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

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

Fundamentals of fractal graphics

What is fractal graphics? It is one or more each of which is similar to the other. That is, the image is composed of identical 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 drawing. Zooming in doesn't make things worse. The image always remains equally complex.
• Each part of the figure is self-similar.
• There is a mathematical dimension.
• Built with repetition.

Many objects of natural or artificial origin are endowed with the properties of fractals. These include the circulatory systems of humans and animals, 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 using the appropriate equipment. You just need to set the correct mathematical formula and specify the number of repetitions.

How to create a fractal graphic element?

The creation of fractal graphics will differ depending on its classification: geometric, algebraic or stochastic. Regardless of the difference, the result will always be the same. Since fractal graphics start with geometry, you should consider its creation with a corresponding example:

1. Set a condition. This is the shape on which the entire image will be built.
2. Set up a procedure. It transforms the condition.
3. Get a geometric fractal.

The null condition is usually represented as a triangle.

To construct an image, two procedures must be applied. First, DrawTriangle. It builds a triangle based on user-specified points. Second, DrawGenerator. It indicates the number of points. Each procedure can be repeated several times or indefinitely. The numerical argument n is used to determine this indicator.

Other actions with fractal graphics

After a fractal graphic element has been created, various additional actions can be performed with it:

• Turns and stretches. This is how the individual details of the picture are enlarged, or they take the form desired by the user.
• Grouping objects. Usually this function is used to assign the desired scale.
• Color conversion. The image can be painted in any shade, set the tone.
• Changing the shape of an entire object or individual parts.

It must be remembered that the images of fractal graphics are ultimately impossible to predict. When the triangle is too large, the view will be unrealistic, the user will see only a black window. When the desired texture is found, all changes to it must be carried out in a minimal order, constantly maintaining a valid variant.

Programs for generation

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, you need to figure out the most suitable for beginners.

The Art Dabbler product represents the best option if the user has not dealt with its taxes before. 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 the manufacturers have implemented it using the example of a regular Photoshop. If the user has dealt with this program, then he will understand the buttons quickly. The peculiarity of Ultra Fractal is that not only fractal graphics are performed here as a standard and regular image, but also animation. Formulas for compilation are attached, but if necessary, the user will be able to 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 not by archiving, but directly in the file. If you choose it correctly, then compression will occur automatically. There are several algorithms for this procedure.

If the user has an application, most of which is designed in one color, then it is reasonable to use the BMP and PCX formats. Here, a sequence of repeating values ​​is replaced.

A diagram that is very rarely, but still used in fractal graphics, is logically placed in TIFF or GIF.

Some formats are universal. That is, they can be viewed in most editors. But if quality is important to the user, then you need to use the original program.

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

Applications

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

1. Computer graphics. Reliefs and natural objects are depicted realistically. This is used in the creation of computer games.
2. Analysis of stock markets. Fractals are used here to mark repetitions that will later play into the hands of traders.
3. Natural Sciences. In physics, using fractal graphics, nonlinear processes are modeled. In biology, it describes the structure of the circulatory system.
4. to reduce the amount of information.
5. Creation of a decentralized network. Through fractals, it is possible to provide a 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 pipeline has already been launched to create antennas that perfectly receive signals.

Examples

Examples of fractal graphics range from primitive to highly complex repeating elements. The unique feature of this type is that the pattern can be composed exclusively of exclamatory or

Standard, but relatively complex examples of computer fractal graphics are clouds, mountains, sea coasts, and so on. They are often used in the creation of 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 at all. Therefore, it is impossible to construct a tangent.

Advantages and disadvantages

Fractal graphics have recently gained their distribution. it is too vague, 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 lie in several factors:

1. Small size for scale drawing.
2. There is no end to scaling, the complexity of the picture can be increased indefinitely.
3. There is no other tool that will allow you to create complex shapes.
4. Realism.
5. Ease of creating work.

The disadvantages of fractal graphics are also present. First, you can't do without a computer. Moreover, 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 cannot be created using fractals.

