Three-dimensional graphics operate with objects in three-dimensional space. Usually the results are a flat picture, a projection. 3D computer graphics are widely used in cinema, computer games Oh. In three dimensions computer graphics all objects are represented as a collection of surfaces or particles. The minimal surface is called a polygon. Triangles are usually chosen as polygons.

All visual transformations in 3 D-graphics are controlled by three types of matrix: rotation, shift and scaling. Any polygon can be represented as a set of coordinates of its vertices. So, the triangle will have 3 vertices. The coordinates of each vertex are a vector ( x, y, z). By multiplying the vector by the corresponding matrix, we get a new vector. Having made such a transformation with all the vertices of the polygon, we get a new polygon, and having transformed all the polygons, we get a new object, rotated/shifted/scaled relative to the original one.

Three-dimensional graphics have found wide application in such areas as scientific calculations, engineering design, computer modeling of physical objects, and the real physical body.

Rice. 6. Example 3 D-graphs.Fig. 7. Fractal example

In a simplified form, for spatial modeling of an object it is required: to design and create a virtual frame (“skeleton”) of the object that most fully corresponds to its real shape; design and create virtual materials that are similar in physical visualization properties to real ones; assign materials to different parts of the surface of an object (in professional jargon - “project textures onto an object”); configure the physical parameters of the space in which the object will operate - set lighting, gravity, atmospheric properties, properties of interacting objects and surfaces; set the trajectories of objects; calculate the resulting sequence of frames; apply surface effects to the final animation video.

1.5 Fractal graphics

Fractal- an object whose individual elements inherit the properties of parent structures. Since a more detailed description of smaller-scale elements occurs using a simple algorithm, such an object can be described with just a few mathematical equations.

Fractals make it possible to describe entire classes of images, the detailed description of which requires relatively little memory. On the other hand, fractals are poorly applicable to images outside of these classes.

A fractal is an object of infinite complexity, allowing you to see as many of its details up close as from afar. The Earth is a classic example of a fractal object. From space it looks like a ball. If we approach it, we will find oceans, continents, coastlines and mountain ranges. Let's look at the mountains closer - even finer details will become visible: a piece of land on the surface of the mountain, in its scale, is as complex and uneven as the mountain itself. And even greater magnification will reveal tiny particles of soil, each of which is itself a fractal object.

By changing and combining the color of fractal figures, you can simulate images of living and inanimate nature (for example, tree branches or snowflakes), and also create a “fractal composition” from the resulting figures.

Fractal graphics, like vector and three-dimensional graphics, are computational. Its main difference is that the image is constructed using an equation or system of equations. Therefore, in order to perform all calculations, nothing needs to be stored in the computer memory except the formula.

It is probably difficult to find people who would not be fascinated by the contemplation of fractal graphics - in its mysterious elements, some may imagine the night flames of a fire, for others - long lashes of swaying algae in the water column, for others - 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 step that will allow us to get closer to real fractal creativity, especially since they are all relatively easy to learn.
Using fractals, not only surreal images can be constructed, 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, ranging from creating ordinary textures and background images and ending with fantastic landscapes for computer games or book illustrations. And such fractal masterpieces (as well as vector ones) are created through 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 intricate it is) is built solely on the basis of equations.
1. Art Dabbler program
It is best to start getting acquainted with the basics of fractal graphics with the Art Dabbler package. This editor (created by Fractal Design and now owned by Corel) is essentially a stripped-down version of the Painter program. This is an excellent program for teaching not only computer graphics, but especially the basics of drawing. The small amount of memory required (only 10 MB is needed to install it), as well as a simple interface that is 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 developers of the Art Dabbler package focused on two factors:

• creating a simplified interface, the main element of which is tool kit boxes (called here drawers);
• the possibility of using the package as a training program. To achieve this goal, the package, along with the program itself, includes a self-instruction manual “Learn to Draw” and an educational film on a CD. The drawing lessons they offer allow you to watch step by step the process of how experienced artists create color images 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 change or distort images. For example, the Texturize effect creates textures on paper, canvas, etc., expanding the artist's creative capabilities.
It should be noted that in Art Dabbler all tools are called drawers in the same way that, for example, in Photoshop similar tools are called palettes, and in CorelDRAW - dockers. They store brushes, pencils, erasers and other tools, to activate which you just need to click the corresponding icon. On the front walls of the drawers there is a small number of buttons and a handle, by pressing which the user gains access to the entire set of operations carried out through it thanks to the additional buttons that open.
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2. Ultra Fractal program
Ultra Fractal - The best decision to create unique fractal images of professional quality. The package features a user-friendly interface, with many elements 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 you step-by-step through every aspect of working with the program. Ultra Fractal is presented in two There are two editions: Standard Edition and extended Animation Edition, the capabilities of which allow you not only to generate fractal images, but also to create animation based on them. The created images can be visualized 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 to AVI format.
The principle of creating fractal images is quite traditional; the simplest thing is to use one of the supplied formulas (the built-in browser will help you navigate the possible appearance of the image generated by the selected formula), and then edit the formula parameters in the desired way. And if the experiment was unsuccessful, then latest actions 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. Experienced 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 constructs of the fractal formula programming language.
However, you should not think that the mystery of the fractal image lies only in a successful formula. Other aspects are no less important. For example, color settings, which involve choosing a color option and fine-tuning its parameters. Color adjustment is implemented at the level of reputable graphics packages; for example, gradients can be created and configured 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 translucency allows you to generate multi-layer fractals and, by superimposing fractal images on top of each other, achieve unique effects. Using opacity masks ensures that certain areas of the image are masked. Transformation filters allow you to perform various transformations on selected image fragments: scale, mirror, crop according to a pattern, distort through swirl or ripple, multiply like a kaleidoscope, etc.
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3. Fractal Explorer program

Fractal Explorer is a program for creating images of fractals and three-dimensional attractors with quite impressive capabilities. 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.) . Finished 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.
Generation of fractals is possible in two ways - based on basic fractal images constructed using the supplied formulas, or from scratch. The first option makes it possible to obtain interesting results relatively simply, because choosing the appropriate formula is not difficult, 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. The fractal image obtained in this way can change the color palette, add a background image to it and determine the mixing 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 dimensions 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 fractal type from almost 150 options. And then move on to changing various parameters: setting the palette, background, etc. Or you can try to create 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.
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4. ChaosPro program
ChaosPro is one of the best free fractal image generators, with which you can easily create an endless variety of amazingly beautiful fractal images. The program is very simple and user-friendly interface and along with the ability to automatically construct fractals, it allows you to fully control this process by changing a large number of settings (number of iterations, color palette, degree of blur, projection features, image size, etc.). In addition, the created images can be multi-layered (the layer blending mode can be controlled) and a whole series of filters can be applied to them. All changes imposed on the fractals being constructed 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 presence of a built-in compiler. Or exported to raster images or 3D objects (if a 3D representation of the fractal was previously obtained).
The list of program features:

• precise color adjustment, ensuring 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: angles of rotation and rotation, color parameters, etc.;
• creating 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.

