Fractal art - AbsoluteAstronomy.com

Fractal art is a form of algorithmic art

Algorithmic art

Algorithmic art, also known as algorithm art, is art, mostly visual art, of which the design is generated by an algorithm. Algorithmic artists are sometimes called algorists.- Overview :...

created by calculating fractal

Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

objects and representing the calculation results as still images, animations, and media

Algorithmic composition

Algorithmic composition is the technique of using algorithms to create music.Algorithms have been used to compose music for centuries; the procedures used to plot voice-leading in Western counterpoint, for example, can often be reduced to algorithmic determinacy...

. Fractal art developed from the mid 1980s onwards. It is a genre of computer art

Computer art

Computer art is any art in which computers play a role in production or display of the artwork. Such art can be an image, sound, animation, video, CD-ROM, DVD-ROM, videogame, web site, algorithm, performance or gallery installation...

and digital art

Digital art

Digital art is a general term for a range of artistic works and practices that use digital technology as an essential part of the creative and/or presentation process...

which are part of new media art

New media art

New media art is a genre that encompasses artworks created with new media technologies, including digital art, computer graphics, computer animation, virtual art, Internet art, interactive art, computer robotics, and art as biotechnology...

. The Julia set

Julia set

In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function...

and Mandlebrot sets can be considered as icon

Icon

An icon is a religious work of art, most commonly a painting, from Eastern Christianity and in certain Eastern Catholic churches...

s of fractal art.

Fractal art is not 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

Graphics software

In computer graphics, graphics software or image editing software is a program or collection of programs that enable a person to manipulate visual images on a computer....

are used to further modify the images produced. This is called post-processing. Non-fractal imagery may also be integrated into the artwork.

Fractal art could not have developed without computers because of the calculative

Calculation

A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition...

capabilities they provide. Fractals are generated by applying iterative

Iteration

Iteration means the act of repeating a process usually with the aim of approaching a desired goal or target or result. Each repetition of the process is also called an "iteration," and the results of one iteration are used as the starting point for the next iteration.-Mathematics:Iteration in...

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 Fractal Art Manifesto

As stated by Kerry Mitchell in The Fractal Art Manifesto, "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

Printmaking

Printmaking is the process of making artworks by printing, normally on paper. Printmaking normally covers only the process of creating prints with an element of originality, rather than just being a photographic reproduction of a painting. Except in the case of monotyping, the process is capable...

, 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."

Types

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
Koch snowflake
The Koch snowflake is a mathematical curve and one of the earliest fractal curves to have been described...

), a triangle (the Sierpinski triangle
Sierpinski triangle
The Sierpinski triangle , also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13th-century Cosmati mosaics in the cathedral...

), or a cube (the Menger sponge
Menger sponge
In mathematics, the Menger sponge is a fractal curve. It is a universal curve, in that it has topological dimension one, and any other curve is homeomorphic to some subset of it. It is sometimes called the Menger-Sierpinski sponge or the Sierpinski 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
Strange Attractors
Strange Attractors Audio House is a record label from Portland, Oregon. It was founded in 2000 by Chris Scofield.-History:SAAH was as spin-off of KAOS Olympia 89.3 FM Community Radio's "Strange Attractors" program — a show which Scofield hosted for about eight years...

.
Fractal flame.
L-system
L-system
An L-system or Lindenmayer system is a parallel rewriting system, namely a variant of a formal grammar, most famously used to model the growth processes of plant development, but also able to model the morphology of a variety of organisms...

fractals.
Fractals created by the iteration of complex polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

s: perhaps the most famous fractals.
Newton fractals, including Nova fractal
Nova fractal
Nova fractal is a family of fractals related to the Newton fractal. Nova is a formula that is implemented in most fractal art software.-Formula:The formula for novaMandelbrot is a special case of the generalized Newton fractal:...

s
Quaternionic and (recently) hypernionic fractals.
Fractal terrains generated by random fractal processes.

