In fact, fractals are still relatively common in our lives.

Take a chestnut~~

Snowflakes!

It's not snow beer, it's snowflake!

A snowflake, if you look at it with the naked eye, is in the shape of a hexagon.

When you put it under a microscope and magnify it hundreds of thousands of times, you can see that the details are also hexagonal.

In other words, a snowflake, a large hexagonal crystal made up of n extremely tiny hexagonal crystals!

And, of course, spermatozoa, which also conform to the fractal principle.

So people used mathematical methods to represent these fractal phenomena.

After hundreds of years of research, fractal theory, in the field of mathematics, has three very important models.

They are: the three-point Cantor set, the Koch curve, and the Julia set.

The event that the two contestants challenged this time is related to the Julia set.

The definition of Giulia's sum is simple: Z(n+1)=Z(n)^2+c (c is a constant)

The definition is so simple that an average high school student can understand the meaning.

But the magic of Giulia's collection is that its mathematical definition is very simple, but the images he produces are incredibly complex, containing profound mathematical principles – or philosophical ideas that we humans have imagined ourselves.

Well, philosophical issues have already been touched ♂.

A Giulia set, simply put, is formed by iterative formation of the formula Z(n+1)=Z(n)^2+c.

Most people should know about iterations.

For example, consider the function f(z)=z^2-0.75. After fixing the value of z0, we can calculate a series of z-values by iterating over and over again: z1=f(z0), z2=f(z1), z3=f(z2),...。 For example, when z0 = 1, we can iterate sequentially:

z1 = f(1.0)= 1.0^2 – 0.75 = 0.25

z2 = f(0.25)= 0.25^2 – 0.75 =-0.6875

............

z5 = f(-0.6731)=(-0.6731)^2 – 0.75 =-0.2970

.........

It can be seen that the Z(n) function, after continuous iteration, the result will gradually tend to a certain value.

Of course, this is just a change in Z(0)=1.

After a series of indescribable studies of Giulia's sets, mathematicians discovered that not all Z(0) values can form bounded fractal graphs.

Only if Z(0) is in the range of -1.5,1.5, the value of Z(n) is limited.

In other words, only within [-1.5,1.5] can the Giulia set form a bounded fractal figure.

This time, the program team fixed the value of Z(0) and asked questions for the change of parameter c.

Parameter c, which can be written as c(x,y)=x+iy.

The value of c is determined by a real part x and an imaginary part y.

Change the values of x,y, and the corresponding fractal diagram will also change.

Moreover, the change of x and y is nonlinear, sometimes fast and sometimes slow.

Guests will randomly select 7 of the 100 fractal animations generated by x,y in a certain interval (-1,1 to be exact).

50 fractal diagrams were taken from each fractal animation.

Cheng Nuo and Li Shiye can choose 2 sheets each to display the values of x and y corresponding to the fractal diagram.

Then, through on-site learning, the two deduced the formula to the generation logic of the graph.

Then, according to the generation logic that is pushed out, the specific value of x and y is determined, accurate to 3 decimal places. Error, between -0.001, 0.001!

Seven questions, seven fractal animations, seven production logics, one hundred and seventy-five fractal figures, and 28,000,000 possible values for x,y.

What the player needs to do is to find the one right one among the 28,000,000 possibilities!

Only with seven questions can there be a rush mode.

One point is added for a correct answer and one point is added for an incorrect answer.

Whoever gets four points first wins!

rules, the broadcast is over.

The audience, you look at me, I look at you.

A bewildered face!

Confused!

......

All confused!

"Do you understand what you're talking about?"

"Barely understood...... 0.0001%。 ”

......

"After reading this question, I feel like I didn't bring my brain today!"

"Haha...... Me too...... The brain has already let me flush it down the toilet!"

......

"It's too nerve-wracking to talk about this topic, so let's change the subject. What are you going to eat at noon today?"

"I feel like I need to make up for it with Kidney Treasure. Kidney treasure, a bottle of refreshing!"

This is a special question......

What the hell is it?

Is it because my Mandarin Chinese is not up to standard or what?

I recognize all of these words. But why am I blindfolded when they are connected?

Is your strongest brain floating, or are we, the viewers, unable to hold the knife?

Usually take some brain-burning projects to insult our IQ, even if we can understand it a little.

But this question, to be honest, is really ...... Didn't understand it at all!

It was hard for them to imagine that two teenagers in their twenties on the field were going to challenge a project that they couldn't even understand the rules of the question.

Really......

I'm waiting for scum, the only meaning of being born is to make up the numbers for human beings.

Maybe sometimes when the school bully starts pretending to be forced, it's good to be a salted fish who shouts 666!

Mr. Jiang also saw the confusion in the audience's eyes, and said with a smile, "There may be many viewers who don't understand the challenge rules of this project, it's okay, let's animate it." ”

"First of all, these fractal animations are all after the value of the complex number c in the iterative function f(z)=z^2+c in the complex plane changes continuously similarly, and we ......"

Gave up, gave up completely......

Kneel, really kneel......

Teacher Jiang, are you really sure that you are not talking about the Book of Heaven?

I thought we would understand something after you said it?

But...... The more you talk about it, the more confused you become!

The audience already had little hope of understanding the question.

I just looked forward to the game starting immediately, and then quietly watched Cheng Nuo and Li Shiye pretending to be forced.

Melon seeds, beer, and small maza are all ready.

Two big guys, please start your show!

I'm waiting for salted fish, I don't have any other skills, and I've practiced the ability to shout 666!

............

"Now, four guests are invited to choose seven out of 100 fractal animations as the contestants' questions!"

Finally, in the expectation of a group of salted fish spectators, the competition officially began!

Cheng Nuo and Li Shiye sat side by side in the challenge seat.

In front of each person, there is a display screen for uploading questions.

The guests quickly picked out 7 fractal animations.

Seven fractal animations, corresponding to seven different x,y values and the laws of fractal figures.

"Okay, let's change the x,y values of these seven fractals. ”

On the big screen, I saw the values of seven fractal animation imaginary numbers (x,y), starting from [1,1] according to 0.001 per step.

Next, 50 fractal diagrams were randomly taken on each fractal animation. ”

In fact, according to the 0.001 step, there will be 1,000,000 variations for each fractal animation.

If you take only 50 of them, there will be a lot of fractal shapes in between.

It will also have a great impact on the judgment of the two players!