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5. Apophysis program
Apophysis - interesting tool
nt for generating fractals based on basic fractal formulas. Fractals created using ready-made formulas can be edited and changed beyond recognition by adjusting various parameters. So, for example, in the editor you can transform them, 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, 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 the existing one raster image, which is relevant, 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 write its visualized version in the form graphic file(jpg, bmp, png).
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6. Mystica program
Mystica is a universal 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,
design of children's books. The package has a non-standard and rather complex interface and can work in two modes: Sample (targeted for beginners and contains a minimum of settings) and Expert (intended for professionals). The generated images can be any size and then exported to popular 2D graphics formats. You can send them directly from the program window via e-mail, publish in an Html gallery or create a video based on them in divx formats, mpeg4, etc. The program's built-in 3D engine can be used to create 3D scenes for computer games, such as fantastic backgrounds and landscapes.
Image generation is carried out on the basis of fractal formulas embedded in the package, and the image preparation system is multi-level and includes very detailed setup colors, the possibility of simple transformations of generated elements and a lot of other transformations. These include applying filters, changing lighting, adjusting colors, brightness and contrast, changing the material used in generation, adding “chaotic” structures to the image, etc.
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Fractal images are used in a variety of areas, from creating ordinary textures and background images to fantastic landscapes for computer games or book illustrations. Fractal images are created through mathematical calculations. Basic element Fractal graphics is a mathematical formula itself - this means that no objects are stored in the computer's memory, and the image is constructed 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 settings, transformation filters, etc.
There are many programs for creating fractal images. These programs have their advantages and disadvantages. With the development of technology, the number of programs increases, and their quality and capabilities improve. Apophysis - a program for creating fractals

Apophysis - a program for creating fractals

A fractal is a holistic geometric figure consisting of separate parts, each of which is similar to the whole. Fractals are very popular in web design as they represent a combination of simplicity and hypnotic beauty.

For those who want to learn how to draw fractals there is free program Apophysis. Despite the English interface, the program is quite understandable, but at the same time it has a large number of settings and functions that allow you to achieve unique effects. In addition to the program, you can download special plugins.

Installation is very simple. Using this program you can get the following effects:

This is what the program interface looks like:

You can enlarge it by clicking on the screenshot. The program interface consists of the following parts:

1. Menu. It contains all the program commands, starting with opening a file, processing the image and ending with saving the fractal to the computer.

2. Toolbar - a list of the most frequently used functions.

3. Flames. This is what the program calls a list of ready-made fractals, by modifying which you can get new fractal images.

4. View the fractal diagram. All changes in the fractal that occur as a result of modifications are displayed here.

5. The status bar (not marked in the screenshot) is located at the very bottom of the program. It informs us about the time it takes to repel the flame.

Stages of work in the Apophysis program:

1. Create a new flame (CTRL+N) or File - New

3. Now you need to open the created file using the CTRL+O or File -Open keys.

4. Change the image parameters at your discretion (more on this below).

5. Save the flame to your computer using CTRL+S or the button. In order to save the fractal to your computer, press the Ctrl + R button or the button and select required format(PNG or JPG) images.

Main functions of the Apophysis program:

Editor. Using this command you can control the components of fractals. In the window that opens, you can manually (using the mouse) change these components, resize, rotate, add, delete, move, etc.

Gradient changes the color scheme of the fractal.

Adjust brings up a control panel for the color scheme of the fractal, its background, its coordinates and other program settings.

Mathematics is literally permeated with harmony, and fractal graphics are direct confirmation of this. Science is present in the creation of every element, 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 basis, one integration. But if the code begins to repeat itself, then a person appears.

Basics of Fractal Graphics

What is fractal graphics? This is one or more, each of which is similar to the other. That is, the image is made up 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 entire image is examined, the fragment is similar to the entire picture. Increasing the scale does not lead to deterioration. The image always remains equally complex.
• Each part of the drawing is self-similar.
• There is a mathematical dimension.
• Builds through 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 one mathematical formula and indicate the number of repetitions.

How to create a fractal graphic element?

The creation of 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, we should consider its creation using an appropriate example:

1. Set the condition. This is the figure on which the entire image will be based.
2. Set the procedure. It transforms the condition.
3. A geometric fractal is obtained.

Typically the null condition is represented as a triangle.