Similarities and differences between fractal and vector

Vector and fractal graphics are very different from each other:

1. Image coding. The vector uses the contours of different geometric shapes, the fractal is a mathematical formula based on a triangle.
2. By application. The vector is used wherever you need to get a clear outline. Fractal graphics are more specialized and have found their way into mathematics and art.
3. By analogy. 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 are united by image quality. It remains the same regardless of the zoom level.

Three-dimensional, vector, raster, fractal graphics are similar in one thing - 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 features of fractals

Fractal graphics are unparalleled. She is unique in her kind. Firstly, one small section of it can tell about the whole drawing or image at once. Information about the entire fractal is available, because it is self-similar.

In the center of any image related to this type of graphics, there is an equilateral triangle. All other details of the drawing are either parts of it, or reduced / enlarged copies. That is, one specific 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, having at hand only one mathematical formula.

Conclusion

Fractal graphics are very realistic. This happens because its details and elements are constantly found in the human environment - mountains, clouds, sea shores, various natural phenomena. Some of them remain constantly in the same state, like trees, rocky 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 areas 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 this world much better.

Last year, especially in autumn-winter, when, due to personal circumstances, I turned out to be the farthest from fractal graphics and everything connected with it, they began to ask me questions about writing formulas for generating fractals on my own. Once I had an interest in this area. Probably, if there was additional time, and more - a great desire, then I would have gone headlong into this issue. But I understood that the programming knowledge that I once had during my studies at the university was safely forgotten because it had not been used for too long. Having the most powerful tools for creativity in the form of programs already studied and loved, I did not see the point in looking for something that might not live up to expectations in the end. However, I cannot stay away from the topic, which personally seems to me largely symbolic, since it can become decisive. This is an interest and craving for something new, for development, for uniqueness.
Today I will tell you about one interesting program designed for people who are good at programming.

So - Fractorama. freeware. Program author John F. Dumas is a software engineer, teacher, and has a degree in applied mathematics. The program interface is quite concise. There are two windows in front of you. The first is a text editor in which you need to write formulas, and the second is designed to visualize the result of your work - your own finished fractal.
Let's look at the works from the program gallery:

How are you? It reminds me of three programs at once, but it looks very nice.
Some features of the Fract-O-Rama! (that's what the author calls it).
All fractals are created using the Fract-O-Rama fractal scripting language, which allows you to explore a wider range of fractal types than a number of other fractal generators. The program can run on both win32 and Unix environments due to the fact that it was written using Qt. Comes with full source code. Each download contains documentation and a large number of example formulas. There are different download options available - choose the one that suits you.
If you are interested in the process of creating a fractal in this program, take a look at "About Us".
Here is the gallery: https://fractoramafractalart.com/
Project page on deviantart http://fract-o-rama.deviantart.com/
Let me summarize. Before us is a curious program designed for those who know programming or want to learn. It is difficult to judge the state of the project today, since the latest fractals in the gallery are dated 2015. In any case, the program is worthy of attention.

fractal is a figure with a fractional dimension (not 2D or 3D, but, for example, 1.5D or 2.3D). Thanks to this feature, the figure turns out to be self-similar, i.e. consisting of many parts, each of which is a reduced copy of the whole figure as a whole. The concept of a fractal was introduced into mathematics by an American scientist of Polish origin Benoit Mandelbrot (1924-2010). Here is a classic book on fractals (in djvu format) by the founder of this area of ​​mathematics.

Apophysis

To generate, display fractals and save them as a picture, there are more than a dozen computer programs. Apophysis is one of the most popular. There is a basic version of the program (current version Apophysis 2.09) and an advanced version (Apophysis 7X). The latter has more settings, more varied templates and parameters by which the template can be changed. In both versions, in addition to a static image, you can create a video (morphing one fractal into another). Version 7X provides plugins for creating 3D fractals. The program interface is 90% the same.