Fractal expressionism is a term used to differentiate traditional visual art that incorporates fractal elements such as self-similarity

Self-similarity

In mathematics, a self-similar object is exactly or approximately similar to a part of itself . Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales...

for example. Perhaps the best example of fractal expressionism is found in Jackson Pollack's dripped patterns. They have been analysed and found to contain a fractal dimension

Fractal dimension

In fractal geometry, the fractal dimension, D, is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. There are many specific definitions of fractal dimension. The most important theoretical fractal...

which has been attributed to his technique.

Techniques

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

Mainstream

Mainstream is, generally, the common current thought of the majority. However, the mainstream is far from cohesive; rather the concept is often considered a cultural construct....

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 human-assisted 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 cumbersome or unpredictable parameters, or collectively, like in the Electric Sheep

Electric Sheep

Electric Sheep is a distributed computing project for animating and evolving fractal flames, which are in turn distributed to the networked computers, which display them as a screensaver.-Process:...

project, where people use fractal flame

Fractal flame

Fractal flames are a member of the iterated function system class of fractals created by Scott Draves in 1992. Draves' open-source code was later ported into Adobe After Effects graphics software and translated into the Apophysis fractal flame editor....

s rendered with distributed computing

Distributed computing

Distributed computing is a field of computer science that studies distributed systems. A distributed system consists of multiple autonomous computers that communicate through a computer network. The computers interact with each other in order to achieve a common goal...

as their screensaver

Screensaver

A screensaver is a type of computer program initially designed to prevent phosphor burn-in on CRT and plasma computer monitors by blanking the screen or filling it with moving images or patterns when the computer is not in use...

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 pattern

Pattern

A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects.These elements repeat in a predictable manner...

s which emerge from the balance of order and chaos

Chaos theory

Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

. Similar qualities have been described in Chinese painting

Chinese painting

Chinese painting is one of the oldest continuous artistic traditions in the world. The earliest paintings were not representational but ornamental; they consisted of patterns or designs rather than pictures. Early pottery was painted with spirals, zigzags, dots, or animals...

and miniature trees and rockeries

Penjing

Penjing , also known as penzai , tray landscape, potted scenery, potted landscape, and miniature trees and rockery is the ancient Chinese art of growing trees and plants, kept small by skilled pruning and formed to create an aesthetic shape and the complex illusion of age...

.

Some of the most popular fractal rendering programs used to make fractal art include Ultra Fractal

Ultra Fractal

Ultra Fractal is a fractal generation and rendering software application. The program works using a similar paradigm to Photoshop, allowing multiple layers to be combined using layer blending modes, transformations and custom fractal formulas....

, Apophysis, Bryce

Bryce (software)

Bryce is a 3D modeling, rendering and animation program specializing in fractal landscapes. The name is taken from Bryce Canyon—a rugged region with many of the same landscapes that were first simulated with the software.- History :...

and Sterling

Sterling (program)

Sterling is a fractal-generating computer program written in the C programming language in 1999 for Microsoft Windows by Stephen C. Ferguson. Sterling was initially released as freeware but currently a $35 fee is required to download it from Ferguson's site. Sterling2 is a freeware version of...

. Fractint

Fractint

FractInt is a freeware program that can render and display many kinds of fractals.-Name:Its name comes from the words fractal and integer, since the first versions of it computed fractals by using only integer arithmetic , which led to much faster rendering on x86 computers without math coprocessors...

was the first widely used fractal generating program.

Landscapes

The first fractal image that was intended to be a work of art was probably the famous one on the cover of Scientific American
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...

, August 1985. This image showed a landscape

Landscape

Landscape comprises the visible features of an area of land, including the physical elements of landforms such as mountains, hills, water bodies such as rivers, lakes, ponds and the sea, living elements of land cover including indigenous vegetation, human elements including different forms of...

formed from the potential function on the domain outside the (usual) Mandelbrot set

Mandelbrot set

The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable two-dimensional fractal shape...

