Fractal graphics: description, examples, formats, advantages and disadvantages

Mathematics is literally permeated with harmony, and fractal graphics are a direct confirmation of that. Science is present in the creation of each of its elements, so it reflects all the beauty.

The founder of fractal geometry, Professor Malderbrot, wrote in his books that the graphics in question are not just repetitive images. It is the structure of any being or object on the planet, living and nonliving. For example, DNA is the basis, one integration. But if the code begins to repeat, then a person appears.

Fundamentals of fractal graphics

What is fractal graphics? This is one or more geometric figures, each of which is similar to the other. That is, the image is made up of identical parts.

The very word "fractal" can be used if the figure has one or more of these properties:

• Nontrivial structure. When a small detail of the entire image is viewed, the fragment is similar to the entire picture. The increase in scale does not lead to deterioration. The image always remains equally complex.
• Each part of the picture is self-similar.
• There is a mathematical dimension.
• It is built with the help of repetition.

A lot of objects of natural or artificial origin are endowed with the properties of fractals. These include the circulatory systems of man and animal, the crowns and roots of trees and so on.

Fractal computer graphics are becoming popular because beauty and realism can be achieved through simple construction with the help of appropriate equipment. You just need to specify the correct mathematical formula and indicate the number of repetitions.

How to create an element of fractal graphics?

Creation of fractal graphics will differ depending on its classification: geometric, algebraic or stochastic. Despite the difference, the total will always be the same. Since fractal graphics begin with geometry, you should consider creating it in the corresponding example:

1. Specify the condition. This is the figure on the basis of which the entire image will be built.
2. Specify the procedure. It converts the condition.
3. Get a geometric fractal.

Usually, the zero condition is represented as a triangle.

To build an image, you need to apply two procedures. First, DrawTriangle. It builds a triangle by the points specified by the user. Secondly, DrawGenerator. It indicates the number of points. Each procedure can be repeated several times or infinitely long. To determine this indicator, use the numerical argument n.

Other actions with fractal graphics

After the element of fractal graphics has been created, it is possible to perform various additional actions with it:

• Turns and stretching. So the individual details of the picture increase, or they take the form desired by the user.
• Grouping objects. Usually this function is used to assign the required scale.
• Convert colors. The image can be painted in any shade, set the tone.
• Change the shape of the whole object or individual parts.

It must be remembered that images of fractal graphics can not be predicted ultimately. When the triangle is too large, the view will be unrealistic, the user will see only the black window. When the desired texture is detected, all changes with it must be done in the minimum order, keeping the permissible version at all times.

Generation programs

There is no such person who would not be attracted to fractal graphics. The programs involved in its creation are presented in large numbers. Therefore, we need to understand the most suitable for beginners.

The Art Dabbler product is the best option if the user has not previously dealt with his taxes. Here you can not only learn the graphics, but also learn how to draw on the computer. Other advantages include a small amount of memory and an intuitive interface.

Another program is Ultra Fractal. It is already focused on the work of professionals, newcomers will find it difficult to understand. The interface here is quite complicated, but the manufacturers have performed it on the example of the usual Photoshop. If the user has dealt with this program, then the buttons will figure out quickly. The peculiarity of Ultra Fractal is that not only fractal graphics are executed here as a standard and normal image, but also animation. Formulas for compilation are attached, but if necessary, the user will be able to use his own.

Existing formats

Formats of fractal graphics determine the form and method of storing the file data. Some of them include a large amount of information. Therefore, they must be compressed. And do this not through archiving, but directly in the file. If you select it correctly, the compression will occur automatically. There are several algorithms for this procedure.

If before the user application, most of which is sustained in one color, then it is reasonable to use the formats BMP and PCX. Here, the sequence of repeated values is replaced.

The diagram, which is very rare, but still used in fractal graphics, is logical to place in TIFF or GIF.

Some formats are universal. That is, they can be viewed in most editors. But if the user is interested in high-quality image processing, then you need to apply the original program.

Fractal formats are not supported by browsers. That is why they are transformed, if there is a need to upload to a particular site.

Applications

The use of fractal graphics can be called virtually ubiquitous. Moreover, this area is constantly expanding. At the moment, you can note the following areas:

1. Computer graphics. Relics and natural objects are depicted realistically. This applies in the creation of computer games.
2. Analysis of stock markets. Fractals here are used to mark repetitions, which will later play traders on hand.
3. Natural Sciences. In physics, nonlinear processes are modeled using fractal graphics. In biology, she describes the structure of the circulatory system.
4. Compress images to reduce the amount of information.
5. Establishment of a decentralized network. By means of fractals it is possible to provide direct connection, and not through central regulation. Therefore, the network becomes more stable.

At the moment, the use of fractals in the production of various equipment is practiced. For example, a conveyor has already been launched to create antennas that perfectly receive signals.

Examples

Examples of fractal graphics are common from primitive to very complex repeating elements. A unique feature of this type is that the drawing can be composed entirely of exclamation or question marks.

Standard, but relatively complex examples of computer fractal graphics are clouds, mountains, seashores and so on. They are often used to create games.

The simplest example is the Koch curve. First, it does not have a specific length, and it is called infinite. Secondly, there is no smoothness here. Therefore, it is impossible to construct a tangent.

Advantages and disadvantages

Fractal graphics has recently gained its distribution. Advantages and disadvantages of it are too blurred, since there is no normal theoretical basis. Terminology and the principles of its use are not fully understood, despite the fact that they are effective and working.

Advantages of fractal graphics are in several factors:

1. Small size with a large-scale figure.
2. There is no end to scaling, the complexity of the picture can be increased endlessly.
3. There is no other such tool that will allow you to create complex shapes.
4. Realistic.
5. Simplicity in creating works.

Disadvantages of fractal graphics are also present. First, you can not do without a computer. And, the longer the number of repetitions, the more the processor is loaded. Accordingly, only high-quality computer equipment is able to cope with the construction of complex images.

Secondly, there are limitations in the original mathematical figures. Some images can not be created using fractals.

Similarities and differences between a fractal and a vector

Vector and fractal graphics are very different:

1. Image encoding. The vector uses the contours of different geometric shapes, fractal is a mathematical formula based on a triangle.
2. On application. Vector is used wherever you need to get a clear outline. Fractal graphics are more specialized, it has found its application in mathematics and art.
3. By analogy. Vector analogs are slides or functions on the charts. Fractals have snowflakes or crystals.

Despite the diversity of distinctive features, these two types of graphics combine image quality. It remains unchanged, regardless of the zoom level.

Three-dimensional, vector, raster, fractal graphics are similar in one - all of them are widely used in solving various computer problems. To get a really high-quality image, you need to use each of them.

Unique features of fractals

Fractal graphics have no analogues. It is unique in its kind. First, one of its small plot can tell at once about the whole picture or image. Information about the entire fractal is available, because He is self-similar.

At the center of any image related to this type of graphics, is an equilateral triangle. All other details of the drawing are either parts of it or smaller / enlarged copies. That is, one particular element takes part in drawing up the image.

In order to use fractal graphics, no objects stored in the computer's memory are needed. You can start creating with only a mathematical formula at your fingertips.

Conclusion

Fractal graphics are very realistic. This is because its parts and elements are constantly encountered in the environment of a person - mountains, clouds, seashores, various natural phenomena. Some of them remain constantly in the same state, like trees, stony areas. The rest are constantly changing, like a flickering fiery flame or blood moving through the vessels.

The development of fractal technologies today is one of the progressive fields of science. It is used not only in computer graphics. Perhaps, if scientists manage to get to the bottom of their essence, a person will begin to understand the world much better.