The image of fractals is built according to complex mathematical formulas. The mathematical apparatus is hidden from the user of the program, but it is possible to change various parameters of formulas that affect the transformation and color of the final image. One of the simplest scenarios for working with the program: a) choose a template that is closest to what you want to get in the end; b) assign additional transformations in the editor or change the parameters of the transformations specified for this template; c) adjust the color scheme; d) save to disk in a standard png graphic format with a transparent background. Templates are called flames. Saving to disk is called rendering (render flame).

flames

Any distribution of the program includes a large or not so large collection of flames. Each flame is a saved set of fractal parameters. Externally, the user can see the flames in the form of a list in the left part of the program window. This is a list of titles in the form of text or previews. You can switch between display modes using the Classic view and Trumbnail view buttons on the toolbar. Clicking on an item in this list will cause this template to be loaded into the central window of the program and you will see the generated image. The rendering speed of the image depends on the quality setting. The select element on the toolbar with values ​​5, 10, 15, 50 is responsible for this... The higher the quality is set, the longer the image is drawn. And the picture will be redrawn often, with each change of at least one parameter, so I recommend setting the quality to the weakest 5, and increasing it one-time if you still want to consider some details before saving to disk.

In Apophysis 7X, you can generate a new flame by clicking the New button. In both versions, you can use a flame downloaded from the Internet - just open the file from the disk with the flame extension in the program. You can also create a flame yourself as a file on disk - in the File menu, the Save Parameters sub-item.

For beginners, working with the program is not so much a purposeful change of parameters as a choice between options that the program itself has generated. There is a Mutation button on the panel - it randomly creates 8 variations relative to the current flame. In the window that opens - 9 combinations, your initial option is in the center. You can set the program parameter that will participate in mutations.

Editor

The most interesting module of the program is the editor (Editor). In the editor, you fine-tune and fine-tune the formulas (which are still hidden, but you work with their parameters). In the editor, you can also create your own fractal from scratch (the leftmost New Flame button on the editor toolbar). The New Transform button adds a new transformation, which is displayed on the main editor field in the form of a triangle. On the Variations tab, a parameter is selected for transformation and its value is set to something other than 0 (if 0, then the parameter does not participate in the formula). In the Weight field, the weight of the transformation is set (the degree of influence on the entire image). You can read more about working with the editor.

Colors

The color scheme for your fractal can be assigned both for a separate transformation (this is done in the editor on the Colors tab), and for the entire composition (the Gradient button on the Apophysis main window panel). Gradients as well as flames can be saved to disk and shared between users. On the gradient tab, you can adjust the color gamut, contrast, brightness, blur, saturation...

It is probably difficult to find people who would not be fascinated by the contemplation of fractal graphics - in its mysterious elements, someone may imagine the night flame of a fire, someone - long lashes of swaying algae in the water column, someone - the whole mystery of the Universe.
But one way or another, fractal graphics definitely attract our attention, and software packages for its creation can become the stepping stone that will allow you to get closer to real fractal creativity, especially since all of them are relatively easy to learn.
With the use of fractals, not only surreal images can be built, but also quite realistic ones (for example, fractals are often used to create clouds, snow, coastlines, trees and bushes, etc.). Therefore, fractal images can be used in a variety of areas, from creating ordinary textures and background images to fantastic landscapes for computer games or book illustrations. And such fractal masterpieces (as well as vector ones) are created by mathematical calculations, but unlike vector graphics, the basic element of fractal graphics is the mathematical formula itself - this means that no objects are stored in the computer’s memory, and the image (no matter how intricately) is built solely on the basis of equations.
1. Art Dabbler program
It is best to start your acquaintance with the basics of fractal graphics with the Art Dabbler package. This editor (by Fractal Design and now owned by Corel) is actually a truncated version of Painter. This is an excellent program for teaching not only computer graphics, but above all the basics of drawing. The small amount of memory required (only 10 MB is needed to install it), as well as a simple interface accessible even to a child, allow it to be used in the school curriculum. Like the raster editor MS Paint, the fractal editor Art Dabbler is especially effective at the initial stage of mastering computer graphics.
The main attention of the developers of the Art Dabbler package was paid to two factors:

• creating a simplified interface, the main element of which are toolboxes (here called drawers);
• the possibility of using the package as a training program. To realize this goal, along with the program itself, the "Learn to draw" tutorial and a training film on a CD are included in the package. The drawing lessons offered in them allow you to observe step by step the process of creating color images by experienced artists using the Art Dabbler package.

