"So you made a second lap?"In the intercom communication channel, Xing He looked confused, "Nothing


    happened?""No, it''s not a second lap."Wang Bulu, who was in the same team, thought for a moment, and his eyes lit


    up, "To be precise, looking down from a high altitude, they walked through a


    total of seven rooms and circled a tiny figure eight symbol.And, during the detour process, the conditions encountered have also changed-


    when they first arrived in the initial room, the candle was automatically lit


    from the extinguished state, and the back door was automatically opened.And when I arrived at the initial room for the second time, the right doorOr the rear door from the very beginning is also open.But the candle is automatically extinguished,Explain that after they left the initial room again, the candle in the room


    was extinguished for some reason. ""The candle goes out?"Xing He frowned and asked: "The changes in the grotto began when the candles


    in the room went out.Does this represent something? ""I still do not know yet."Li Ang said with interest in the communication channel: "But if I guess


    correctly, we will soon find the pattern..."After all, he threw the walkie-talkie to Hohenheim, pushed open the door


    behind the initial room, made the ninth move, and walked into the (0, \-1)


    room.The furnishings in the room did not change, but the candles were extinguished


    at first.After the door is opened, the candle slowly ignites automatically, and the


    door on the right can be pushed open.The cycle broke?Li Ang strode the meteor into the room. Before the opening sequence of the


    rooms was a figure-eight symbol, now a new room has been opened.He pushed open the door on the right,Perform the tenth move, enter the (-1, \-1) room, the candle changes from


    bright to dark, and the door on the left opens.The eleventh move, enter the (-1, \-2) room, the candle changes from bright to


    dark, and the left door opens.The twelfth move, enter the (0, \-2) room, the candle changes from bright to


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


    bright to dark, and the left door opens.Fourteen, (-1, \-1), the candle becomes dark and bright, and the door on the


    right opens.Fifteen, (-1, 0), the candle becomes dark and bright, and the door on the


    right opens.Sixteen, (0, \-1), the candle becomes dark and bright, and the door on the


    right opens.Seventeen, (-1, \-1), the candle light becomes darker, and the left door opens.....Li Ang moved extremely fast,At the beginning, he will continue to try to push the four doors in each room.


    When he gets to the back, he seems to know how he is going.The striding meteor stepped into the room without hesitation to the left or


    right.Along the way, the candle in the room changed from bright to dark, or from


    dark to bright, and the scene we saw remained unchanged from beginning to end.For the other players in the team, the atmosphere is depressed and silent.tread.As he walked, Li Ang suddenly stopped, and everyone behind him hurriedly


    stopped moving to avoid hitting him."It doesn''t make sense to go on like this."Li Ang raised his arm, twisted the beard on the dragon''s 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 long time. ""...Need support?"In the communication channel, Nebula took a deep breath and asked, "Or we call


    Michael?""Support? No. Now only our team is moving. If you start to move too, the


    result may be the same."Li Ang lightly said: "Let''s do it, in order to verify, you choose a direction


    at random in your initial room and push the door open.Then walk through the only door you can pass and move eight times. ""Choose any direction?"Nebula paused when he heard the words. The location of the grotto fans could


    not be detected. The north, south, east, and north sides between the teams


    were disordered. There was no difference between choosing a direction and


    walking casually.So, except for the other groups of the fifth team where Li Ang was, they chose


    the direction and made eight moves.Like Li Ang, they also used the coordinate axis to record the course of


    action.And report in the communication channel.The result of the eight moves is to walk through seven rooms and draw a figure


    eight symbol on the spot."It seems that everyone is the same."Li Ang said lightly: "No matter the orientation you choose at the beginning,


    whether it is front or back, left or right, the final result is the same.The purpose of the grotto fan lock is indeed to use the rules to trap us here


    for a long time. "He paused and explained in the communication channel: "Have you noticed the


    regularity of everyone''s movement?The candles in the room were lit and then extinguished. Only one of the four


    doors in the room could be opened. When someone in one room stays in place and


    does not move, other people cannot go to the next room.These three laws are essentially the same,It is to allow us to circle in a fixed area. ""Circle?"Xing Hechou asked: "That''s not right, the first eight moves are to draw a


    figure eight on the spot.If the grotto fan lock wants us to circle around, we can directly limit death


    to the seven rooms.There is no need to open up the new room (-1, \-1).And even the following (-1, \-2), (-2, \-2), (-3, \-2), (-3, \-1) paths. ""Lao Xing, have you 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


    soon, even if it runs the hamster wheel all day, it will not help.Animals in the zoo also suffer from stress diseases due to the narrow living


    space, too few elements, and lack of social interaction.Crazy self-harm, such as hunger strikes, crashing into a cage, etc.If you want to make the creatures in the cage not feel pain and despair,


    naturally you have to expand the cage space and make the creatures think that


    they can go out.Of course, the grotto fan lock can indeed go out, but to really break the


    cycle, or start another cycle to go out, I think it will be at step 10055. ""Step 10055?"Xing He worried his heart beat, and said solemnly: "So accurate?"The reason for the change in his tone is not only because the number is too


    large, but also because Li Ang''s tone is calm and calm, and even more because


    he knows,When Li Ang changed back to a frivolous attitude, it meant that this guy


    already knew the answer.The other parties on the communication channel also lit up when they heard Li


    Ang reported 10055, thoughtfully, as if they understood something."Yes, 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 candle in the room, which


    changes because of our push to open the door.Either from dark to bright, or from bright to dark.When the candle in the room kept burning at first, when we opened the door and


    walked in, the candle would go out and the door on the left opened.When the candles in the room remain extinguished at first, when we push open


    the door and walk in, the candles will automatically burn and the door on the


    right opens.In other words, if the candle is burning at first, turn left,If the candle is extinguished at first, turn right.Along the way, we seem to be moving according to our own will, but in fact, we


    are completely restricted by the rules of the grotto fan lock.At first we felt like we were walking in a symmetrical or repetitive shape,But the more we go, the more chaotic and irregular the path-because we will


    walk back to the room we walked through before.After the unnamed yin wind hit, all the candles in the rooms were


    extinguished. Our passing caused the candles in some rooms to be lit, and when


    we passed by again, the candles would be extinguished again.According to the state of the candle in the room, the law of opening the door,Presents a chaotic random form.However, this chaotic randomness is essentially a pseudo-random with limited


    rules, no matter where our five teams are located,Which direction is selected,If they don’t interfere with each other, they will stop the chaotic pseudo-


    random at about 10055 steps and start a cycle with a period of 104 steps.Move in a fixed direction.Like... ants. "The nebula in the communication channel shined, and he blurted out


    subconsciously, "Landon Ant!""Yes."Li Ang smiled and snapped his fingers, "The mysterious lock of the grotto


    constructed by King Shibi is the cage that binds the Langton ants.""Landon what?"Xing He was stunned for a moment, his brain swiftly running, searching for


    relevant information."ant."Li Ang casually explained: "You don''t need to look for it in the database. It


    has nothing to do with the extraordinary elements of Ant King or the killing


    game.The Langton ant is a concept proposed by Christopher Langton in the mid-1980s.


    It is a classic example of cellular automata and belongs to 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 a black grid, turn to the right 90 degrees to enter the next


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


    change the grid to a black grid, and move forward one step;Just like us, the ant will return to the initial grid on the eighth move,And after the eighth move, continue to draw chaotic shapes.Until about 10,000 steps, start to draw a cycle of 104 steps, moving in a


    fixed direction, like building a highway, extending indefinitely.Langton Ant’s example is to explain a point of view,That is, extremely simple initial conditions and rule logic can also evolve


    into a random situation that seems chaotic and disorderly, and this chaos will


    become regular again after reaching a certain level.Become beautiful.It''s like the wild earth bred its first life from the boiling hot soup. ""..."Xing Hechou digested this passage in his mind, and imagined the specific


    patterns of Langton ants, "From chaos to order."Okay, I understand.The ultimate goal of the Grotto Mystery Lock is to protect King Shibi,It knows that it can''t trap us and can only delay a certain degree, so it sets


    up a seemingly simple, but in fact, complicated logic to make us fall into a


    maze.If the game is played according to its rules, it will take at least 10,000


    more steps to move forward efficiently.And this kind of high efficiency is still fixed in a certain direction, not


    necessarily leading to King Shipi. ""Yes."Li Ang smiled and said: "Considering that there is an upper limit on the


    energy of the grottoes, the entire maze will not extend indefinitely.In other words, as long as we take more than 10,000 steps, it will not take


    too long before we will walk out of the maze and return to the outside world.But King Shibi might not be able to get close.And if we want to change our destiny and continue to explore in the


    checkerboard, there are only two ways.One, demolish the wall with brute force.Second, find a way to rendezvous. Let one team go ahead and change the color


    of the square. When another team arrives, the color of the square changes in


    advance, and the direction of the final path will also change.Neither method is very reliable.With brute force, a dozen or even dozens of walls or doors can be demolished,


    but it will quickly run out of spiritual power and fall into a dilemma.It is possible to find a way to rendezvous, but that would be too time-


    consuming. When we plan everything, it is estimated that the day lily will be


    cold——The path of a Langton ant is very well painted,Put multiple Langton ants together, then the path will become extremely


    chaotic and disorderly,Even because of the different speeds of each team, it was impossible to start


    painting at all, and it fell into a dead end.Regardless of the angle of thinking, this grotto mystery lock is very delicate


    ~ ~ Only a few rules are set, and it is almost between square


    inches, deducing the complexity and chaos to the extreme.From the perspective of an ancient supernatural being, King Shibi is indeed


    very, very smart. "Can I think of the structure of cellular automata thousands of years in


    advance if I am not smart?Xing Hechou took the walkie-talkie and listened to Li Ang’s sincere praise.He smiled helplessly, but his heart calmed down. There was a kind of


    inexplicable peace of mind that Nobita saw Doraemon picking out magic items


    from the fourth-dimensional pocket, "Then Brother Li, how can we go out?"Dora Aang, hurry up and tell the method."go out?"Li Ang smiled when he heard the words, "No, no, no, if we follow the rules of


    the grotto fan lock, we will lose everything.Either it consumes too much spiritual power, or it drags on for too long,In any case, it can buy enough time for King Shipi to recover.If you want to break the mystery, you have to start from the initial positions


    of the five teams and find the pattern. "While talking, he took out a large piece of metal from the backpack bar,


    released alchemy at will, transformed the iron into a blackboard-like


    rectangle, and placed it on it,Draw a square grid and the initial positions of the five teams."Through the square-walking activity before the candles are extinguished, we


    already know where the other teams are currently and their initial positions.If the conditions are brought in and the interference caused by other teams


    advancing at the same time is eliminated, then the Langton ant road map for


    each team can be drawn.It is 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 route


    map is the location where King Shibi may exist. "