To construct an image, you need to apply two procedures. First, DrawTriangle. It constructs a triangle using 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 actions with fractal graphics

Once a fractal graphics element has been created, you can perform various additional actions with it:

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

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

Generating programs

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

The Art Dabbler product is the best option if the user has not dealt with its taxes before. Here you can not only master graphics, but also learn how to draw on a computer. Other advantages include a small amount of memory footprint 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 complex, but the manufacturers implemented it using the example of regular Photoshop. If the user has dealt with this program, then he will quickly understand the buttons. The peculiarity of Ultra Fractal is that it performs not only fractal graphics as a standard and ordinary image, but also animation. Formulas for compiling are included, 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 need to be compressed. Moreover, this should not be done through archiving, but directly in the file. If you select it correctly, compression will occur automatically. There are several algorithms for this procedure.

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

It is logical to place a diagram that is very rarely, 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 quality is important to the user, then you need to use the original program.

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

Areas of application

The use of fractal graphics can be called virtually ubiquitous. Moreover, this area is constantly expanding. On this 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, which will later work to the traders' advantage.
3. Natural Sciences. In physics, fractal graphics are used to model nonlinear processes. 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, rather than through central regulation. Therefore, the network becomes more stable.

Currently, 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. A unique feature of this type is that the pattern can be composed exclusively of exclamation or

Standard but relatively complex examples of computer fractal graphics are clouds, mountains, sea coasts, and so on. They are often used when creating games.

The most simple example can be called the Koch curve. Firstly, it has no specific length and is called infinite. Secondly, there is a complete lack of smoothness here. Therefore it is impossible to construct a tangent.

Advantages and disadvantages

Fractal graphics have recently become widespread. it is too blurred because there is no normal theoretical basis. The terminology and principles of its use have not been fully studied, despite the fact that they are effective and working.

The advantages of fractal graphics lie in several factors:

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

Disadvantages of fractal graphics are also present. Firstly, you can’t do without a computer here. Moreover, the longer the number of repetitions, the more the processor is loaded. 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 from each other:

1. On image coding. A vector uses the contours of various geometric shapes, a 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; they have found their application in mathematics and art.
3. By analogy. Vector analogues are slides or functions on charts. For fractals these are snowflakes or crystals.

Despite the diversity 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 truly high-quality image, you need to use each of them.

Unique features of fractals

Fractal graphics have no analogues. She is unique in her own way. Firstly, one small section of it can immediately tell about the entire drawing or image. Information about the entire fractal is available, because it is self-similar.

In the center of any image related to this type graphics, an equilateral triangle is located. All other details of the picture are either parts of it or reduced/enlarged copies. That is, one specific element takes part in composing the image.

In order to use fractal graphics, you do not need any objects stored in the computer's memory. You can start creating with only one mathematical formula at hand.

Conclusion

The fractal graphics are very realistic. This happens because its details and elements are constantly found in the human environment - mountains, clouds, seashores, various natural phenomena. Some of them remain constantly in the same state, such as 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 them, people will begin to understand this world much better.

(tab=Mandelbulber}

Mandelbulber - an experimental application designed to create and work with 3D Mandelbrot fractals as well as with some other types of 3D fractals, such as Mandelbox, Bulbbox, Juliabulb, Menger sponge, etc.
Features: excellent flexibility for working with 3D fractals, working with lighting, shadows, color, support for ambient occlusion effects, depth of field, etc.
Unlimited image resolution on 64-bit systems. Easy to use 3D fractal navigator. Animation support. Mac and Win versions. Free.

Official site:

(tab=Apophysis 7x}

Apophysis 7x The Apophysis fractal generator has many features for creating and editing 2D fractals, including an editor that allows you to directly edit a fractal by manipulating triangles (a kind of transformation blocks). The mutation function applies random editing of triangles. Adjust the size of program windows to suit your needs. Serious capabilities for manipulating fractal color and even a scripting language with direct access to most fractal components. Animation support. Export and then render to programs such as FLAM3 and Chaotica. Support for several languages, Russian, unfortunately, not yet. Lots of plugins that allow you to achieve incredible results with fractals. Free.

