Mathematics is literally permeated with harmony, and fractal graphics are a direct confirmation of this. Science is present at the creation of each of its elements, so it reflects all the beauty.
The creator of fractal geometry, Professor Malderbrot, wrote in his books that the graphics in question are not just repeating images. This is the structure of any creature or object on the planet, living and nonliving. For example, DNA is the foundation, one integration. But if the code begins to repeat, then a person appears.
The basics of fractal graphics
What is fractal graphics? This is one or more geometric shapes, each of which is similar to another. That is, the image is made up of the same parts.
The word "fractal" itself can be used if the figure has one or more of these properties:
- Non-trivial structure. When a small detail of the whole image is considered, the fragment is similar to the whole picture. An increase in scale does not lead to deterioration. The image always remains equally complex.
- Each part of the figure is self-similar.
- There is a mathematical dimension.
- Built by repetition.
Many objects of natural or artificial origin are endowed with fractal properties. These include the circulatory systems of humans and animals, the crowns and roots of trees, and so on.
Fractal computer graphics become popular because beauty and realism can be achieved through simple construction using appropriate equipment. It is only necessary to set the correct mathematical formula and indicate the number of repetitions.
How to create a fractal graphic element?
Creating fractal graphics will vary depending on its classification: geometric, algebraic or stochastic. Despite the difference, the outcome will always be the same. Since fractal graphics begin with geometry, you should consider its creation using the corresponding example:
- Set the condition. This is the figure on the basis of which the entire image will be built.
- Set the procedure. She transforms a condition.
- A geometric fractal is obtained.
Usually, the null condition is represented as a triangle.
To build an image, you need to apply two procedures. Firstly, DrawTriangle. It builds a triangle based on points specified by the user. Secondly, DrawGenerator. It indicates the number of points. Each procedure can be repeated several times or indefinitely. To determine this indicator, the numerical argument n is used.
Other fractal graphics
After the fractal graphic element has been created, it is possible to perform various additional actions with it:
- Bends and stretches. So the individual details of the picture are increased, or they take the form that the user needs.
- Grouping objects. Usually this function is used to set the desired scale.
- Color conversion. The image can be painted in any shade, set the tone.
- Change the shape of the entire object or individual parts.
It must be remembered that images of fractal graphics are ultimately impossible to predict. When the triangle grows too large, the view will be unrealistic, the user will see only a black window. When the desired texture is detected, all changes with it must be carried out in a minimal order, while constantly maintaining the acceptable option.
Programs for generating
There is no person who is not attracted to fractal graphics. Programs involved in its creation are represented in large numbers. Therefore, you need to understand the most suitable for beginners.
Product Art Dabbler is the best option if the user has not previously dealt with its counterparts. Here you can not only master the graphics, but also learn how to draw on a computer. Other advantages include a small amount of occupied memory and an intuitive interface.
Another program is Ultra Fractal. It is already focused on the work of professionals, it will be difficult for beginners to understand it. The interface here is quite complicated, but manufacturers performed it on the example of ordinary Photoshop. If the user was dealing with this program, then the buttons will figure it out quickly. The peculiarity of Ultra Fractal is that not only fractal graphics are performed here as a standard and ordinary image, but also animation. Formulas for compilation are attached, but if necessary, the user can use his own.
Existing Formats
Fractal graphics formats determine the form and method of storing file data. Some of them include a large amount of information. Therefore, they must be compressed. And to do this is not through archiving, but directly in the file. If you select it correctly, then the compression will occur automatically. There are several algorithms for this procedure.
If the user has an application, most of which is in the same color, then it is reasonable to use the BMP and PCX formats. Here, the sequence of repeating quantities is replaced.
It is logical to place a diagram, which is very rare, but still used in fractal graphics, in TIFF or GIF.
Some formats are universal. That is, they can be viewed in most editors. But if high - quality image processing is important to the user , then you need to use the original program.
Fractal formats are not supported by browsers. That is why their transformation is carried out, if there is a need to upload to a particular site.
Fields of application
The use of fractal graphics can be called virtually universal. Moreover, this area is constantly expanding. At the moment, the following areas can be noted:
- Computer graphics. Realistically depicted reliefs and natural objects. This is used in the creation of computer games.
- Stock market analysis. Fractals are used here to mark repetitions, which subsequently will play into the hands of traders.
- Natural Sciences. In physics, non-linear processes are modeled using fractal graphics. In biology, she describes the structure of the circulatory system.
- Image compression to reduce the amount of information.
- Creation of a decentralized network. Through fractals, it is possible to provide a direct connection, and not through central regulation. Therefore, the network is becoming more stable.
At the moment, the use of fractals in the production of various equipment is practiced. For example, a pipeline 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 picture can only be composed of exclamation or question marks.
Standard, but relatively complex examples of computer fractal graphics are clouds, mountains, coasts, and so on. They are often used when creating games.
The simplest example is the Koch curve. Firstly, it does not have a specific length, and it is called infinite. Secondly, smoothness is completely absent here. Therefore, it is impossible to construct a tangent.
Pros and cons
Fractal graphics have recently gained their distribution. Its advantages and disadvantages are too blurry, since there is no normal theoretical basis. The terminology and principles of its use are not fully understood, despite the fact that they are effective and working.
The advantages of fractal graphics are several factors:
- Small size with large-scale drawing.
- There is no end to scaling, the complexity of the picture can be increased endlessly.
- There is no other tool that allows you to create complex shapes.
- Realism.
- Easy to create work.
Disadvantages of fractal graphics are also present. Firstly, you can’t do without a computer. Moreover, the longer the number of repetitions, the more the processor loads. Accordingly, only high-quality computer equipment can cope with the construction of complex images.
Secondly, there are limitations in the original mathematical figures. Some images cannot be created using fractals.
Similarities and differences between fractal and vector
Vector and fractal graphics are very different:
- On image coding. Vector uses the contours of different geometric shapes, fractal - a mathematical formula, which is based on a triangle.
- 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.
- By analogs. Vector analogues are slides or functions on graphs. In fractals, these are snowflakes or crystals.
Despite the variety 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 - they are all widely used in solving various computer problems. To get a really high-quality image, you need to use each of them.
Unique fractal features
Fractal graphics have no analogues. It is unique in its kind. Firstly, one small section of it can tell immediately about the whole picture or image. Information about the entire fractal is available, because he is self-similar.
In 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 reduced / enlarged copies. That is, one particular element takes part in the compilation of the image.
In order to use fractal graphics, no objects stored in computer memory are needed. You can start creating, having at hand only one mathematical formula.
Conclusion
Fractal graphics are very realistic. This happens because its details and elements are constantly found surrounded by humans - mountains, clouds, sea shores, various natural phenomena. Some of them remain constantly in the same condition, such as trees, rocky areas. The rest is constantly changing, like a flickering fiery flame or blood moving through 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 can get to the bottom of their essence, a person will begin to understand this world much better.