The menu bar includes six items: standard for most programs - File, Edit and Help, as well as Effects, Options and Tutors, which are present in most graphics programs and do not need additional comments.
Art Dabbler provides a set of effects (Effects menu) that can be used to alter or distort images. For example, the Texturize effect creates textures for paper, canvas, and more, expanding the artist's creative options.
It should be noted that in Art Dabbler all tools are called drawers in the same way as, for example, similar tools are called palettes in Photoshop, and dockers in CorelDRAW. They store brushes, pencils, an elastic band and other tools, to activate them, just click the icon corresponding to them. On the front walls of the drawers, a small number of buttons and a handle are displayed, by pressing which the user gets access to the entire set of operations carried out through it thanks to the additional buttons that open.
Download
2. Ultra Fractal program
Ultra Fractal is the best solution for creating unique professional quality fractal images. The package features a user-friendly interface, many elements of which are reminiscent of Photoshop (which makes it easy to learn), and is accompanied by incredibly detailed and beautifully illustrated documentation with a series of tutorials that walk through all aspects of working with the program step by step. Ultra Fractal is represented by two There are several editions: Standard Edition and extended Animation Edition, the capabilities of which allow not only generating fractal images, but also creating animation based on them. Created images can be rendered in high resolution, suitable for printing, and saved in the program's own format or in one of the popular fractal formats. Rendered images can also be exported to one of the raster graphic formats (jpg, bmp, png and psd), and finished fractal animations can be exported to AVI format.
The principle of creating fractal images is quite traditional, the simplest thing is to use one of the formulas included in the delivery (the built-in browser will help you navigate the possible type of image generated by the selected formula), and then edit the formula parameters in the desired way. And if the experiment was unsuccessful, then the last action is easy to cancel. There are a lot of ready-made fractal formulas, and their number can be expanded by downloading new formulas from the program website. Advanced users can try their luck in creating their own formula, for which the package has a built-in text editor with support for basic templates based on standard fractal formula programming language constructs.
However, one should not think that the mystery of a fractal image lies only in a successful formula. Other aspects are no less important. For example, color tuning, which involves choosing a color option and fine-tuning its parameters. Color adjustment is implemented at the level of solid graphics packages, for example, gradients can be created and adjusted independently, adjusting many parameters, including translucency, and saving them in the library for later use. The use of layers with the ability to change their blending modes and adjust the translucency allows you to generate multilayer fractals and achieve unique effects by superimposing fractal images on each other. The use of opacity masks provides masking of certain areas of the image. Transformation filters allow you to perform various transformations on selected image fragments: scale, mirror, crop according to a pattern, distort by swirling or ripples, multiply by the kaleidoscope principle, etc.
Download
3. Fractal Explorer

Fractal Explorer is a program for creating images of fractals and 3D attractors with quite impressive features. It has an intuitive classic interface that can be customized according to user preferences and supports standard fractal image formats (*.frp; *.frs; *.fri; *.fro; *.fr3, *.fr4, etc.) . Ready fractal images are saved in *.frs format and can be exported to one of the raster graphic formats (jpg, bmp, png and gif), and fractal animations are saved as AVI files.
Fractal generation is possible in two ways - based on basic fractal images built according to the formulas included in the delivery, or from scratch. The first option allows you to get interesting results relatively easily, because it is not difficult to choose the appropriate formula, especially since a convenient file browser will allow you to evaluate the quality of a fractal from the database even before creating a fractal image based on it. For a fractal image obtained in this way, you can change the color palette, add a background image to it, and determine the blending mode of the fractal and background layers, as well as the degree of transparency of the fractal layer. Then it will be possible to transform the fractal image, scale it if necessary, determine the size of the image and render it. Creating an image from scratch is much more difficult and involves choosing one of two methods. You can choose the type of fractal from almost 150 options. And then move on to changing various parameters: setting the palette, background, etc. Or you can try creating your own custom formula using the built-in compiler. Before rendering the finished image, it may be necessary to perform automatic color balance correction and / or manual correction of brightness, contrast and saturation.
Download
4. Program ChaosPro
ChaosPro is one of the best free fractal image generators with which you can easily create an endless number of amazingly beautiful fractal images. The program has a very simple and user-friendly interface and, along with the ability to automatically generate fractals, allows you to fully control this process by changing a large number of settings (number of iterations, color palette, blur level, projection features, image size, etc.). In addition, the created images can be multi-layered (layer blending mode can be controlled) and a whole series of filters can be applied to them. All changes applied to the fractals under construction are immediately reflected in the viewing window. The created fractals can be saved in the program's own format, or in one of the main fractal types thanks to the built-in compiler. Or exported to raster images or 3D objects (if a three-dimensional representation of the fractal was previously obtained).
In the list of program features:

• precise color adjustment, providing smooth gradient transitions of colors into each other;
• simultaneous construction of several fractals in different windows;
• the ability to create animation based on fractal images with the definition of key animation phases, which can differ in any variable parameter: rotation and rotation angles, color parameters, etc.;
• creation of three-dimensional representations of fractals based on ordinary two-dimensional images;
• support for many standard fractal image formats, images in which can be imported and edited in the ChaosPro environment.

Download
5. Apophysis Program
Apophysis is an interesting tool
nt for generating fractals based on basic fractal formulas. Fractals created according to ready-made formulas can be edited and unrecognizably changed by adjusting various parameters. So, for example, they can be transformed in the editor, either by changing the triangles underlying the fractals, or by applying the transformation method you like: wave-like distortion, perspective, Gaussian blur, etc. Then you should experiment with colors by choosing one of the basic gradient fill options. The list of built-in fills is quite impressive, and if necessary, you can automatically select the most suitable fill for an existing bitmap, which is important, for example, when creating a fractal background in the same style as other images of a certain project. If necessary, it is easy to adjust the gamma and brightness, change the background, scale the fractal object and clarify its location on the background. You can also subject the result to various mutations in the desired style. Upon completion, you should set the dimensions of the final fractal image and save its rendered version as a graphic file (jpg, bmp, png).
Download
6. Program Mystica
Mystica is a versatile generator of unique fantastic 2D and 3D images and textures that can later be used in various projects, for example as real textures for Web pages, desktop backgrounds or fantastic background images that can be used, for example, in
design of children's books. The package has a non-standard and rather complex interface and can work in two modes: Sample (focused on beginners and contains a minimum of settings) and Expert (designed for professionals). Created images can be any size and then exported to popular 2D graphics formats. Directly from the program window, they can be sent by e-mail, published in an Html gallery, or based on them, create a video in divx, mpeg4 formats, etc. The built-in 3D engine of the program can be used to create 3D scenes for computer games, such as fantastic backgrounds and landscapes .
Images are generated based on the fractal formulas embedded in the package, and the image preparation system is multi-level and includes a very detailed color setting, the possibility of simple transformations of the generated elements and a lot of other transformations. Among them are the use of filters, changing lighting, adjusting the color gamut, brightness and contrast, changing the material used in the generation, adding "chaotic" structures to the image, etc.
Download
Fractal images are used in a variety of areas, from creating simple textures and background images to fantastic landscapes for computer games or book illustrations. Fractal images are created by mathematical calculations. The basic element of fractal graphics is the mathematical formula itself - this means that no objects are stored in the computer's memory, and the image is built solely on the basis of equations.
The mystery of a fractal image does not lie in just one successful formula. Other aspects are no less important. For example, color adjustment, transformation filters, etc.
There are a lot of programs for creating fractal images. These programs have their advantages and disadvantages. With the development of technology, the number of programs is increasing, and their quality and capabilities are improving.

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In the world of fractal graphics

Svetlana Shlyakhtina

It is probably difficult to find people who would not be fascinated by the contemplation of fractal graphics - in its mysterious elements, someone may imagine the night flame of a fire, someone - long lashes of swaying algae in the water column, someone - the whole mystery of the Universe.

But one way or another, fractal graphics definitely attract our attention, and software packages for its creation can become the stepping stone that will allow you to get closer to real fractal creativity, especially since all of them are relatively easy to learn.

