universal data

Chapter 149 I Doubt I Forgot My Brain
In fact, fractals are quite common in our daily life.

Take a chestnut~~
snowflake!

It's not snow beer, it's snowflakes!
A snowflake looks like a hexagon when you look at it with the naked eye.

When you put it under a microscope and magnify it 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 also sperm, which also conform to the fractal principle.

So people use mathematical methods to express 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, Koch curve, and Julia set.

The project that the two contestants challenged this time was related to the Julia Set.

The definition of the Julia set sum is very simple: Z(n+1)=Z(n)^2+c (c is a constant)
The definition is very simple, and an ordinary high school student can understand its meaning.

But the magic of the Julia set is that its mathematical definition is very simple, but the images it generates are incredibly complex, containing profound mathematical principles—or perhaps our own imaginary philosophy.

Well, philosophical issues have been touched upon.

A Julia set, simply put, is formed by continuously iterating the formula Z(n+1)=Z(n)^2+c.

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 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 function Z(n) will gradually tend to a certain value after repeated iterations.

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

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

The value of Z(n) is finite only if Z(0) is in the range [-1.5, 1.5].

That is to say, only within [-1.5, 1.5], the Julia set can form a bounded fractal figure.

But this time, the program group fixed the value of Z(0), and made questions for the change of parameter c.

The parameter c 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 and y, and the corresponding fractal diagram will also change.

Moreover, the changes in x and y are non-linear, sometimes fast and sometimes slow.

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

Cut 50 fractal images from each fractal animation.

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

Then the two deduced the generation logic from formulas to graphics through on-site learning.

Then based on the inferred generation logic, the specific x and y values ​​are determined, accurate to 3 decimal places.The error is between [-0.001, 0.001]!
Seven questions, seven fractal animations, seven production logics, 170 five fractal graphics, 28000000 possible values ​​of x and y.

What the players need to do is to find the only correct one among 28000000 possibilities!
There are seven questions, and there is a rush-answer mode.

One point is added for a correct answer and one point for the opposite answer.

Whoever gets four points first wins!
Rules, it's over.

All the audience, you look at me, and I look at you.

Confused!
Dumbfounded!
……

Everyone is confused!
"Did you understand what was said?"

"Barely understand... 0.0001%."

……

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

"Haha... me too... my brain has already been flushed away by me in the toilet!"

……

"It's too nerve-wracking to talk about this topic, let's change the subject. What are you going to have for lunch today?"

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

What a special question...

What the hell is it?

Is it because my Mandarin Chinese is not up to standard or what?
I know all these words.But why am I confused when they are connected together?

Is it because you are the strongest and your brain is wandering, or are we the audience unable to hold the knife?
Even if they insult our IQ with some brain-burning projects, we can still understand a little bit.

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

It was hard for them to imagine that two 20-year-old boys on the field were going to challenge him in a project that they didn't even understand the rules of the question.

really……

I'm a scumbag, the only reason for being born is to make up for the human race.

Maybe sometimes when the top academics start to show off, just be a salty fish called 666!

Teacher Jiang also saw the bewilderment in the audience's eyes, and said with a smile, "Maybe there are many audiences who don't understand the challenge rules of this project. It's okay, let's do an animation demonstration."

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

Give up, give up completely...

I knelt down, I really knelt down...

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

I thought we could understand something after you said it?
But... the more I talk, the more confused I become!

The audience no longer had much hope of understanding the topic.

I just look forward to the game starting soon, and then quietly watch Cheng Nuo and Li Shiye show off.

Melon seeds, beer, and Mazza are all ready.

Two big guys, please start your performance!
I wait for salted fish, I have no other skills, but I have practiced the ability to call 666!

…………

"Now, four guests are invited to choose seven of the 100 fractal animations as the contestant's topic!"

Finally, amidst the expectations of the salted fish audience, the competition officially began!
Cheng Nuo and Li Shiye sat side by side in the challenge seats.

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

The guests quickly selected 7 fractal animations.

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

"Okay, next, change the x and y values ​​of these seven fractals."

On the big screen, the values ​​of seven fractal animation imaginary numbers (x, y) can be seen, starting from [1, 1] and changing at a step of 0.001.

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

In fact, according to 0.001 step, each fractal animation will have 1000000 change maps.

If you only capture 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!
(End of this chapter)