How to conquer fractals or introductory acquaintance with ChaosPro
There are many interesting activities in the world. Mathematics is usually associated with anything, but not with such a pastime. This can be challenged. But I, by virtue of my professional activities, know what I am saying. It is especially difficult to explain the charm of mathematics to the younger generation. And after all, it is up to him to solve all the problems of the future. Accordingly, the need arises to somehow interest a young (and not only) person with a subject.
This can be done with the help of computer programs that will help the student or student to visually see the beauty of the result. Today I would like to take a closer look at the program for generating fractals.
The concept of "fractal" was introduced by the great French-American mathematician of Jewish origin, Benoit Mandelbrot. In a broad sense, a fractal denotes a shape, small parts of which in an arbitrary magnification are similar to it.
There are many programs for generating fractals. We will focus on one of them - the free fractal generator ChaosPro, which runs under the MS Windows operating system. With it, you can create an infinite number of amazingly beautiful fractal images.
')
The program has a fairly simple and convenient interface. Along with the ability to automatically build fractals, you can fully control this process by changing a large number of settings. Separate windows are provided for the parameters, and the number of simultaneously open windows can be very large. All changes applied to fractals under construction are almost instantly reflected in the viewing window.
ChaosPro supports different types of fractals (2D and 3D), precise color adjustment that provides smooth gradient transitions, true color support, animation support, has a fairly fast built-in compiler. Download the generator here: www.chaospro.de/download.php .
Having installed and running the generator in front of us, the working window of the program opens.
Let's take a closer look at this generator. So let's get started.
Select the menu: Fractal / New DefaultType / Attractor (you can just press Ctrl + 1):
Now we change the formula. In the Parameters window (it is on the right above), select the Formula tab. Let's change the formula we work with. Left click on the icon next to the name of the formula. A list will open before us:
In the paragraph "AttractorConstructor.cfm" choose the formula "Sphere":
We will have such a figure:
If we hover the mouse over the shape and click the left key, we can rotate it.
Now let's set the value “rotators” in the “base shape” (“Base shape”), and “degree”, “height” in the “starting points” points. "(" Height ") set the value" 0 ":
We have a ball:
This object can also be rotated. By the way, it seems that the object rotates itself, but in fact we are rotating around it. Moreover, it would be more correct to say that we revolve around a certain point of view. If we go to the View section, we can see the coordinates of this point (“View Point”) - (0/0/0):
Our sphere is centered around this point. Let's try changing its coordinates. This can be done by entering values ​​for x, y and z. And you can hold down the "Shift" button to "capture" the figure with the mouse and move it. The values ​​in the “View Point” will change.
You can also zoom in by moving the mouse over it and scrolling the wheel.
Let's go back to the File / Fractal / Escape Time menu (or just press Ctrl + 4):
We get an image of the classic Mandelbrot fractal:
"Let's play" with him. In the “Parameters” window already known to us, select the “Inside” item. In the "Mapping" section, we have allocated "None" (that is, nothing is selected). Select a linear image ("Linear"):
Our image has changed:
Go to the "Outside" ("Outside") and change the "Speed" ("Speed") from 1, for example, 10:
The fractal image took the form:
Let's zoom in on the image:
We got such an interesting and colorful fractal image.
As we can see, the program has many different settings, which in one article is not so difficult to consider, but also impossible. Therefore, at this stage I finish the story about the program ChaosPro, as the article promises to drag on. I hope I managed to interest you and it will become easier for many to understand this program.
And if interest appears, the continuation will follow.
Successes to you, mathematicians and just lovers to learn something new.
This can be done with the help of computer programs that will help the student or student to visually see the beauty of the result. Today I would like to take a closer look at the program for generating fractals.
The concept of "fractal" was introduced by the great French-American mathematician of Jewish origin, Benoit Mandelbrot. In a broad sense, a fractal denotes a shape, small parts of which in an arbitrary magnification are similar to it.
There are many programs for generating fractals. We will focus on one of them - the free fractal generator ChaosPro, which runs under the MS Windows operating system. With it, you can create an infinite number of amazingly beautiful fractal images.
')
The program has a fairly simple and convenient interface. Along with the ability to automatically build fractals, you can fully control this process by changing a large number of settings. Separate windows are provided for the parameters, and the number of simultaneously open windows can be very large. All changes applied to fractals under construction are almost instantly reflected in the viewing window.
ChaosPro supports different types of fractals (2D and 3D), precise color adjustment that provides smooth gradient transitions, true color support, animation support, has a fairly fast built-in compiler. Download the generator here: www.chaospro.de/download.php .
Having installed and running the generator in front of us, the working window of the program opens.
Let's take a closer look at this generator. So let's get started.
Select the menu: Fractal / New DefaultType / Attractor (you can just press Ctrl + 1):
Now we change the formula. In the Parameters window (it is on the right above), select the Formula tab. Let's change the formula we work with. Left click on the icon next to the name of the formula. A list will open before us:
In the paragraph "AttractorConstructor.cfm" choose the formula "Sphere":
We will have such a figure:
If we hover the mouse over the shape and click the left key, we can rotate it.
Now let's set the value “rotators” in the “base shape” (“Base shape”), and “degree”, “height” in the “starting points” points. "(" Height ") set the value" 0 ":
We have a ball:
This object can also be rotated. By the way, it seems that the object rotates itself, but in fact we are rotating around it. Moreover, it would be more correct to say that we revolve around a certain point of view. If we go to the View section, we can see the coordinates of this point (“View Point”) - (0/0/0):
Our sphere is centered around this point. Let's try changing its coordinates. This can be done by entering values ​​for x, y and z. And you can hold down the "Shift" button to "capture" the figure with the mouse and move it. The values ​​in the “View Point” will change.
You can also zoom in by moving the mouse over it and scrolling the wheel.
Let's go back to the File / Fractal / Escape Time menu (or just press Ctrl + 4):
We get an image of the classic Mandelbrot fractal:
"Let's play" with him. In the “Parameters” window already known to us, select the “Inside” item. In the "Mapping" section, we have allocated "None" (that is, nothing is selected). Select a linear image ("Linear"):
Our image has changed:
Go to the "Outside" ("Outside") and change the "Speed" ("Speed") from 1, for example, 10:
The fractal image took the form:
Let's zoom in on the image:
We got such an interesting and colorful fractal image.
As we can see, the program has many different settings, which in one article is not so difficult to consider, but also impossible. Therefore, at this stage I finish the story about the program ChaosPro, as the article promises to drag on. I hope I managed to interest you and it will become easier for many to understand this program.
And if interest appears, the continuation will follow.
Successes to you, mathematicians and just lovers to learn something new.
Source: https://habr.com/ru/post/236083/
All Articles