Just a few decades ago computer art opened a new window towards a world in which mathematics, directly or indirectly, played a significant role in the creation processes of art, in form of algorithms and equations. The first steps just invited the mathematical and logical aspects of the world around, known as chance, randomness, probability, regulability and programmability in a mathematical context to the art area. Computer artists by taking such bizarre steps, in parallel with artists of other fields, tried to push art borders from modernism to what is better known today as postmodernism, a domain in which borders among art, artist, artwork and even the audience are blurred. Apart from the good and ever-lasting job of computers as fast and accurate assistances for artists, the golden end that digital postmodernism was looking for in was creativity. Postmodernism expected computers to enter artists into a world of infinite possibilities with different and adjustable degrees of intermediation in creation process, which was not possible before. Computers could introduce infinite opportunities and possibilities, test, alter, develop or limit them, select the preferred or even random results and finally show them in different and mixed forms, all according to the desire and direct or indirect orders of the artist.
One of the well known areas of mathematics which was very soon welcomed by computers was geometry of fractals. Fractals due to their basic properties had an algorithmic nature and so were created and depicted well through computational calculations. Fractals due to their repeatable constructing mechanics, their tight connection with the concept of infinity and also their fractional dimensionality very soon became one of the satisfying results of digital generative world and one of the fields challenging modern abilities of computers due to their complexity and massiveness. At first, fractals were 2D constructions that could not be truly imagined, depicted and more importantly explored without several opportunities that the computational technology of Postmodernity presented.
Magnification is one of the artistic sides of creating fractals in computers, as artists in search for satisfying views can walk through fractals digitally in form of mathematical magnifications. In fact, this is the continuity of numbers in mathematics, the idea of the infinity of the possible fractional numbers between every two fractions and on the whole the tendency of fractals towards infinity that makes such connected magnifications infinitely possible. In a 2D fractal generating program, fractals look like dreamy flat spaces which could be magnified and altered on desire of creative artist. They are 2D worlds that small changes in a tiny part of which could cause titanic changes in the architecture of their whole construction. But, the result of these creative processes could be either still images or animations.
Fractal animations stem from the idea of presenting all these properties together in a connected form so that it seems as if the fractal artist is really experiencing a continuous journey (better known as exploration) inside fractal spaces; inserting magnifications and other manipulations, identifying key frames and finally rendering animations by connecting all these consecutive steps and key-frames together. Mandelbrot Yantra shows a zoom trip in a composition of Mandelbrot fractals with a magnification of 2.74×1018. It was shown at 2010 Bridges conference in Pécs, Hungary (http://bridgesmathart.org/uploads/2010/bridges-2010-movie-night.pdf).

Figure 1. Mandelbrot Yantra, 2010, Mehrdad Garousi (Please log in to view with username: mehrdad_fractal , pass: mehrdad , during review I will provide a youtube link to this animation!)

Naturally, properties like exploration make more sense in environments of three dimension. In the third dimension, things get more tangible and elements like lighting and shading look up. It was why 3D fractals spread very fast virally. 3D fractals are in fact three dimensional representations of fractals belonging to fourth or higher dimensions. Therefore, what is viewed, in spite of the huge amount of bizarreness, potentially has similarities to the physical elements of the real world, too. However, differences say hello specially during explorations (during creation process) and in 3D animations as final forms of presentation in comparison to still images. Such 3D fractal worlds present different experiences of perspective and amazing properties like 3D morphing to provide amazing environments and physical actions that exist but in dreams. Worlds composed of very intricate details which could easily changed and altered according to certain mathematical rules. Animations Quest, Sierpinski Dream, Investigation and Let Me Go are all 3D fractal animations created in Mandelbulb3D program. They show my different adventures in different fractal spaces with different music pieces. Music of Quest and Sierpinski Dream is also composed of compilations of generative sequences made by myself. Quest has been presented at conferences 2011 Bridges in Coimbra, Portugal (http://bridgesmathart.org/past-conferences/bridges-2011/2011-short-movie-festival/) and 2011 Art, Science and Technology: Interaction between Three Cultures in Karmiel, Israel (http://www.artscience-ebookshop.com/1stAST_book.htm), Sierpinski Dream at 2011 GenerativeArt in Roma, Italy (http://generativeart.com/GA2011/x_mehrdad.pdf , http://www.artscience-ebookshop.com/ga2011_book.htm) and Let Me Go at 2012 Bridges in Towson, USA. More information regarding these animations could found at the proceedings or brochures of these events, printed or online (provided links above).

Figure 2. Quest, 2011, Mehrdad Garousi, http://www.youtube.com/watch?v=lrIzpDtxgCY .

Figure 3. Sierpinski Dream, 2011, Mehrdad Garousi, http://www.youtube.com/watch?v=P5EkdJRtF-4 .

Figure 4. Investigation, 2011, Mehrdad Garousi, http://www.youtube.com/watch?v=6v1KU-C4QVQ .

Figure 5. Let Me Go, 2012, Mehrdad Garousi (A music Video for Flinch), http://www.youtube.com/watch?v=KugjZHS5ayY .

In making every 3D fractal animation things normally start from defining a physical world according to the basic mathematical parameters and the artist can alter and morph everything every time they want according to their desire by changing parameters. Adjustment of lots of other elements like colors, types, amounts and directions of lights and the like are also carried out at the same time. So, artist is simultaneously a creator and also an explorer amazed by the oddity in front of them in equal measure. Stepping in a fractal, they start a discovery in and among unknown and odd fractional dimensions. This kind of digital adventure is more understandable and tangible specially when is experienced in a real-time navigator in a program like Mandelbulb3D during art creation. Mandelbulb3D is the program I use for creating 3D fractal images and animations. Its 3D navigator makes it possible to have live continuous strolls in the environments instead of jumping between identified certain key-frames during the explorations. These continuous explorations are in fact live real-time adventures in generative spaces full of complexity. In other words, artists can travel lively in unknown worlds and decide to film which paths and views to show to others later.
3D fractal artists have pushed the erstwhile limitations of generative art farther and instead of staying beside and controlling the currents from outside, step inside and become a part of the digital world while affected by the generative world around as much as they can have effect and control over it.