Chapter 91 Ants (Four K)

"So you went around the second time?"

In the intercom communication channel, Xing Hechou looked confused, "Nothing happened?"

"No, not the second round."

Wang Buliuxing, who was in the same team as him, thought for a moment and said with bright eyes, "To be precise, looking down from a high altitude, they walked through a total of seven rooms and made a tiny figure 8 symbol.

Moreover, during the detour, the conditions encountered also changed - when they arrived at the initial room for the first time, the candles were automatically lit from the extinguished state, and the back door automatically opened.

When arriving at the initial room for the second time, the door on the right,

Or the rear door from the initial angle is also open.

But the candle is automatically extinguished.

It means that after they left the initial room again, the candles in the room went out for some reason. "

"Candle out?"

Xing He frowned and asked: "The changes in the grotto also started when the candles in the room were extinguished.

Does this mean something? "

"I still do not know yet."

Li Ang said with great interest in the communication channel: "But if I guess correctly, we will find the pattern soon..."

After that, he threw the walkie-talkie to Hohenheim, pushed open the door at the back of the initial room, made his ninth move, and walked into the (0, -1) room.

The furnishings in the room have not changed, but the candles were extinguished at first.

After the door is opened, the candle slowly and automatically lights up, and the door on the right can be pushed open.

Cycle broken?

Li Ang strode into the room. Previously, the opening sequence of the room was a figure-8 symbol, but now a new room has been opened.

He pushed open the door on the right,

Make the tenth move and enter the (-1, -1) room. The candle changes from light to dark, and the door on the left opens.

Move for the eleventh time, enter the (-1, -2) room, the candle changes from light to dark, and the door on the left opens.

Move for the twelfth time, enter the (0, -2) room, the candle changes from light to dark, and the door on the left opens.

Move for the thirteenth time, enter the (0, -1) room, the candle changes from light to dark, and the door on the left opens.

Fourteen, (-1, -1), the candle dims and brightens, and the door on the right opens.

Fifteen, (-1, 0), the candle dims and brightens, and the door on the right opens.

Sixteen, (0, -1), the candle dims and brightens, and the door on the right opens.

Seventeen, (-1, -1), the candle lights up and dims, and the door on the left opens.

....

Li Ang moves extremely fast,

At first, he would keep trying to push the four doors in each room. Later, he seemed to know how to go.

He strides into a room without hesitation, turning left or right.

Along the way, the candles in the room changed from light to dark, or from dark to light, but the scene I saw did not change from beginning to end.

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

tread.

While walking, Li Ang suddenly stopped, and everyone behind him hurriedly stopped moving to avoid collision.

"It makes no sense to continue like this."

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

(-1,-2), (-2,-2), (-3,-2), (-3,-1)...

If I guess correctly, according to the rules provided by the grotto, we will be trapped here for a long time. "

"...Need support?"

In the communication channel, Nebula took a deep breath and asked, "Or should we call Michael?"

"Support? No. Only one of our teams is moving now. If you start moving too, the result may be the same."

Li Ang said lightly: "Let's do this. To verify it, you can choose a direction in your initial room and open the door.

Then take the only passable door and move eight times. "

"Choose any direction?"

Xingyun paused after hearing this.

It is impossible to determine the direction in the grotto mystery. The directions between the southeast, northwest and the various teams are chaotic. There is no difference between choosing a direction and walking casually.

So, except for Li Ang's fifth team, the other groups chose directions and made eight moves.

Like Li Ang, they also recorded their route using coordinate axes.

and report in the communication channel.

The result of the eight moves was that he walked through seven rooms and drew a figure 8 symbol on the spot.

"It seems that everyone is the same."

Li Ang said calmly: "No matter which direction you choose at the beginning, whether it is front or back, left or right, the final result will be the same.

The purpose of the mysterious lock in the grotto is indeed to use the 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 movement?

The candles in the room were lit and extinguished, and only one of the four doors in the room could be opened. When someone in a room stayed in place without moving, others could not move to the next room.

These three laws are essentially the same.

Just to allow us to circle around a fixed area. "

"Circle?"

Xing Hechou asked: "That's not right. The previous eight moves were to draw a figure 8 on the same spot.

If the Grotto Mystery Lock wants us to go around in a circle, we can just restrict ourselves to going back and forth in these seven rooms.

There is no need to open up the new room (-1, -1).

Even the following paths (-1, -2), (-2, -2), (-3, -2), (-3, -1). "

"Lao Xing, have you ever raised a hamster?"

Li Ang smiled and said calmly: "Domestic hamsters only need a very small space to survive.

But a space that is too narrow will make the hamster feel depressed and die quickly, even if it is running on the hamster wheel all day long, it will not help.

Animals in zoos may also suffer from stress diseases due to their narrow living space, too few exposures to elements, and lack of social interaction.

Crazy self-harm, such as hunger strikes, hitting the cage, etc.

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

Of course, it is possible to get out of the Grotto Mystery Lock, but to really break the cycle, or start another cycle and get out, I think it will be at step 10055. "

"Step 10055?"

Xing Hechou's heart skipped a beat and he said in a deep voice, "So accurate?"

The reason for his change of tone was not only because the number was too huge, but also because Li Ang's tone was calm and calm, and even more because he knew,

When Li Ang changes back to his frivolous attitude, it means that this guy already knows the answer.

When other parties in the communication channel heard Li Ang report 10055, their eyes lit up and they looked thoughtful, as if they understood something.

"That's right, not 9999, not 10086, not 114514, but 10055."

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 changing because of our action of pushing the door open.

Either from dark to light, or from light to dark.

When the candle in the room remains burning at first, when we open the door and walk in, the candle will go out and the door on the left will open.

When the candles in the room remain extinguished at first, when we open the door and walk in, the candles will automatically burn and the door on the right will open.

In other words, if the candle is burning at the beginning, then turn left,

If the candle is initially extinguished, turn right.

Along the way we seemed to be moving according to our own will, but in fact we were completely under the rules of the grotto's mysterious lock.

At first we felt like we were walking in symmetrical or repeating shapes;

But the further we go, the more chaotic and irregular the path becomes—because we end up walking back into the rooms we walked through before.

After the unknown evil wind hit, the candles in all the rooms were extinguished. As we passed by, the candles in some rooms were lit, and when we passed by again, the candles were extinguished again.

This leads to a pattern of opening the door according to the status of the candles in the room.

Showing chaotic random form.

However, this kind of chaotic randomness is essentially pseudo-randomness with limited rules. No matter where our five teams are,

Which direction is chosen?

If there is no interference with each other, the chaotic pseudo-random will stop at about 10055 steps and start a cycle with a period of 104 steps.

Move in a fixed direction.

Like... ants. "

Nebula's eyes lit up in the communication channel, and she subconsciously blurted out, "Langton Ant!"

"That's right."

Li Ang smiled and snapped his fingers, "The mysterious lock in the grotto built by King Shibi is exactly the cage that binds Langton Ant."

"Landon what?"

Xing Hechou was stunned for a moment, his brain working rapidly, retrieving relevant information.

"Ant."

Li Ang explained casually: "No need to search in the database, it has nothing to do with the Ant King or the extraordinary elements of the Killing Fields game.

Langton's Ant is a concept proposed by Christopher Langton in the mid-1980s. It is a classic example of cellular automata and is a two-dimensional Turing machine.

The rules are also very simple. Draw square grids of the same size on the plane, and fill all the grids with black or white.

In one of the square grids, place an ant.

If the ant is in the black grid, turn 90 degrees to the right, enter the next grid, change the grid to a white grid, and move forward one step;

If the ant is in the white grid, turn 90 degrees to the left, enter the next grid, change the grid to a black grid, and move forward one step;

Just like us, the ants will return to the initial grid when they move for the eighth time.

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

Until about 10,000 steps, a cycle of 104 steps begins to be drawn, moving in a fixed direction, like building a highway, extending infinitely.

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

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

Become beautiful.

Just like the wild earth gave birth to the first life from boiling hot soup. "

"..."

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

Okay, I understand.

The ultimate purpose of the cave mystery lock is to protect King Sibi.

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

If you play the game according to its rules, you will have to wait at least ten thousand steps before you can move forward efficiently.

And this high efficiency is still oriented in a certain direction, not necessarily leading to King Sibi. "

"That's right."

Li Ang smiled and said: "Considering that there is an upper limit to the energy of the Grotto Mystery Lock, the entire maze will not extend indefinitely.

In other words, as long as we take more than 10,000 steps, it won't take long before we get out of the maze and return to the outside world.

But King Sibi is probably inaccessible.

And if we want to change our destiny and continue exploring on the square chessboard, there are only two ways.

One, use brute force to tear down the wall.

Second, find a way to meet up, let one team go in front and change the color of the square. When the other team arrives, because the color of the square changes in advance, the direction of the final path will also change.

Neither method is very reliable.

Relying on brute force, you can demolish dozens or even dozens of walls or doors, but you will soon run out of spiritual power and get into trouble.

We can find a way to meet up, but it would be too time-consuming. By the time we have planned everything, the day lilies will probably be cold——

The path of a Langton ant is easy to draw,

If multiple Langton ants are put together, the path will become extremely chaotic and disorderly.

Even because the traveling speeds of each team were different, it was impossible to start painting and it was a dead end.

No matter which angle you think about it, this grotto mystery lock is very delicate and ingenious. With only a few rules, the complexity and chaos can be deduced to the extreme within a few inches.

From the perspective of an ancient supernatural being, King Sibi was indeed very, very smart. "

How could someone not be smart come up with the structure of a cellular automaton that only exists in modern times thousands of years in advance?

Xing Hechou held the walkie-talkie and listened to Li Ang's sincere praise.

He smiled helplessly, but his heart became calm. He felt an inexplicable sense of relief when Nobita saw Doraemon taking out magical props from his fourth-dimensional pocket, "So Brother Li, how can we get out?"

Dora Ang, tell me the method quickly.

"go out?"

Li Ang smiled when he heard this, "No, no, no, if we follow the rules of the Grotto Mystery Lock, we will lose no matter what.

Either it consumes too much spiritual power, or it takes too long.

In any case, it could buy enough time for King Sibi to recover.

If you want to crack the mystery, you have to start from the initial positions of the five teams and find the pattern. "

As he spoke, he took out a large piece of metal from the backpack column, released alchemy, and transformed the iron piece into a blackboard-like rectangle, and placed on it,

Draw out each square grid and the initial positions of the five teams.

“By walking the square before the puzzle candle is extinguished, we already know where the other teams are currently, as well as their initial positions.

If the conditions are brought in and the interference caused by other teams advancing at the same time is eliminated, then each team's Langton Ant route map can be drawn.

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

Five teams, twenty directions,

The isolated island area on the entire map that is not covered by the road map is where King Sibi may exist. "