Chapter 125 Chaotic Fractals
"Brother, play with me!" the little boy pleaded, having just returned from Alice's lab.
"Can we talk about it tonight? I still have things to take care of."
"That's precisely why I need to keep you occupied!"
Conan instinctively felt that Osiris's insane plan was about to reach a crucial juncture. Although he didn't know the specific details yet, adhering to the principle of delaying as much as possible, he absolutely couldn't let Osiris succeed.
"No, brother promised to tell me the story of crystal yesterday."
"Sweetie, go wait for me in the library, okay? I'll play with you again tonight."
Conan went to the library dejectedly, sighing, "I just wish I had a tranquilizer dart! Otherwise, I would have taken care of him long ago!"
The young detective arrived at the central holographic projection screen, only to find he didn't have permission to open it. He could only glance at the extensive collection of books, thinking: Why not take this opportunity to brush up on my biology knowledge?
Conan immersed himself in a vast sea of documents, accompanied only by a solitary lamp, reading voraciously amidst a sea of obscure and difficult text. Yet, he persevered, bit by bit, using his brain, honed over 18 years, to search for the theoretical basis of the crystal network.
As Conan was engrossed in reading "On the Origin of Species," Osiris finally appeared. Seeing the book in Conan's hands, Osiris couldn't help but laugh and asked, "Conan, how much did you know about evolution before?"
"I know that humans evolved from monkeys."
"That's good! It's great that you can accept the idea of evolution."
Conan looked up at Osiris in disbelief, making sure the other man wasn't being sarcastic, and said, "I thought this was common sense."
"Even today, not everyone is willing to accept this theory. At the very least, creationists don't buy into it; they firmly believe that humanity was created on the sixth day."
"Brother, even though I agree with the idea of evolution, crystal networks are still so confusing to me..."
“Hmm, accepting this concept all at once is quite a leap. Let me start with a simpler example.” Osiris opened the holographic projection screen, displaying a creature that Conan recognized all too well. “It all started with this butterfly. See the pattern on its wings?”
"Yes, it's very beautiful." It's extremely similar to the one Osiris gave to Conan.
"Conan, can you explain this?"
"Explain what?" Conan was completely confused.
How are these beautiful patterns generated?
"Huh? This is etched into the butterfly's DNA. By controlling the distribution of pigments, patterns appear on the wings."
"That's right, DNA! But the fact that all plants and animals on Earth are governed by DNA doesn't quite get the truth. What if I wanted a more elegant, concise, and straightforward explanation? For example, could I use a mathematical formula to describe this geometric shape?"
"Numbers, mathematics?" Conan was puzzled. Compared to the usual circles and squares, the patterns on the butterfly wings were complex and disordered. What kind of mathematics was this?
“It’s not just butterflies; the patterns on cows, cheetahs, zebras, and tropical fish can also be described using mathematical models. These are called ‘Turing patterns,’” O’Sirius explained. “Simply put, you can think of each organism as a system. In this system, catalysts and inhibitors act like two opposing forces controlling pigment production. When the two are evenly matched, the system reaches a stable state, forming a symmetrical pattern. However, this system is very easily disturbed; even a slight imbalance can produce a strong diffusion reaction. Through self-organization, the system gradually develops certain features, eventually forming these complex and beautiful patterns.”
"Hmm, uh, that's amazing..." Conan stared wide-eyed, trying to understand Osiris's words. He belatedly asked, "Eh? Turing Bantu? Alan Turing?"
In Conan's memory, Turing's major contributions that have made him famous throughout history are threefold: first, the infinite paper tape model Turing machine, which laid the mathematical foundation for modern computers; second, the cracking of the Engelma cipher machine; and third, the famous Turing test, which is the basis for judging artificial intelligence.
"I never knew Turing studied biology?!"
“That’s right, it was Turing who started this game: explaining the mysteries of life with mathematics. Any form of life in the universe can be described as a mathematical process,” Osiris asserted.
Conan was shocked; his worldview was completely shattered.
"So, crystallography is essentially a mathematical problem?"
"Why did I spend so much time in the biology section's library?!"
Seeing Conan's incredulous expression, Osiris tapped the control panel a few times, and a dazzling array of mysterious images appeared on the projection screen: "It's a pity that Turing died too young and couldn't continue his research. Later generations pioneered a new field: fractal geometry. Do you see these beautiful patterns? These are all fractals. Although they all look irregular at first glance, careful observation reveals that every magnified part of the pattern reflects the whole; this is called self-similarity."
"Is it like a crystal network that maps out the entire universe?"
“Yes, that is my intention. All the answers to the universe reside within us; this is the ultimate truth,” Osiris said proudly. “When we become one with the universe, the limitations of spacetime cease to exist. Just think how pathetic humans are, who consider themselves at the top of the food chain! Even though we have intelligent brains, the constraints of our cognition confine us to a narrow scope. We cannot listen to and understand the voices of others, nor can we truly perceive the grandeur and beauty of the world. The time we can perceive is no more than a second, no more than a few decades, and the space we can perceive is no more than the height of Mount Fuji. The distance around the Earth is difficult for many to grasp.”
"With the crystal network, will everyone be able to read minds and hear what others are thinking?"
"Strictly speaking, the heart is a product of DNA biological evolution, and by then there may no longer be organs like the heart or brain. Even concepts like species differences and reproductive isolation will be redefined. Because once the foundation of life is changed, the edifice above will naturally be renovated and reconstructed. However, I am sure that organisms will understand each other better, and in turn, understand the whole world."
"Has my brother already mastered this amazing ability?"
Osiris chuckled: "Conan, of course I don't have any crystals in my body. But mind reading isn't exactly a mysterious thing, is it?"
"Huh?"
"Our thoughts and ideas are nothing more than the firing of neurons in the brain," Osiris replied calmly, giving Conan a meaningful look.
"You knew I was lying to you from the very beginning, didn't you?"
It's all just a charade, and both sides know it's a deception. In the interactions between con artists, the only genuine thing is the deception itself.
Conan's motivation for continuing to lie is to uncover the truth, so what is Osiris after? What exactly makes him willingly wear one mask after another, tirelessly deceiving the masses?
They got into character instantly; both are experienced actors.
"Brother, how can DNA be replaced by a crystal network?"
“Let’s start with this butterfly!” O’Siris asked. “You should be familiar with the story, right? When a butterfly from South America flapped its wings…”
“It will trigger a tornado in Texas,” Conan continued. “The butterfly effect.”
"Yes, this theory has a wide influence and has almost become synonymous with it. In fact, the butterfly effect also describes a mathematical problem: chaos theory."
Conan blinked, as if he didn't understand.
Osiris patiently explained, “Like fractals, chaos theory also studies nonlinear dynamic systems. Here, we consider a local climate model as a system, and butterflies, air currents, clouds, and so on are all part of the system. When a butterfly flaps its wings, it triggers an initial disturbance, which then triggers a series of chain reactions. Quantitative changes lead to qualitative changes, eventually causing the entire system to reach a new state: the formation of a tornado.”
"Is this something that can be explained by mathematics?"
Osiris smiled slightly: "It seems your understanding of mathematical physics is still at the Gauss and Newton stage. But mathematics is not just 1+1=2 or ruler and compass constructions, and physics is not just a small slider doing uniformly accelerated linear motion. You know what a simple pendulum is, right?"
Conan thought to himself: Of course, the impression of the one in Swan Castle is extremely deep.
A simple pendulum model was displayed on the holographic projection screen. Osiris pointed to it and said, "For an ideal simple pendulum model, its position, velocity, and angular momentum at every moment can be calculated. However, what do you think would happen if we tied another ball to the bottom of the first ball, turning the double pendulum into a simple pendulum?"
“They’ll both move in circles together,” Conan said, gesturing. However, when the double pendulum model on the screen started moving, he was surprised to find that it was far from what he had imagined. Compared to the simple and regular periodic motion of a single pendulum, the motion pattern of the double pendulum was truly baffling. “Why are they becoming…so strange?”
“This is a chaotic system,” Osiris said, pointing to a point on the screen. “If you just stare at this ball, it swings around here and there, sometimes high and sometimes low. You can’t see any pattern at all, right? Isn’t it incredible? How can such a simple model, two balls, two ropes, and a fixed point, achieve such complex motion? Even more amazing is what happens if I slightly change the initial angle?”
Conan shook his head blankly.
Osiris's smile deepened: "Actually, I don't know the answer either. Let's find out together!"
What happened next shocked Conan even more. When the two pendulum systems were compared side by side, the differences became even more obvious: at first, their trajectories were very similar, but as time went on, the gap widened and eventually they went their separate ways.
Osiris enthusiastically exclaimed, "The beauty of chaos lies in the fact that it exhibits uncertain behavior in a deterministic system. It is neither repeatable nor predictable; the entire system appears chaotic, completely random, and without any rules, which is why it is called chaos. However, it still falls under the category of dynamics, except that nonlinear systems are no longer under Newton's jurisdiction."
"Chaotic systems are extremely sensitive to initial conditions, just like the timing of a butterfly flapping its wings or the initial state in a pendulum model. A tiny change can have a huge impact on the entire system."
"On the other hand, chaotic systems also exhibit fractal characteristics, namely self-similarity. Do you see the superimposed trajectories of the two pendulums? If you zoom in on a local area, doesn't it look very similar to the whole?"
"The universe is the largest system that mankind has ever observed. Everything in it originated from a singularity, and the Big Bang gave birth to all the splendor and glory. Conan, this is the ultimate mystery of the universe. I want to answer this question and find the only truth."
In a daze, Conan felt the boundaries of his imagination being broken, his entire being merging with the vast sky. Everything was mathematics, everything was a variable! As a DNA-based being, he was part of the most complex ecosystem in the entire universe, and his every move affected this system. And the feedback changes of this system were constantly affecting his nerves.
The butterfly effect—what a beautiful phrase! From a single beginning, it can give rise to this colorful and ever-changing world.
Shinichi, a 15-year-old junior high school student at the time, noticed his missing junior high school classmate Yuuki and followed the clues deeper and deeper, never expecting that this detective game would lead him here.
So, what kind of future will the butterfly that Osiris gave him lead humanity to?
The little detective, who was swimming in the vast universe, realized a serious problem and suddenly came to his senses: "Brother, you just said that the chaotic system is unpredictable. So how do you know what initial conditions to set to make the crystal network replace DNA?"
According to Osiris's wild idea, the Crystal Network Project is not a simple biological "modification", but a social experiment. Can human resistance and predation by other species really be explained by mathematics?
Osiris nodded in satisfaction: "That's an excellent question! In fact, I've been working on solving this problem for years. Although chaotic systems cannot accurately predict future evolution, they still have local predictive power. Simply put, analytical solutions are unavailable, but numerical solutions can be calculated. However, when the modeling object is the entire Earth, the computational difficulty is quite complex."
"Brother figured it out?!"
"Haha, how could I be so capable on my own? It was a supercomputer that helped me complete this task. Through tens of thousands of simulations, I calculated the structure of the crystal network. However, the initial conditions haven't been fully tested yet. This is an extremely crucial point, and we must be careful, otherwise, we might accidentally cause a disaster..."
"So it's still in the computer simulation stage and hasn't been put into practice yet!"
This was the best news Conan had heard in all these days, and he couldn't help but breathe a sigh of relief.
"Hey, big brother, I want to see your simulation game!"
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