Three-dimensional graphics operate with objects in three-dimensional space. Usually the results are a flat picture, a projection. Three-dimensional computer graphics are widely used in cinema and computer games. In three-dimensional 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.
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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.
The last of the species considered computer graphics - This fractal graphics. Fractal graphics is today one of the fastest growing promising species computer graphics.
Mathematical basis fractal graphics is fractal geometry. Here, the image construction method is based on the principle of inheritance from the so-called "parents" geometric properties heir objects.
Concepts fractal, fractal geometry And fractal graphics, which appeared in the late 70s, are now firmly established in the everyday life of mathematicians and computer artists. Word fractal derived from Latin fractus and translated means "made up of fragments". It was proposed by a mathematician Benoit Mandel-Brothome V 1975 year to designate the irregular but self-similar structures with which he was concerned.
Fractal is a structure consisting of parts that are in some sense similar to the whole. One of the main properties fractals is self-similarity. The object is called self-similar, when enlarged parts of an object resemble the object itself and each other. To paraphrase this definition, we can say that in the simplest case, a small part of a fractal contains information about the entire fractal.
At the center of a fractal figure is its simplest element - equilateral triangle, which was named "fractal". Then, on the middle segment of the sides, equilateral triangles are constructed with a side equal to (1/3a) from the side of the original fractal triangle. In turn, on the middle segments of the sides of the resulting triangles, which are successor objects first generation, lining up successor triangles second generation with side (1/9a) from the side of the original triangle.
Thus, small elements of a fractal object repeat the properties of the entire object. The resulting object is called "fractal figure". The inheritance process can be continued indefinitely. Thus, one can describe such a graphic element as direct.
Changing and combining colors fractal figures you can simulate images of living and inanimate nature (for example, tree branches or snowflakes), and also compose from the resulting figures "fractal composition". Fractal graphics, as well as vector And three-dimensional, is computable. 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.
Only by changing the coefficients of the equation can you get a completely different image. This idea has found use in computer graphics due to the compactness of the mathematical apparatus necessary for its implementation. Thus, using several mathematical coefficients, you can define lines and surfaces of very complex shapes.
So, the basic concept for fractal computer graphics are "Fractal Triangle". Then comes "Fractal figure", "Fractal object"; "Fractal line";"Fractal composition"; "Parent object" And "Object heir". Please note that fractal computer graphics like a view computer graphics The twenty-first century has become widespread not so long ago.
Its capabilities are difficult to overestimate. Fractal computer graphics allows you to create abstract compositions where you can implement such compositional techniques as horizontals and verticals, diagonal directions, symmetry and asymmetry, etc. Today, few computer scientists in our country and abroad know fractal graphics. What can you compare it to? fractal image? Well, for example, with a complex crystal structure, with a snowflake, the elements of which are arranged into one complex structure. This property of a fractal object can be successfully used when composing a decorative composition or to create an ornament. Today, coefficient synthesis algorithms have been developed fractal, which allows you to reproduce a copy of any picture as close as you like to the original.
From a computer graphics perspective fractal geometry indispensable for generating artificial clouds, mountains, and sea surfaces. Thanks in fact fractal graphics a way has been found to effectively implement complex non-Euclidean objects, the images of which are very similar to natural ones. Geometric fractals on the computer screen is patterns built by the computer itself according to a given program. Besides fractal painting exist fractal animation and fractal music.
Fractal Creator- is an artist, sculptor, photographer, inventor and scientist rolled into one. You yourself set the shape of the drawing using a mathematical formula, explore the convergence of the process by varying its parameters, choose the type of image and color palette, that is, create the drawing “from scratch.” This is one of the differences between fractal graphic editors and other graphic programs.
For example, in Adobe Photoshop The image, as a rule, is not created “from scratch”, but only processed. Another unique feature of the fractal graphic editor is that a real artist working without a computer will never achieve with a brush, pencil and pen the capabilities that are possible in fractal GR by programmers.
In our article today you will learn: how and with what help you can draw fascinating, mysterious futuristic fractals, and there will be something to do this coming weekend.
A fractal is a complex geometric figure consisting of parts similar to the entire figure. Some objects from our life, for example, snowflakes, tree crowns, etc., have fractal properties. Fractal graphics fascinate with their mystery and definitely attract our attention, and most people like such drawings - this is how the magic of fractals works on people. Fractal patterns can be surreal and quite realistic. Therefore, fractals are used in various fields: from creating textures and backgrounds to fantastic landscapes for games or illustrations.
Fractals are created not simply by moving the brush, like real artists create paintings, but by mathematical calculations, the basic element of which is a mathematical formula. This is how simple fractals are built only on the basis of mathematical equations.