With the use of fractals, not only surreal images can be built, but also quite realistic ones (for example, fractals are often used to create clouds, snow, coastlines, trees and bushes, etc.). Therefore, fractal images can be used in a variety of areas, from creating ordinary textures and background images to fantastic landscapes for computer games or book illustrations. And such fractal masterpieces (as well as vector ones) are created by mathematical calculations, but unlike vector graphics, the basic element of fractal graphics is the mathematical formula itself - this means that no objects are stored in the computer’s memory, and the image (no matter how intricately) is built solely on the basis of equations.

There are not so many programs for generating fractal images on the market, and it is problematic to find them in popular software catalogs. Existing solutions are mostly free and developed by enthusiasts (of course, very unstable), although there are quite solid commercial options. Let's try to cover the most interesting of them.

Ultra Fractal

Developer: Frederik Slijkerman
Program website:
http://www.ultrafractal.com/
Distribution size: 5 MB
Distribution method: shareware (watermark demos: Ultra Fractal Animation Edition - http://www.ultrafractal.com/uf403ani.exe, Ultra Fractal Standard Edition - http://www.ultrafractal.com/uf403std.exe)
Price: Ultra Fractal Animation Edition - $129, Ultra Fractal Standard Edition - $59
Work under control:
Windows 98/2000/XP/2003

Ultra Fractal is the best solution for creating unique professional quality fractal images. The package features a user-friendly interface, many elements of which are reminiscent of Photoshop (which makes it easy to learn), and is accompanied by incredibly detailed and beautifully illustrated documentation with a series of tutorials that walk through all aspects of working with the program step by step. Ultra Fractal is presented in two editions: Standard Edition and extended Animation Edition, the capabilities of which allow not only generating fractal images, but also creating animation based on them. Created images can be rendered in high resolution, suitable for printing, and saved in the program's own format or in one of the popular fractal formats. Rendered images can also be exported to one of the raster graphic formats (jpg, bmp, png and psd), and finished fractal animations can be exported to AVI format.

The principle of creating fractal images is quite traditional, the simplest thing is to use one of the formulas included in the delivery (the built-in browser will help you navigate the possible type of image generated by the selected formula), and then edit the formula parameters in the desired way. And if the experiment was unsuccessful, then the last action is easy to cancel. There are a lot of ready-made fractal formulas, and their number can be expanded by downloading new formulas from the program website. Advanced users can try their luck in creating their own formula, for which the package has a built-in text editor with support for basic templates based on standard fractal formula programming language constructs.

However, one should not think that the mystery of a fractal image lies only in a successful formula. Other aspects are no less important. For example, color tuning, which involves choosing a color option and fine-tuning its parameters. Color adjustment is implemented at the level of solid graphics packages, for example, gradients can be created and adjusted independently, adjusting many parameters, including translucency, and saving them in the library for later use. The use of layers with the ability to change their blending modes and adjust the translucency allows you to generate multilayer fractals and achieve unique effects by superimposing fractal images on each other. The use of opacity masks provides masking of certain areas of the image. Transformation filters allow you to perform various transformations on selected image fragments: scale, mirror, crop according to a pattern, distort by swirling or ripples, multiply by the kaleidoscope principle, etc.

fractal explorer

Developer:
Sirotinsky Arthur, Olga Fedorenko
Program website: http://www.eclectasy.com/Fractal-Explorer/index.html
Distribution size: 1.46 MB
Distribution method:
freeware (http://www.eclectasy.com/Fractal-Explorer/download.htm)
Price: is free
Work under control:
Windows 95/98/ME/NT/2000/XP

Fractal Explorer is a program for creating images of fractals and 3D attractors with quite impressive features. It has an intuitive classic interface that can be customized according to user preferences and supports standard fractal image formats (*.frp; *.frs; *.fri; *.fro; *.fr3, *.fr4, etc.) . Ready fractal images are saved in *.frs format and can be exported to one of the raster graphic formats (jpg, bmp, png and gif), and fractal animations are saved as AVI files.

Fractal generation is possible in two ways - based on basic fractal images built according to the formulas included in the delivery, or from scratch. The first option allows you to get interesting results relatively easily, because choosing the right formula is easy, especially since a convenient file browser will allow you to evaluate the quality of a fractal from the database even before creating a fractal image based on it. For a fractal image obtained in this way, you can change the color palette, add a background image to it, and determine the blending mode of the fractal and background layers, as well as the degree of transparency of the fractal layer. Then it will be possible to transform the fractal image, scale it if necessary, determine the size of the image and render it. Creating an image from scratch is much more difficult and involves choosing one of two methods. You can choose the type of fractal (classical Mandelbrot, cubic Mandelbrot, etc.) from almost 150 options. And then move on to changing various parameters: setting the palette, background, etc. Or you can try creating your own custom formula using the built-in compiler. Before rendering the finished image, it may be necessary to perform automatic color balance correction and / or manual correction of brightness, contrast and saturation.

ChaosPro

Developer: Martin Pfingstl
Program website:
http://www.chaospro.de/
Distribution size: 5 MB
Distribution method: freeware
(http://www.chaospro.de/cpro32.exe)
Price: is free
Work under control:
Windows 95/98/Me/NT/2000/XP

ChaosPro is one of the best free fractal image generators with which you can easily create an endless number of amazingly beautiful fractal images. The program has a very simple and user-friendly interface and, along with the ability to automatically generate fractals, allows you to fully control this process by changing a large number of settings (number of iterations, color palette, blur level, projection features, image size, etc.). In addition, the created images can be multi-layered (layer blending mode can be controlled) and a whole series of filters can be applied to them. All changes applied to the fractals under construction are immediately reflected in the viewing window. The created fractals can be saved in the program's own format, or in one of the main fractal types thanks to the built-in compiler. Or exported to raster images or 3D objects (if a three-dimensional representation of the fractal was previously obtained).

In the list of program features:
- accurate color adjustment, providing smooth gradient transitions of colors into each other;
- simultaneous construction of several fractals in different windows;
- the ability to create animation based on fractal images with the definition of key animation phases, which can differ in any variable parameter: rotation and rotation angles, color parameters, etc.;
- creation of three-dimensional representations of fractals based on ordinary two-dimensional images;
- support for many standard fractal image formats, images in which can be imported and edited in the ChaosPro environment.

Apophysis

Developer:
Mark Townsend, Peter Sdobnov, Piotr Borys, Susan Chambless, Ronald Hordijk
Program website:
http://www.apophysis.org/
Distribution size: 1.21 MB
Distribution method: freeware()
Price: is free
Work under control: Windows (all)

Apophysis is an interesting tool for generating fractals based on basic fractal formulas. Fractals created according to ready-made formulas can be edited and unrecognizably changed by adjusting various parameters. So, for example, they can be transformed in the editor, either by changing the triangles underlying the fractals, or by applying the transformation method you like: wave-like distortion, perspective, Gaussian blur, etc. Then you should experiment with colors by choosing one of the basic gradient fill options. The list of built-in fills is quite impressive, and if necessary, you can automatically select the most suitable fill for an existing bitmap, which is important, for example, when creating a fractal background in the same style as other images of a certain project. If necessary, it is easy to adjust the gamma and brightness, change the background, scale the fractal object and clarify its location on the background. You can also subject the result to various mutations in the desired style. Upon completion, you should set the dimensions of the final fractal image and save its rendered version as a graphic file (jpg, bmp, png).

Chaoscope

Developer: Nicolas Desprez
Program website: http://www.btinternet.com/~ndesprez/index.htm
Distribution size: 2.5 MB
Distribution method:
freeware (http://www.btinternet.com/~ndesprez/download/chaoscope_0_3_1_setup.exe)
Price: is free
Work under control: Windows (all)

Chaoscope is a program for generating conventional 2D fractal images and obtaining their 3D representations during rendering. Created 2D and 3D fractal images are saved in the program's own formats or exported to bmp format.

Two-dimensional fractals can be generated in two ways. You can open one of the built-in fractal image library projects and modify it in the intended way by adjusting the parameter values ​​and choosing a color palette. And you can create a new image based on a certain type of fractal - in this case, you will not see any image in the working window, since all parameters characterizing this type are initially equal to zero. Therefore, it is required to determine their values, which is very problematic for an unprepared user manually - there are many parameters, and their specific names (p1, p2, p3, etc.) do not mean anything, and they are not described in Help either. It is wiser to go the other way - use the Attractor=>Search command, and the program itself will find the necessary values ​​for a possible fractal image. In this way, using the Search command a couple of dozen times, you can find some interesting option, for further refinement of which you still have to turn to the options and color palettes. At the last stage, you may need to perform color auto-correction. After that, you can immediately export the fractal image to bmp-format, or visualize it, during which its three-dimensional fractal analogue will be generated.