Official site: Apophysis 7x

Work examples:

(tab=Ultra Fractal)

Ultra Fractal- fractal generator allows you to create images of fractal sets, as well as perform their animation. The process of constructing images is determined by a set of algorithms that describe the types of visualized fractals, methods for coloring them, and transformations applied to them.
Features: modular architecture allows you not only to use algorithms already created by someone, but also to create your own. built-in programming language. Unique options for working with color and gradients.The ability to work with alpha channels, layers and masks has been implemented, which makes it easy to combine different image fragments. Conditionally free.

Official site: Ultrafractal

Work examples (selected from the official website gallery)

(tab=Xenodream}

Xenodream - a unique program for creating fractal 3D graphics. Creating or studying from the simplest shapes to complex recursive 3D structures, experimenting with lighting and textures. Export textures or depth maps for other rendering programs. Creating stereograms, animations and much more. The program is intended for both professionals and those who like to have fun creating fantastic 3D models.

Conditionally free.

Official site

Sample images:

(tab=JWildFire)

JWildFire is a relatively good and at the same time powerful fractal graphics editor. In terms of functionality, it can be compared with the well-known Apophysis program. Just like Apophysis, JWildFire works with flames, but unlike Apophysis, written in Delphi, JWildFire is written in Java.

Key features of the program are:

1. -the ability to use stunning 3D effects such as waves, ripples on the water, etc.
2. -3D overlay effects
3. -powerful built-in flame editor-T.I.N.A.
4. -built-in image generator (the ability to generate images with clouds, plasma, etc.)
5. -many effects of image processing in 2D (eg: Rotation, twisting, destruction, etc.)
6. -simple yet powerful user interface that allows you to animate almost any parameter in just a few mouse clicks
7. -integration with Sunflow for High Quality visualization.

The main differences from Apophysis are the following:

With JWildfire, the editor previews in real time. - But Apo's viewing is more accurate.

JWildfire allows you to use flames as plugins (Variations)

JWildfire has HDR output (32 bits per channel)

JWildfire has a Pseudo3D shader which gives more realistic results for 3D rendering.

A huge set of plugins has been created for Apo, but they cannot all be used together. JWildfire has a smaller set, but still has a fairly large number of plugins built in that can be used all together.

JWildfire has a built-in compiler for creating your own plugins on the fly.

The JWildfire platform is independent and very stable - but in Apo the rendering is faster (2 times, depending on the formula)

JWildfire does not require any additional tools.

Is free

Example images include images of the Apophysis generator.

(tab= Fractal Explorer}

Fractal Explorer is a free fractal generator that allows you to create very beautiful fractal images based on mathematical formulas.

The program is designed not only for professionals, but also for ordinary users, and therefore working with it will not be any difficulty. You can work in it both for professional purposes and for fun, in both cases the program will bring a lot of pleasure and many hours of pleasant time!
Fractal Explorer allows you to create fractals based on classical polynomial sets (Mandelbrot Set, Julia Set, Newton Set and their variations), as well as some others. For example: 4D complex fractals (fractals based on quaternions), 3D “strange” attractors, as well as IFS systems. In addition, Fractal Explorer has many functions for creating various effects and improving the quality of generated images.

Official website of the program: http://www.eclectasy.com/Fractal-Explorer/

Examples of work from website:

(tab=Incendia)

Incendia is a full-fledged, free, multi-processor 3D fractal generator.
The program is constantly being developed and updated. At the moment, it has a rich and powerful range of capabilities for generating full-fledged three-dimensional fractals. The key features are:
-Generation of images with resolutions: 1024, 2048, 2560 and 3072 pixels (4096 and 8192 pixels for donors, i.e. users who made a voluntary financial contribution to the author of the program)
-Supports double anti-aliasing for smoother and more perfect images.
-45 varieties of three-dimensional fractals (although many will be included in only future versions of the program)
-Support for fractal scripts to create new types of fractals.
-Large library of textures, as well as the ability to import external textures.
-Support for color gradients.
-Multiple rendering styles (including volumetric fog, and many new rendering shaders).
-Support for multi-core processors.
-The presence of built-in three-dimensional basic shapes for the construction of complex fractals. (Includes six different base shape map offsets).
-Powerful fractal transformation editor.
-Editor of three-dimensional basic shapes.
-Material editor
-3D Mesh export (up to 1000x1000x1000 voxels for donors)
-Save to buffer (for long rendering)
-Animation support.
In addition, starting with version EX V, the program includes the Geometrica application, specially designed for exporting three-dimensional fractals from Incendia to other 3D graphics editors.