There are not as many programs that can be used to create fractal images as we would like. In this regard, it is problematic to find a functional program on the Internet and even in popular program directories, one of which is our website. Therefore, we decided to correct this error by writing for our readers this article-digest of programs for generating fractals, which you can also download from our catalog.
Apophysis
Apophysis is an interesting tool for creating fractals based on basic formulas. Fractals created using such fractal formulas can be changed beyond recognition using various parameters (transformation, color, transformation, gamma, brightness, scale).
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Download the Apophysis fractal generator.
ChaosPro
ChaosPro is one of the best free fractal generators with which you can easily create many futuristic fractal designs.
The program is quite easy to understand due to its simple and user-friendly interface and automatic generation of fractals. Having gained more experience in creating fractals, you can switch to full control of the generation of fractals with a large number of settings (color, blur, iteration, projection, size, layering of images, filters, etc.).
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2D fractals can be converted to 3D fractals using 3D transformation. The program allows you to create animation based on fractal images.
The created fractals are saved as projects in own format programs are either exported to raster images (JPG, BMP, PNG). 3D transformations are saved as 3D objects in POV format, and animations are saved in AVI format.
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Download the program for creating fractals ChaosPro.
Fragmentarium
Fragmentarium is a free fractal program, the main beauty of which is the ability to write your own formulas and use them to build fractals.
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Before you try to write your own formulas for creating fractals, you can use some of the standard formulas that are already included in the program.
The program can create 2D and 3D fractals with high resolution and excellent quality. In addition, you can also create fractal animations in Fragmentarium.
The main criterion for using this program to create fractals is the presence of a more or less modern video card in your computer.
Download the Fragmentarium fractal generator.
Incendia
Incendia is a complete free and multi-processor program for generating 3D fractals.
The latest version of the program has quite rich functionality for generating full-fledged three-dimensional fractals, allowing you to generate perfect images with a resolution of 1024 to 8192 pixels.
The program includes 45 varieties of all kinds of fractals and a large library of textures, as well as the ability to export fractals in the form of animation.
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Beginning with latest versions Incendia program, along with it comes the Geometrica application, with which you can export 3D fractals to other three-dimensional graphics editors.
Download the full-fledged Incendia fractal generator.
Ultra Fractal
Ultra Fractal is best program to create unique fractals of professional quality. The program interface is simple and somewhat reminiscent of the interface Adobe programs Photoshop, especially the program is accompanied by detailed illustrated documentation.
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Created and finished fractal images can be visualized in high resolution, which can be used in printing, and saved in the program’s own format or in popular formats raster images(jpg, png, bmp, psd), and the animation is exported to video format (avi).
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The program already comes with several built-in formulas for creating fractals - this is the most in a simple way creating fractal images for beginners. Subsequently, the created fractals using standard formulas can be edited to your taste by adding translucency, gradient, multi-layering, masks, scale, distortion or cropping to the fractal.
Download the best fractal generator Ultra Fractal.
XenoDream
XenoDream - this program is an environment for creating a variety of futuristic volumetric structures by combining simple shapes and fractals.
You don't need to know fractal formulas to create a 3D fractal; in XenoDream you can create random fractal structures with just one click. Using a variety of settings, of which there are a huge number, you can change the position, size, rotate, add gradients, etc. In addition to all this, you can control the camera by changing its position, focus and tilt, you can also change the light sources and the presence or absence of shadows, even for separate forms.
The program allows you to create animations of fractals, which are saved as separate images.
Ready-made futuristic fractals can be saved in the program’s own format or exported to popular graphic formats(jpg, bmp, psd, tga), three-dimensional objects can be saved in obj, povray inc and Depth Maps formats.
Download the software environment for creating fractals XenoDream.
In this article, we looked at several well-known solutions that are still being developed and updated to this day. They allow you to generate futuristic fractals. Each program has its own characteristics and directions, so it is impossible to say which one is 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:
- -the ability to use stunning 3D effects such as waves, ripples on the water, etc.
- -3D overlay effects
- -powerful built-in flame editor-T.I.N.A.
- -built-in image generator (the ability to generate images with clouds, plasma, etc.)
- -many effects of image processing in 2D (eg: Rotation, twisting, destruction, etc.)
- -simple yet powerful user interface that allows you to animate almost any parameter in just a few mouse clicks
- -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. On this 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 further development programs!
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 and runs on the Windows and Linux platforms.
Official site:
Example images:
(tab= ChaosPro }
ChaosPro free generator 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 a limited number of functions. 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). More than 60,000 lines 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 engine, printing quality images is easier to produce, 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. The maximum size that 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, which 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:
