Omnipotent Data

In fact, fractals are quite common in our lives.

Give a chestnut

snowflake!

Not Snow Beer, it's Snow!

A snowflake, if you look at it with the naked eye, it has a hexagonal shape.

When you put it under a microscope and zoom in hundreds of thousands of times, the shape of the details you see is also hexagonal.

In other words, a snowflake is a larger hexagonal crystal composed of n extremely tiny hexagonal crystals!

Of course, there are sperms, which also conform to the fractal principle.

So people use mathematical methods to represent these fractal phenomena.

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

They are: three-point Cantor set, Koh curve, Julia set.

The project that the two contestants challenged this time is related to the Julia Collection.

The definition of Julia set sum is very simple: Z(n+1)=Z(n)^2+ (is a constant)

The definition is very simple, and an ordinary high school student can understand the meaning.

But the magic of Julia's collection is that its mathematical definition is very simple, but the images he generates are incredibly complex, which contains profound mathematical principles or philosophies that we humans imagine.

Well, the issue of philosophy has already been involved.

A Julia set, in simple terms, is formed by continuous iteration of the formula Z(n+1)=Z(n)^2+.

Most people should know about iteration.

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 ​​through continuous iteration: z1=f(z0), z2=f(z1), z3=f(z2),... For example, when z0=1, we can iterate out:

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 function of Z(n) will gradually tend to a certain value after continuous iteration.

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

After a series of indescribable studies on Julia sets, mathematicians discovered that not all Z(0) values ​​can form a bounded fractal figure.

Only when 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 Julia set constitute a bounded fractal figure.

But this time, the program group fixed the value of Z(0) and asked questions for the change of parameters.

The parameter can be written as (x, y)=x+iy.

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

Change the value of x and y, the corresponding fractal graph will also change.

In addition, the changes of x and y are non-linear, fast and slow.

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

Take 50 fractal images from each fractal animation.

Cheng Nuo and Li Shiye can choose two each to show the corresponding x and y values ​​of the fractal graph.

Then the two of them deduce the logic of generating formulas to graphics through on-site learning.

Then, according to the generated logic, determine the specific x and y values, accurate to 3 decimal places. The error is between [-0.001, 0.001]!

Seven problems, seven fractal animations, seven production logics, 175 fractal graphics, 28 million possible values ​​of x and y.

All the players need to do is to find the only correct one among 28 million possibilities!

Only seven questions have a quick answer mode.

One point for correct answers, one point for wrong answers.

Whoever gets four points first wins!

Rules, it's over.

The audience in the audience look at me and I look at you.

Look confused!

Confused!

...

All dumbfounded!

"Do you understand what is being said?"

"Reluctantly understand...0.0001%."

...

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

"Haha... Me too... The mind has already let me flush away in the toilet!"

...

"Talking about this topic is too damaging, let's change the topic. What do you plan to eat at noon today?"

"I think I need to supplement Shenbao. Shenbao, a bottle of refreshing!"

What a special question...

What the **** is it?

Is my Mandarin not up to the standard or is it something wrong?

I know all these words. But why are I being trapped together?

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

Even if we use some brain-burning items to insult our IQ, we can still understand a little bit.

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

It's hard for them to imagine a project that they don't even understand the rules of the title, and two teenagers in their twenties on the field are going to challenge him.

really……

I wait for the scum, the only purpose of being born is to make up the number for humans.

Maybe sometimes when the schoolmaster begins to pretend to be forceful, just be a salted fish shouting 666!

Teacher Jiang also saw the awkwardness in the audience's eyes, and said with a smile, "Perhaps many audiences don't understand the challenge rules of this project. It doesn't matter. Let's animate it again."

"First of all, these fractal animations are all iterative functions on the complex plane f(z)=z^2+. After the values ​​of the complex numbers in the complex change continuously similarly, we..."

Give up, give up completely...

Kneeling, really kneeling...

Teacher Jiang, are you really sure that you are not talking about the heavenly scriptures?

I thought we could understand a little bit after you said it?

But... the more you talk, the more confused!

The audience does not have much hope for understanding the topic.

I only look forward to the start of the game, and then quietly watch Cheng Nuo and Li Shiye act hard.

Sunflower seeds, beer, and small Mazar are all ready.

Two big guys, please start your performance!

I'm waiting for salted fish, but I don't have any other skills. The ability to call 666 is still practiced!

…………

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

Finally, in the anticipation of the audience, the competition officially began!

Cheng Nuo and Li Shiye ~www.readwn.com~ sat side by side in the challenge position.

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

The guests quickly selected 7 fractal animations.

Seven fractal animations correspond to seven different x, y values ​​and the laws of fractal graphics.

"Okay, next, change the x and 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] and changing every step of 0.001.

"Next, randomly cut 50 fractal images on each fractal animation."

In fact, according to 0.001 step, each fractal animation will have 1,000,000 changes.

If you only take 50 of them, there will be a lot of fractal graphics in the middle.

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