Chapter 149 (1/2)

In fact, fractal is quite common in our life.

Take a chestnut ~ ~

snowflake!

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

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

When you put it under a microscope and magnify it a few hundred thousand times, the details you see are hexagonal.

In other words, a snowflake is a large hexagonal crystal composed of n extremely small hexagonal crystals!

Of course, there are 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, in the field of mathematics, there are three very important models.

They are: Cantor set, koch curve, Julia set.

The events that the two players are challenging are related to Julia and Julia.

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

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

But what's amazing about Julia's collection is that its mathematical definition is very simple, but the images it produces are incredibly complex, including profound mathematical principles - or even our own imaginary philosophy.

Well, zhe has been involved A kind of Learning problems.

A Julia set, simply put, is the formula of Z (n + 1) = Z (n) ^ 2 + C.

Iteration should be known to most people.

For example, consider the function f (z) = Z ^ 2-0.75. We can obtain the fixed values of ZF (1, Z2), ZF = 0 by iteration. For example, when Z0 = 1, we can iterate in sequence:

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 result of Z (n) function tends to a certain value after continuous iteration.

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

After a series of indescribable researches on Julia sets, it is found that not all Z (0) values can form bounded fractal figures.

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 the range of [- 1.5,1.5], can Julia sets form bounded fractal figures.

This time, the program group fixed the value of Z (0) and made a question according to 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.

Changing the value of X, y, the corresponding fractal image will also change.

And, the change of X, y is nonlinear, fast and slow.

Guests will randomly select 7 of the 100 fractal animations generated by X and Y changing in a certain range (or [- 1,1]).

50 fractal images are captured from each fractal animation.

Cheng Nuo and Li shiye can choose 2 pieces each to display the values of X and Y corresponding to the fractal diagram.

Then, through the on-the-spot study, they deduce the logic from the formula to the graph.

Then, according to the generated logic, the specific value of X and y can be determined, and the value can be accurate to three decimal places. The error is between [- 0.001, 0.001]!

Seven topics, seven fractal animations, seven production logic, 175 fractal graphics, 28 million possible values of X, y.

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

Only when there are seven questions can there be a preemptive answer mode.

One point for correct answer and one point for wrong answer.

Whoever gets four points first wins!

Rules, it's over.

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

A face of muddle force!