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Mystic mapping 7

I'm sorry for not uploading my blog for a long time.

Today, I introduce the Japanese map.
Off course, it doesn't mean the geographical map.

This is it.
The Japanese map was discovered by Prof. Ryo Ueda in 1961.
It was just the same year as the discovery of the Lorenz map by Lorenz.

Mystic mapping 6

The formula of the Ikeda map that has been promised is shown.

It is an expression of the rotation, the translation, and the expansion of the point, simply.
An it is a strange attractor of the streamline shape by complex dynamic system.


In this results, parameter u is 0.9.
Yes, mysterious figure is obtained.

I think that I will introduce a Japanese map at the end next time.

Mystic mapping 5

In addition, I introduce another map.

It is called the Ikeda map.
Off course this is the chaos map, too.

I will show you its formula next.
Mr.Ikeda, Japanese, creates it as understood from the name.

All complex figures which I show can be written by simple formula.
But, for instance, the system that causes such chaos has been thought as a system to avoid.
It is because of their chaos nature.

Mystic mapping 4

I show you the formula of Henon mapping.


This is Henon mapping.
In this formula ,a and b are parameters.
You can see the expression studied in the junior high school.

Figure introduced before can be obtained by plotting the point one by one while increasing t.
For me, it was a surprise to show the character of chaos in such a simple expression.

I drew this map by using attractor on web
by the condition of a=1.4 b=0.3 and plot 2000 point.
This figure is almost equal to figure which I showed before, I think.

Mystic mapping 3

In addition, I will introduce you another mapping which chaos is generated.


This mapping is called, the Henon[Hénon] mapping.
This is an example of the representative.
And it was found by Henon who was an astronomer of France.

This mapping is famous because the fractal nature of chaos has come out remarkably.
We can express this mapping easier than mapping which I introduced before.

I will introduce the fomula next time.

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