. Judging from its shape, it seems to be just an ordinary symmetrical figure , and there is nothing special about it. But if we zoom in on this graph , you will find that the original details have super high self-similarity with the whole.

Mandelbrot set

 Essentially, this is an iterative formula in which the variables are all complex numbers. So when you perform substitution calculations according to this formula, the local graphics can show similarities with the whole , and this similarity is often concentrated in the subtleties, which can only be discovered by careful observation.

The Mandelbrot set zoomed in

 The person who discovered the fingerprint of God was Benoit Mandelbrot , who not only created this peculiar figure, but also the founder of fractal theory .

As a mathematician, he is very interested in some fragmented things in nature, and under long-term observation, he actually discovered the hidden laws in these fragments.

Benoit Mandelbrot

 In 1973, Mandelbrot first proposed the idea of ​​fractal geometry, which later became a new branch of modern mathematics.

And fractal geometry is actually all around us. For example, the broken coastline you see and the cauliflower used as ingredients all imply fractal. To put it further, the distribution of the cortex and capillaries of the human brain is actually fractal.

The famous American physicist Wheeler even said directly: "In the future, whoever is not familiar with fractals cannot be called a cultural person in science."

What is fractal geometry 

Therefore, fractals are essentially all things in nature, which seem to have nothing to do with each other, but actually have similarities in subtleties.

For example, the intersecting and staggered blood vessels in your wrist are as intricate as the veins of a river , as are the branches on a tree , and even have similarities with the Internet you use now . It should be noted that what is said here is not exactly the same , but "similar".

Presumably, everyone has already understood why the seemingly ordinary Mandelbrot set is called "God's fingerprint", because fractals are like the password lock for human beings to solve all complex puzzles , telling you whether No matter how large and complex the universe is, it will eventually show similarities with the capillaries in your body.

Intricate capillaries 

Because of this, many people began to doubt the authenticity of the entire universe , thinking that the universe may have been designed . After all, if it came from the same program, it would not be surprising to show similarities.

The universe was designed?

Many people may think that they do not need to worry about whether there is a creator in the universe after earning thousands of dollars. But in fact, exploring the unknown and curiosity are the talents that everyone is born with, so why not think about the possibilities of the universe in your spare time occasionally?

human beings are naturally curious

If the Mandelbrot set led people to realize the natural "law" of all things , then the coincidence of the earth and life has deepened this doubt. You know, if there are laws in the universe, does that mean there is a person who has designed laws?

We often attribute the birth of human beings to the word luck. But in fact, if you think about this probability carefully , you will find that our luck does not seem to be "natural", but man-made. First of all, judging from the results of the current exploration of other planets in the solar system, except for the life on the earth, the universe is lonely everywhere, so the earth and human beings seem too "obtrusive".

different earth 

Secondly, when we observe the distance between the earth and the sun , we will also find that we are in a just right position. After all, we are too close and very hot, and we are too far away and cannot receive enough heat, so that we become cold and silent. .

And everyone thinks about it, if we raise a very delicate flower , will we keep it exposed to the sun or never let it bask in the sun? And when the flowers are replaced with the earth, everything makes sense.

The Earth's Position Is Just Right 

Finally, human beings live in the universe. The time of civilization may not even count as a microsecond for the universe, but we can know and understand the universe in various ways. In every era, there seems to be a god-man who communicates with the "creator" and finds and presents more laws of the universe to us, allowing the development of human civilization to reach another peak.

The "God Men" in History 

In summary, coupled with fractal theory, the "design traces" of the universe are indeed somewhat obvious . However, when there is no definite conclusion, we can't take it as the truth, because although everyone will complain about why "Nuwa" doesn't pinch herself better in daily life, it is difficult to accept that we are really designed. from.

On the one hand, we are afraid of the Creator who designed us , and on the other hand, we feel that since everything has been designed, our life will go according to the established procedures. The ups and downs of this life have already been arranged at the time of birth , so why bother to fight against fate?

cosmic creator 

Therefore, human beings are more willing to believe that the universe was created through the big bang, which is an accidental or natural process and has nothing to do with the so-called creator.

While more scientists believe in the power of nature, they also point out that the universe is indeed chaotic, and countless random results are produced in the chaos . Whether it is the solar system or the earth, or any flower and plant on the human beings and the earth, they are all born from chaos.

The Big Bang 

The world is the result of "chaos"

The so-called Chaos Theory was discovered by Edward Lorenz , a meteorologist and mathematician who, while observing the weather, discovered many unusual things, among them Chaos Theory.

The most typical representative of chaos theory is the well-known "butterfly effect". This vibrating butterfly wing is actually an image after a computer program simulates climate change.

It is reported that "chaos theory" is considered to be: "has had a profound impact on basic science, and after Newton, it has brought about earth-shaking changes in human's view of nature."

The Butterfly Effect

It is worth mentioning that many people have misunderstood the term chaos , thinking that chaos is something complicated and unexplainable. But in fact, chaos refers to the fact that even in a precisely operating system, using a simple algorithm will still produce unpredictable results, so chaos itself represents the unknown .

Determinism and Chaos Theory

 And among these unknowns, the same law can be hidden. Therefore, in essence , the world we see is indeed composed of accidents under the algorithm, but these accidents are not irrelevant, but are governed by the simplest laws. A thing, no matter how messy it looks, actually comes from simple rules.

It is precisely because of this that generations of physicists will continue to search for the "most basic law" in the universe . After all, the complex universe is actually born in this simple law. At this time, many people may have thought of the expression that Laozi mentioned in the "Tao Te Ching", "Tao begets one, one begets two, two begets three, and three begets all things". The profound meaning of this sentence is exactly the same as what we said today. Things are connected.

Everything is related to Tao

 Chaos tells us that complex things arise from simple rules. Fractals tell us that self-similarity can always show you the same pattern in a large scale on a smaller scale.

Therefore, the "thousands of stars" in your eyes may have a close relationship with your eyes. The more details you see, the closer you will be to the truth of the universe. But if the truth is that the universe is designed, will you have the courage to accept this reality?

Diverse fractal patterns in nature 

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Draw the Mandelbrot set based on Python_Envoy Daya's blog-CSDN blog Recently, I have been a little confused about fractal geometry. I saw the "God's Fingerprint" Mandelbrot set and wanted to implement it with Python. The source code is very simple and less than 20 lines. import matplotlib.pyplot as pltimport numpydef mb(x,y): C = complex(x,y) Z = 0 for i in range(100): Z = Z*Z +C if abs(Z)>2: return False return Truefor x https://blog.csdn.net/m0_49963403/article/details/123772115 Use python library numpy to draw Mandelbrot sets (code + analysis) - Know how to use numpy to draw Mandelbrot sets in this article . What is the Mandelbrot set? Simply put, it is the following formula: Z_{n+1}=(Z_{n})^2+C Zn is a complex number, n is a natural number, increasing from 0, and C is a complex number. Z0=0. On a plane, the center point is 0, and different points correspond to different… https://zhuanlan.zhihu.com/p/603366875

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Origin blog.csdn.net/WakingStone/article/details/129467145