Mystic

Developer: Thomas Renn
Program website:
http://www.dawntec.com/mystica/
Distribution size: 4 MB
Distribution method: shareware (30 day demo that adds a watermark to images - http://www.dawntec.com/mystica/Download/Mystica.exe)
Price: $15
Work under control:
Windows 95/98/Me/NT/2000/XP

Mystica is a versatile generator of unique fantastic 2D and 3D images and textures that can later be used in various projects, for example as real textures for Web pages, desktop backgrounds or fantastic background images that can be used, for example, when decorating children's rooms. books. The package has a non-standard and rather complex interface and can work in two modes: Sample (focused on beginners and contains a minimum of settings) and Expert (designed for professionals). Created images can be any size and then exported to popular 2D graphics formats. Directly from the program window, they can be sent by e-mail, published in an Html gallery, or based on them, create a video in divx, mpeg4 formats, etc. The built-in 3D engine of the program can be used to create 3D scenes for computer games, such as fantastic backgrounds and landscapes .

Images are generated based on the fractal formulas embedded in the package, and the image preparation system is multi-level and includes a very detailed color setting, the possibility of simple transformations of the generated elements and a lot of other transformations. Among them are the use of filters, changing lighting, adjusting the color gamut, brightness and contrast, changing the material used in the generation, adding "chaotic" structures to the image, etc.

fractal extreme

Developer: Cygnus Software
Program website:
http://www.cygnus-software.com/
Distribution size: 2.95 MB
Distribution method: shareware (15 day demo - ftp://ftp.cygnus-software.com/pub/fxsetup.exe)
Price: $34,95
Work under control:
Windows 9x/Me/NT/2000/XP

Fractal Extreme is a simple and quite functional (albeit heavily overpriced) program for generating 2D fractal images, which are usually created by converting basic images or by yourself based on a suitable type of fractal. Setting the parameters of a fractal image includes adjusting the number of iterations, setting the color palette and the nature of the projection. In addition, the fractal image is easy to scale and crop, as well as fit to the required size. If desired, you can generate fractals randomly using the Options=>Plug-In Setup command. Created images are saved as projects in native format or can be exported to bmp format.

fractal world

Developer: YurkinSoft
Program website:
http://yurkinsoft.chat.ru/rus/fractal_r.htm
Distribution size: 740 KB
Distribution method: shareware (30-day demo - http://yurkinsoft.chat.ru/frac_arc.exe)
Price: 135 rub.
Work under control:
Windows 95/98/Me/NT/2000/XP

Fractal World is a simple generator of full screen fractal images that can be created either completely automatically or by defining your own initial parameters. The most liked images are easy to save and use as screensavers for your desktop. The simple interface of the program and its modest size make it possible to recommend its use in the educational process when students study different types of graphics.

Fractal Snowflake Generator

Developer: a-i-studio.com
Program website:
http://a-i-studio.com/snowflake/
Distribution size: 565 KB
Distribution method: Shareware (demo version with save limit - http://a-i-studio.com/snowflake/fsnowgen_setup.exe)
Price: $10
Work under control:
Windows 98/Me/NT4/2000/XP

Fractal Snowflake Generator is a generator of fractal snowflakes with which you can decorate your personal website on the eve of the New Year or a New Year's card created by yourself, for example in Photoshop. The program not only can work in fully automatic mode, generating snowflakes randomly, but if desired, the generation process can also be controlled by determining the size, proportions, rotation of the snowflake, the colors of the snowflakes and the background, etc. The created snowflakes in the demo version can only be saved as a bitmap image by pressing the Print Screen key. After payment, there is an additional opportunity to save snowflakes as a vector image in Adobe Illustrator formats, which allows you to subject snowflakes to further processing and use, for example, when creating appropriate children's illustrations, backgrounds for Web pages, etc.