As already mentioned, the program is free, is constantly being developed and updated, and the author asks everyone to make donations for the further development of the program!

Official website: http://www.incendia.net/index.html

Example Images:

(tab= Chaoscope }

Chaoscope is software rendering 3D strange attractors. This is an ongoing project created and maintained by Nicolas Desprez, Current version 0.3.1. It is free, powered by Windows platform,Linux.

Official site:

Example images:

(tab= ChaosPro }

ChaosPro free real-time fractal generator for MS Windows with support for various fractal types (2D and 3D), true color support, with animation support. Thanks to the built-in compiler it is quite fast, the ability to write your own formulas.

official site:

Sample images:

(tab= Sterling }

Sterling is a fractal generator written in the C programming language in 1999 for Microsoft Windows Stephen S. Ferguson. Sterling2 is free version with various generation algorithms. It was released in September 2008 by Tad Boniecki. Apart from the name, the program looks the same as the original, there are an additional 50 formulas for fractal generation. Files created by Sterling can be used in Sterling2 and vice versa, although they will show different images. Sterling is based on the fact that it uses interesting filters for fractal images using complex color and shadow parameters. Sterling has a simple GUI with limited features. The program saves files in JPEG, BMP or one of six other formats.

Official site:

Sample images:

(tab= Fractron9000 }

Fractron 9000 is a high-performance fractal generator for visualization in Windows environment. Powered by the FractalFlames algorithm/

Fractron 9000 takes advantage of modern programmable GPUs lto significantly speed up rendering. Users with CUDA and OpenCL video hardware support will be able to generate fractal images in real time. Some examples of images created with Fractron are shown below. (taken from the official website). The user interface is written in C#, communicating with OpenCL and CUDA via its own custom compatibility libraries. Fractron uses OpenGL to display fractals.

official website: http://fractron9000.sourceforge.net/index.html

Last Update: 2011-08-09

(tab= Fractals }

You can purchase the program on the App Store!™

(tab=Fractal Science Kit)

Fractal Science Kit is a fractal generator for Windows that creates fractal images from a set of properties that can be set to control the fractal generation process. Example properties include fractal type, image size and parameters for orbital generation control, data normalization, resampling, smoothing, gamma correction, etc. You can work with a variety of built-in algorithms (programs) or develop your own using an interactive programming environment.

The Fractal Science Kit fractal generator supports hundreds of built-in equations, trap orbit transformations, and controllers that allow ordinary users to create stunning fractal images, while providing the experienced developer with a rich set of illustrative examples on which to build his own programs (algorithms). Over 60,000 lines of source code for built-in fractal programs and built-in macros (built-in functions/methods) are accessible through the browser, programs and macro editor.

supports 3 main fractal types:
Mandelbrot Fractals

Orbital Fractals

L-system Fractals

and others: Mandelbrot, Julia, Convergent, Newton, Orbit Traps, Sierpinski Triangle, IFS, Strange Attractors, Rep-N Tiles, Symmetric Icons, Symmetric Attractors, Frieze Group Attractors, Wallpaper Group Attractors, Hyperbolic Attractors, Apollonian Gasket, Circle Inversion, Mobius Dragon IFS, Mobius Patterns, Grand Julian IFS, Elliptic Splits IFS, Schottky Group, Kleinian Group, L-System...