. 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

Plateau

In geology and earth science, a plateau , also called a high plain or tableland, is an area of highland, usually consisting of relatively flat terrain. A highly eroded plateau is called a dissected plateau...

atop a mountain with steep sides. The same technique was used a year after in some images in The Beauty of Fractals
The Beauty of Fractals
The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success....

by Heinz-Otto Peitgen

Heinz-Otto Peitgen

thumb|180px|right|Heinz-Otto PeitgenHeinz-Otto Peitgen is a German mathematician. Peitgen is one of the most prominent researchers in the study of fractals.- Life :...

and Michael M. Richter

Michael M. Richter

Michael M. Richter is a German mathematician and computer scientist. Richter is well known for his career in mathematical logic, in particular non-standard analysis, and in artificial intelligence, in particular in knowledge-based systems and case-based reasoning...

.

In this book you can find 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), and one can wonder why the creator did not use this function instead of the potential function, because it grows in a more natural way (see the formula in the articles Mandelbrot set

Mandelbrot set

The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable two-dimensional fractal shape...

and Julia set

Julia set

In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function...

).

The three pictures show landscapes formed from the distance function for a family of iterations of the form

. If, in a light from the sun. Then we imagine the rays are parallel (and given by two angles), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point. The intensity (on the earth) is independent of the distance, but the light grows whiter because of the atmosphere, and sometimes the ground looks as if it is enveloped in a veil of mist (second picture). We can also let the light be "artificial", as if it issues from a lantern held by the observer. In this case the colour must grow darker with the distance (third picture).

Artists

The British artist William Latham

William Latham

William Latham is a British computer artist, most known as the creator of the Organic Art product as well as for creating album covers and artwork for the dance group The Shamen. Latham is the founder of the company Computer Artworks which released the Organic Art product through Time Warner...

, has used fractal geometry and other computer graphics techniques in his works. Greg Sams

Greg Sams

Gregory Sams is a UK-based, American-born, fractal artist, social thinker, author, publisher, inventor, macrobioticist and creator of the veggie burger.- Life and works :...

has used fractal designs in postcards, t-shirts and textiles. American Vicky Brago-Mitchell

Vicky Brago-Mitchell

Vicky Brago-Mitchell is an American fractal artist known in the 1960s as a Stanford University coed who, while working as a topless dancer, ran for student body president. She won the preliminary election, but lost to eventual Earth Day national coordinator Denis Hayes in a two person runoff...

has created fractal art which has appeared in exhibitions and on magazine covers. Scott Draves

Scott Draves

Scott Draves is the inventor of Fractal Flames and the leader of the distributed computing project Electric Sheep. He also invented patch-based texture synthesis and published the first implementation of this class of algorithms...

is credited with inventing flame fractals. Some artists, such as Reginald Atkins, create fractal art for relaxation. Carlos Ginzburg

Carlos Ginzburg

Carlos Ginzburg is a conceptual artist and theoretician born in 1946 in La Plata, Argentina. He studied philosophy and social theory.-Biography:Germano Celant, when writing about Arte Povera, invited Ginzburg by letter to join his movement....

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.

Exhibits

There has been fractal art exhibits at major international art galleries. One of the first exhibitions of fractal art was called Map Art. It was a travelling exhibition of works which originated from researchers at the University of Bremen

University of Bremen

The University of Bremen is a university of approximately 23,500 people from 126 countries that are studying, teaching, researching, and working in Bremen, Germany...

. Mathematicians Heinz-Otto Peitgen

Heinz-Otto Peitgen

thumb|180px|right|Heinz-Otto PeitgenHeinz-Otto Peitgen is a German mathematician. Peitgen is one of the most prominent researchers in the study of fractals.- Life :...

and Michael M. Richter

Michael M. Richter

discovered 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

New Museum of Contemporary Art

The New Museum, founded in 1977 by Marcia Tucker, is the only museum in New York City exclusively devoted to presenting contemporary art from around the world...

. The show consisted of photographs, installations and sculptures designed to provide greater scientific discourse

Discourse

Discourse generally refers to "written or spoken communication". The following are three more specific definitions:...

to the field which had already captured the public's attention through colourful and intricate computer imagery.

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.