Fractal Art

Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media. Fractal art developed from the mid-1980s onwards. It is a genre of computer art and digital art which are part of new media art. The mathematical beauty of fractals lies at the intersection of generative art and computer art. They combine to produce a type of abstract art.

Fractal art is a form of algorithmic art that consists of producing images, animations and even music from fractal objects. Fractal art developed from the mid-1980s.

Fractal art is rarely drawn or painted by hand, but rather created using computers, which are indeed able to calculate fractal functions and generate images from them. It is also the appearance of computers that has allowed the development of this art because it requires a lot of computing power.

Fractal art (especially in the western world) is rarely drawn or painted by hand. It is usually created indirectly with the assistance of fractal-generating software, iterating through three phases: setting parameters of appropriate fractal software; executing the possibly lengthy calculation; and evaluating the product. In some cases, other graphics programs are used to further modify the images produced. This is called post-processing. Non-fractal imagery may also be integrated into the artwork. The Julia set and Mandelbrot sets can be considered as icons of fractal art.

It was assumed that fractal art could not have developed without computers because of the calculative capabilities they provide. Fractals are generated by applying iterative methods to solving non-linear equations or polynomial equations. Fractals are any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size.

The programs generating fractal images usually operate in three steps: the adjustment of the parameters that frame the generation of the image, the execution of the calculations and finally the application of the results to a plane for generating an image. For an animation, the operation must be repeated for each generated image. In some cases, other graphic programs are then used to modify the image produced: it is the postproduction. Non-fractal images can also be integrated into the artwork.

Fractals are generated using the iterative method to solve nonlinear equations or polynomial equations.

The increase in the power of computers has enabled the creation of software allowing the computation of three-dimensional images in computer-generated images thus offering the functions and effects usually reserved for the classic three-dimensional modeling software (lights, volumetric lights, depth blur, atmosphere , reflection / refraction of certain materials, textures, …).

There are many different kinds of fractal images and can be subdivided into several groups.

Fractals derived from standard geometry by using iterative transformations on an initial common figure like a straight line (the Cantor dust or the von Koch curve), a triangle (the Sierpinski triangle), or a cube (the Menger sponge). The first fractal figures invented near the end of the 19th and early 20th centuries belong to this group.
IFS (iterated function systems)
Strange attractors
Fractal flame
L-system fractals
Fractals created by the iteration of complex polynomials: perhaps the most famous fractals.
Newton fractals, including Nova fractals
Quaternionic and (recently) hypernionic[clarification needed] fractals
Fractal terrains generated by random fractal processes
Mandelbulbs are a kind of three dimensional fractal.
Fractal Expressionism is a term used to differentiate traditional visual art that incorporates fractal elements such as self-similarity for example. Perhaps the best example of fractal expressionism is found in Jackson Pollock’s dripped patterns. They have been analysed and found to contain a fractal dimension which has been attributed to his technique.

The first fractal image that was intended to be a work of art was probably the famous one on the cover of Scientific American, August 1985. This image showed a landscape formed from the potential function on the domain outside the (usual) Mandelbrot set. However, as the potential function grows fast near the boundary of the Mandelbrot set, it was necessary for the creator to let the landscape grow downwards, so that it looked as if the Mandelbrot set was a plateau atop a mountain with steep sides. The same technique was used a year after in some images in The Beauty of Fractals by Heinz-Otto Peitgen and Michael M. Richter. They provide a formula to estimate the distance from a point outside the Mandelbrot set to the boundary of the Mandelbrot set (and a similar formula for the Julia sets).

Fractals of all kinds have been used as the basis for digital art and animation. High resolution color graphics became increasingly available at scientific research labs in the mid-1980s. Scientific forms of art, including fractal art, have developed separately from mainstream culture. Starting with 2-dimensional details of fractals, such as the Mandelbrot Set, fractals have found artistic application in fields as varied as texture generation, plant growth simulation and landscape generation.

Fractals are sometimes combined with evolutionary algorithms, either by iteratively choosing good-looking specimens in a set of random variations of a fractal artwork and producing new variations, to avoid dealing with cumbersome or unpredictable parameters, or collectively, as in the Electric Sheep project, where people use fractal flames rendered with distributed computing as their screensaver and “rate” the flame they are viewing, influencing the server, which reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art.

Many fractal images are admired because of their perceived harmony. This is typically achieved by the patterns which emerge from the balance of order and chaos. Similar qualities have been described in Chinese painting and miniature trees and rockeries.

All kinds of fractals have been used as a basis for digital art. Colorful images in high graphic quality became more and more accessible in scientific research laboratories in the 1980s. Scientific art forms, such as fractal art, developed separately from the dominant culture. Beginning with images showing the details of two-dimensional fractals such as the Mandelbrot set, fractals have found artistic applications in many different areas of textural generation, plant growth simulation and landscape generation.

Fractals are sometimes combined with evolutionary algorithms, either by iteratively choosing specimens that are considered beautiful in a set of random variation of a fractal work and by producing new variations together, to avoid obtaining uncertain or unsatisfactory results, or collectively, as in the Electric Sheep project, where people use fractal flames made using distributed computing as a screen saver. They can then “notice” the fractal flames they see, and these notes influence the server that tailors the algorithm to reduce the chances of getting fractal flames that are deemed undesirable and increase the chances of getting desirable fractal flames. This project is therefore a computer-generated work of art created by an entire community.

Many fractal images are admired for the harmony that people perceive. This result is often successful thanks to the motives emerging from the balance between order and chaos. Similar qualities have been described in Chinese paintings and Penjings.

Notable fractal artists include Desmond Paul Henry, Hamid Naderi Yeganeh and musician Bruno Degazio. The British artist William Latham, has used fractal geometry and other computer graphics techniques in his works. Greg Sams has used fractal designs in postcards, T-shirts and textiles. American Vicky Brago-Mitchell has created fractal art which has appeared in exhibitions and on magazine covers. Scott Draves is credited with inventing flame fractals. Carlos Ginzburg has explored fractal art and developed a concept called “homo fractalus” which is based around the idea that the human is the ultimate fractal. Merrin Parkers from New Zealand specialises in fractal art. Kerry Mitchell wrote a “Fractal Art Manifesto”, claiming that

Fractal Art is a subclass of two-dimensional visual art, and is in many respects similar to photography—another art form that was greeted by skepticism upon its arrival. Fractal images typically are manifested as prints, bringing fractal artists into the company of painters, photographers, and printmakers. Fractals exist natively as electronic images. This is a format that traditional visual artists are quickly embracing, bringing them into Fractal Art’s digital realm. Generating fractals can be an artistic endeavor, a mathematical pursuit, or just a soothing diversion. However, Fractal Art is clearly distinguished from other digital activities by what it is, and by what it is not.

According to Mitchell, fractal art is not computerized art, lacking in rules, unpredictable, nor something that any person with access to a computer can do well. Instead, fractal art is expressive, creative, and requires input, effort, and intelligence. Most importantly, “fractal art is simply that which is created by Fractal Artists: ART.”

Fractal art has been exhibited at major international art galleries. One of the first exhibitions of fractal art was “Map Art”, a travelling exhibition of works from researchers at the University of Bremen. Mathematicians Heinz-Otto Peitgen and Michael M. Richter discovered that the public not only found the images aesthetically pleasing but that they also wanted to understand the scientific background to the images.

In 1989, fractals were part of the subject matter for an art show called Strange Attractors: Signs of Chaos at the New Museum of Contemporary Art. The show consisted of photographs, installations and sculptures designed to provide greater scientific discourse to the field which had already captured the public’s attention through colourful and intricate computer imagery.