Full version costs $30

The trial version can be downloaded here: http://www.fractalsciencekit.com/extra/purchase.htm

Examples:

(tab=Visions Of Chaos)

Another fractal generator in 2D and 3D.

Visions Of Chaos is a professional application software for Windows. It's simple enough for people who don't understand the math behind it, but advanced enough for fractal enthusiasts. This is the most comprehensive all in one application related to chaos theory. Supports video visualization. The program includes hundreds of examples.

You can purchase the program on the official website: http://softology.com.au/voc.htm

The program costs 45 Australian dollars. You can also download on the website trial version, you can use it for an unlimited time, but with closed functions for saving images and working with video.

(tab=Chaotica)

Chaotica represents the next generation of fractal environment creation, designed for both beginners and seasoned professionals. Beginner users can enjoy editing the included examples and random fractals. Professional users will especially appreciate the very fast, modern printing engine high-quality images easier to manufacture, and real-time rendering control will save many hours. Although it is based on mathematics, Chaotica's user interface is powered by an expressive artistic process. Since their invention in 1981, iterated function (IFS) fractals have been popular in software such as flam3 and Apophysis. Chaotica extends the creative capabilities of these programs in a powerful, production-oriented environment.

0.72 version is free

1.0 version Paid

You can download and buy here: http://store.glaretechnologies.com/chaotica

Examples (from the official site)

(tab=Saturn & Titan)

Mars - Another fractal generator program. This program has been used to produce a large number of fractal images that are available for viewing and in some cases purchasing on DeviantArt and Red Bubble. It was written in C++ using Gtkmm also on Linux and is no longer used. Its natural continuation was the Saturn program. When an image is saved using the Mars or Saturn programs, it is saved in what the author calls a seed file. The seed file is a PNG file with all the necessary fractal parameters built into it so that the extension program can generate a greatly enlarged image, typically 12000 by 8000 pixels. Maximum size, which can be rendered is about 700 megapixels. Titan represents an expansion for Saturn.

Works on Linux and Windows.

You can download the program, manuals for it and some files on the developer’s website: http://element90.wordpress.com/software/downloads/

(tab=Silverfractal)

SilverFractal is a new generation fractal generator. It aims to restore and simplify fractal art and open up new possibilities.

Peculiarities

Generation various types 2D/3D - fractals like FractalFlames - algorithm

Fractal animation renderer

Full floating point support for image processing

Supports multiple layers and nested layers

Multi-threaded rendering support

Texture support

Version 1.1.0.2 for Windows 8.1

Supported processors x86, x64, ARM

System requirementsIntel Core i processors

4 GB RAM

You can download for Windows 8.1 (Microsoft website)

(tab=Electric Sheep)

Electric sheep is a resource that uses distributed computing to create fractal animation based on the fractal flame algorithm (developed by Scott Draves).

The name "Electric Sheep" comes from the title of Philip K. Dick's novel Do Androids Dream of Electric Sheep. The name reflects the nature of the project: computers (androids) that began to visualize the screensaver (dreaming) in the form of fractal films (sheep).

The process is transparent to ordinary users who can simply install software as a screensaver. In addition, the user can take a more active part in the project by manually creating sheep (animated video files) for uploading to the server. As a screensaver it (video file) can entertain the user, their computer is also used for rendering commercial projects.

The video motif from the user carries over into other aspects of the project: the 100 or so files stored on the server at any time are referred to as a "herd" for creating a new fractal by interpolating or combining the fractal code of a user's file with another of another user's file and is called mating/breeding; changes in the code are called mutations, etc.

Simply put, software is installed on your computer that uses your machine to calculate and render fractal animation, while at the same time downloading and showing you the finished fractal animation in the form of so-called “live” wallpaper, or screensaver. At the same time, these same wallpapers are saved on the computer in a certain folder and they can be pulled out from there and then used for your own purposes, for example, in video editing (although the length of the videos is a bit short - 5 seconds).

You can read more about and download the distribution on the project website: http://electricsheep.org/

Video screenshots: