“So you went around a second time?”

On the walkie-talkie communication channel, Xing Hechou was perplexed. “Nothing happened?”

“No, not going around a second time.”

Wang Buliuxing, who was in the same team as him, pondered for a moment, his eyes lighting up. “To be precise, looking down from a high altitude, they walked through a total of seven rooms, circling a tiny figure-eight symbol.

“Furthermore, the conditions encountered during the detour also changed—the first time they arrived at the initial room, the candles automatically lit from an extinguished state, and the back door opened automatically.

“And the second time they arrived at the initial room, the door on the right side,

“Or the rear door from the initial angle, was also open.

“However, the candles were automatically extinguished,

“Indicating that after they left the initial room again, the candles in the room were extinguished for some reason.”

“Candles extinguished?”

Xing Hechou frowned and asked, “The changes in the grotto also started with the candles being extinguished in the room.

“Does this represent something?”

“We don’t know yet.”

Li Ang said with interest in the communication channel, “But if I’m not mistaken, we’ll soon be able to discover the pattern…”

With that, he threw the walkie-talkie to Hohenheim, pushed open the back door of the initial room himself, and made his ninth move, entering the (0, -1) room.

The furnishings in the room had not changed, but the candle was initially extinguished.

After the door opened, the candle slowly lit automatically, and the door on the right could be pushed open.

Is the cycle broken?

Li Ang strode into the room. The previous opening order was a figure-eight symbol, but now a new room has been opened up.

He pushed open the door on the right,

Making his tenth move, entering the (-1, -1) room, the candle went from bright to dim, and the door on the left opened.

Eleventh move, entering the (-1, -2) room, the candle went from bright to dim, and the door on the left opened.

Twelfth move, entering the (0, -2) room, the candle went from bright to dim, and the door on the left opened.

Thirteenth move, entering the (0, -1) room, the candle went from bright to dim, and the door on the left opened.

Fourteenth, (-1, -1), candle dimmed to bright, the door on the right opened.

Fifteenth, (-1, 0), candle dimmed to bright, the door on the right opened.

Sixteenth, (0, -1), candle dimmed to bright, the door on the right opened.

Seventeenth, (-1, -1), candle brightened to dim, the door on the left opened.

…

Li Ang moved extremely fast.

At first, he would constantly try to push the four doors in each room, but later, he seemed to know how to walk,

Striding into the room, he unhesitatingly went left or right.

Along the way, the candles in the room either went from bright to dim, or from dim to bright, and the scenery he saw never changed from beginning to end.

For the other players in the team, the atmosphere seemed oppressive and silent.

Step.

Walking, Li Ang suddenly stopped, and the people behind him hurriedly stopped moving to avoid bumping into him.

“There’s no point in continuing like this.”

Li Ang raised his arm, rubbed the beard on his dragon head mask, and said, “I already know the next path.

“(-1, -2), (-2, -2), (-3, -2), (-3, -1)…

“If I’m not mistaken, according to the rules provided by the grotto, we will be trapped here for a very long time.”

“…Do you need support?”

In the communication channel, Xingyun took a deep breath and asked, “Or should we call Michael?”

“Support? No. Only our team is moving now. If you start moving too, the result might be the same.”

Li Ang said lightly, “How about this, to verify it, you guys choose a direction at random in your initial room, push open the door,

“Then walk through the only passable door, and move eight times.”

“Choose a direction at random?”

Xingyun paused upon hearing this. In the grotto maze, it was impossible to detect the orientation, and the east, south, west, and north of each team were chaotic. Choosing a direction was no different from walking randomly.

So, the other teams besides Li Ang’s fifth team chose a direction and moved eight times,

Like Li Ang, they also used the coordinate axis method to record the route of their journey,

And reported it in the communication channel.

The result of the eight moves was that they all walked through seven rooms and drew a figure-eight symbol in place.

“It seems that everyone is the same.”

Li Ang said lightly, “No matter which direction you chose at the beginning, whether it was forward, backward, left, or right, the final result is the same.

“The purpose of the grotto maze is indeed to use rules to trap us here for a long time.”

He paused and explained in the communication channel, “Did you notice the pattern in everyone’s progress?

“The candles in the room light up and go out again, and only one of the four doors in the room can be opened. When someone stays in the same room without moving, others cannot go to the next room.

“These three rules are essentially the same,

“It’s to make us circle around in a fixed area.”

“Circling around?”

Xing Hechou asked, “That’s not right. The first eight moves were to draw a figure-eight in place.

“If the grotto maze wanted us to circle around, it could just limit us to cycling back and forth in these seven rooms.

“There’s no need to open up the new room (-1, -1).

“Or even the subsequent paths of (-1, -2), (-2, -2), (-3, -2), (-3, -1).”

“Old Xing, have you ever raised hamsters?”

Li Ang smiled and said calmly, “Domestic hamsters can survive with a very small space,

“But too narrow a space will make hamsters feel depressed and die quickly, even if they run on the hamster wheel all day long.

“Animals in zoos will also suffer from stress-induced diseases due to the narrow living space, the lack of contact with elements, and insufficient social interaction,

“Crazy self-mutilation, such as anorexia, hitting the cage, etc.

“If you want the creatures in the cage not to feel pain and despair, you naturally have to expand the cage space and make the creatures mistakenly believe that they can get out.

“Of course, you can indeed get out of the grotto maze, but to truly break the cycle, or rather, to start another cycle and get out, I think it will be at the *bu* (step).”

“The *bu* (step)?”

Xing Hechou’s heart skipped a beat, and he said in a deep voice, “So accurate?”

The reason for the change in his tone was not only because the number was too large, but also because Li Ang’s tone was calm and composed, and even more because he knew that,

When Li Ang returned to his frivolous attitude, it meant that this guy already knew the answer.

The other parties in the communication channel also had their eyes light up when they heard Li Ang report the number, and they were thoughtful, as if they understood something.

“That’s right, not 9999, not , not , but .”

Li Ang smiled and said, “(0, 1), (-1, 1), (-1, 0), (0, 0), (0, -1), (1, -1), (1, 0), (0, 0)…

“Every time we move, we can see the state of the candles in the room, which changes because of our actions of pushing open the door,

“Either from dim to bright, or from bright to dim.

“When the candle in the room initially maintains a burning state, when we push open the door and walk in, the candle will go out, and the door on the left will open at the same time.

“When the candle in the room initially maintains an extinguished state, when we push open the door and walk in, the candle will automatically light, and the door on the right will open at the same time.

“In other words, if the candle is initially in a burning state, turn left.

“If the candle is initially in an extinguished state, turn right.

“Along the way, we seem to be moving according to our own will, but in fact, we are completely under the rule restrictions of the grotto maze.

“At first, we thought we were walking symmetrical or repetitive shapes,

“But the more we walk, the more chaotic and irregular the path becomes—because we will walk back to the rooms we walked through before.

“After the nameless Yin wind attacked, all the candles in the rooms were extinguished. Our passage caused the candles in some rooms to light up, and when we passed again, the candles would be extinguished again.

“Leading to the law of opening doors according to the state of the candles in the room,

“Presenting a chaotic and random form.

“However, this chaotic randomness is essentially a pseudo-randomness that limits the rules. No matter where our five teams are located,

“Which direction is chosen,

“If there is no mutual interference, the chaotic pseudo-randomness will stop at around steps, and a cycle with a period of 104 steps will be opened,

“Moving in a fixed direction.

“Like… a bunch of ants.”

Xingyun in the communication channel’s eyes lit up, and subconsciously blurted out, “Langton's ant!”

"That's right."

Li Ang smiled and snapped his fingers, "The grotto maze constructed by Shipi Wang is the cage that binds Langton's ant."

"Langton what?"

Xing Hechou froze for a moment, his brain running rapidly, searching for relevant information.

"Ant."

Li Ang casually explained, "Don't look for it in the database, it has nothing to do with the ant king or the extraordinary elements of the killing field game.

"Langton's ant is a concept proposed by Chris Langton in the mid-1980s. It is a classic example of cellular automata and belongs to the two-dimensional Turing machine.

"The rules are also very simple. Divide a plane into squares of the same size, and fill all the squares with black or white.

"Place an ant in one of the square grids.

"If the ant is in a black grid, it turns 90 degrees to the right, enters the next grid, and changes the grid to a white grid, and moves forward one step;

"If the ant is in a white grid, it turns 90 degrees to the left, enters the next grid, and changes the grid to a black grid, and moves forward one step;

"Just like us, the ant will return to the initial grid at the eighth move,

"And continue to draw chaotic shapes after the eighth move.

"Until about ten thousand steps, it starts to draw a cycle of 104 steps, moving in a fixed direction, like building a highway, extending infinitely.

"The example of Langton's ant is to explain a point,

"That is, extremely simple initial conditions and rule logic can also evolve into seemingly chaotic and disorderly random situations, and this chaos will become regular again after reaching a certain level.

"Becoming full of beauty.

"Just like the barren earth, from the boiling hot soup, bred the first life."

"..."

Xing Hechou digested this passage in his mind and imagined the specific pattern of Langton's ant, "From chaos to order?

"Okay, I understand.

"The ultimate purpose of the grotto maze is to protect Shipi Wang.

"It knows that it cannot trap us to death, but can only delay us to a certain extent, so it sets seemingly simple but actually complex rule logic to trap us in the maze.

"If we play the game according to its rules, then we have to take at least another ten thousand steps to move forward efficiently.

"And this high efficiency is still fixed in a certain direction, and it may not be leading to Shipi Wang."

"That's right."

Li Ang smiled and said, "Considering that the energy of the grotto maze has an upper limit, the entire maze will not extend infinitely.

"That is to say, as long as we take more than ten thousand steps, then it won't be long before we walk out of the maze and return to the outside world,

"But I'm afraid Shipi Wang can't be approached.

"And if we want to change our destiny and continue to explore in the square chessboard, there are only two methods.

"First, use brute force to demolish the walls.

"Second, find a way to meet up, let one team walk in front to change the color of the squares, and when another team arrives, the direction of the final path will also change due to the color of the squares being changed in advance.

"Neither method is very reliable.

"Relying on brute force can demolish a dozen or even dozens of walls or doors, but it will soon exhaust our spiritual energy and put us in a predicament.

"Finding a way to meet up can be done, but that would take too much time. By the time we plan everything, the day lilies will be cold—

"The path of one Langton's ant is easy to draw,

"If multiple Langton's ants are placed together, then the path will become extremely chaotic and disorderly,

"Even because the travel speed of each team is different, it is impossible to start drawing and fall into a dead end.

"No matter from which point of view, this grotto maze is very sophisticated and ingenious, setting only a few rules, it has almost pushed the complexity and chaos to the extreme within a small space.

"From the perspective of an ancient extraordinary person, Shipi Wang is indeed very, very smart."

If he wasn't smart, how could he have thought of the structure of cellular automata that only exists in modern times thousands of years in advance?

Xing Hechou held the walkie-talkie, listening to Li Ang's sincere praise,

He smiled helplessly, but his heart calmed down, with a strange sense of security like Nobita seeing Doraemon taking out magical props from his fourth-dimensional pocket, "Then, Brother Li, how can we get out?"

Dora Ang, tell us the method quickly.

"Get out?"

Li Ang smiled when he heard the words, "No, no, no, if we follow the rules of the grotto maze, we will lose anyway.

"Either we consume too much spiritual energy, or we drag on for too long,

"In any case, it can buy Shipi Wang enough time to recover.

"To crack the maze, we have to start from the initial position of the five teams and find the pattern."

While he was talking, he took out a large piece of metal from the backpack bar, released alchemy at will, transformed the iron block into a blackboard-like rectangle, and on it,

He drew squares and the initial positions of the five teams.

"Through the activity of walking squares before the maze extinguished the candles, we already know the current location of the other teams and their initial positions.

"If we bring the conditions in and eliminate the interference caused by the other teams moving forward at the same time, then we can draw the Langton's ant route map for each team.

"It's nothing more than the upper left, upper right, lower left, and lower right, four directions.

"Five teams, twenty directions,

"The isolated areas on the entire map that are not covered by the route map are the locations where Shipi Wang may exist."