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Random event or random numbers? The ability to generate pseudorandom numbers is important for simulating events, estimating probabilities and other quantities, making randomized assignments or selections, and numerically testing symbolic results. What is Generative Art In ordinary language, the word random is used to express apparent lack of purpose or cause. This suggests that no matter what the cause of something, its nature is not only unknown but the consequences of its operation are also unknown. J. Tarbell - Processing, 2003

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What is Generative Art In most technical senses, randomness has an additional positive meaning related to some of the statistical properties of the observed. Thus, the landing location of water droplets from a waterfall will be random in the ordinary sense as it's impossible to determine just what forces have applied to this or that droplet causing it to fall where it does. But in a statistical sense, and depending on the scale of observation, droplet landing spots are not distributed randomly at all. On the other hand, the instantaneous sound intensity at any chosen frequency of an electrical circuit noise is technically random as well as conventionally random.

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As John Cage pointed out While there are many ways that sounds might be produced [i.e., in terms of patterns], few are attempted. Similarly, the arrangement of art in exhibits is often deliberately non- random. One case of this was Hitler's attempt to portray modern art in the worst possible light by arranging works in worst possible manner. A case can be made for trying to make art in the worst possible way; i.e., either as anti-art, or as actually random art. Dadaism, as well as many other movements in art and letters, has attempted to accommodate and acknowledge randomness in various ways. Often people mistake order for randomness based on lack of information; e.g., Jackson Pollock's drip paintings, Helen Frankenthaler's abstractions (e.g., "For E.M."). Thus, in some theories of art, all art is random in that it's "just paint and canvas" (the explanation of Frank Stella's work). What is Generative Art

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Jackson Pollock was introduced to the use of liquid paint in 1936 at an experimental workshop operated in New York City by the Mexican muralist David Alfaro Siqueiros. He later used paint pouring as one of several techniques on canvases of the early 1940s, such as "Male and Female" and "Composition with Pouring I." After his move to Springs, he developed what was later called his "drip" technique. Therefore, Pollock turned to synthetic resin- based paints called alkyd enamels, which, at that time, was a novel medium. Pollock's technique of pouring and dripping paint is thought to be one of the origins of the term action painting. Pollock: No. 5, 1948 What is Generative Art

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Helen Frankenthaler is an American abstract expressionist painter. She is a major contributor to the history of postwar American painting. Having exhibited her work in six decades she has spanned several generations of abstract painters while continuing to produce vital and ever- changing new work. Frankenthaler: Mountains and Sea, (1952) Initially associated with abstract expressionism her career was launched in 1952 with the exhibition of Mountains and Sea. This painting is large - measuring seven feet by ten feet - and has the effect of a watercolor, though it is painted in oils. In it, she introduced the technique of painting directly onto an unprepared canvas so that the material absorbs the colors. What is Generative Art

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The elucidation most often cited in recent years is attributed to Philip Galanter, Artist and Professor at Texas A&M University, from his 2003 paper What Is Generative Art? Complexity Theory as a Context for Art Theory Generative art refers to any art practice where the artist uses a system, such as a set of natural language rules, a computer program, a machine, or other procedural invention, which is set into motion with some degree of autonomy contributing to or resulting in a completed work of art. While this is accurate and descriptive, and a very long sentence with all the right words, a single phrase like this is not enough. I dont think it quite captures the essence of generative art, which is much more nebulous. In my mind generative art is just another bi-product of our eternal titanic battle between the forces of chaos and order, trying to work out their natural harmony, as expressed in a ballet of light and pixels. But flowery crap like that isnt going to get us anywhere either. What is Generative Art

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James Faure WalkerJames Faure Walker: Loose Eight, archival epson print, 40 x 51 cm, 2007

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All will be better served if the long history of generative art is recognized as being tightly bound to the canon of mainstream art in galleries, museums, and the academy. Generative art is threaded throughout 20th century art movements, but it is rarely called generative art. There are movements and tendencies referred to as systemic art orrules-based art. These are often confusing convolved with movements such as minimalism and conceptual art. Unfortunately the terms generative art and rules-based art are sometimes used interchangeably. What is Generative Art

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Also Wikipedia give us another point of view. Generative Art is art or design generated, composed, or constructed through computer software algorithms, or similar mathematical or mechanical autonomous processes. The most common forms of generative art are graphics that visually represent complex processes, music, or language-based compositions like poetry. Other applications include architectural design, models for understanding sciences such as evolution, and artificial intelligence systems. Frank Richter, 6d-hyperset, c-print, 2006 What is Generative Art

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To define generative art as artwork which uses mathematical algorithm was proposed by Carlo Zanni. Generative software art, as it is usually understood today, is artwork which uses mathematical algorithms to automatically or semi- automatically generate expressions in more conventional artistic forms. For example, a generative program might produce poems, or images, or melodies, or animated visuals. Usually, the objective of such a program is to create different results each time it is executed. And generally, it is hoped that these results have aesthetic merit in their own right, and that they are distinguishable from each other, in interesting ways. Carsten Nicolai, Static 7, acrylic, magnetic tape, polyester, aluminium frame, 200 x 260 cm, 2005 What is Generative Art

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The project SCIENAR explicitly aims in particular to create an interactive environment for both Scientist and Artists, through this environment Scientists can explore the role that Mathematics plays in understanding and making Art, as well as produce mathematical objects that are useful in Art; while Artists can found mathematical structures and forms that they can directly use, without needing the subtleties of Mathematics, to inspire and produce their artworks. ONE OF POSSIBLE WAY - HOW TO FILL UP THIS AIM IS webMATHEMATICA

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We will speak in this speech 1. about webMathematica as a possible tools for producing artistic objects 2. about Lindenmayer systems, fractal plants and Random walking as one of possible concepts 3. about our result achieved by the interaction between science and art sphere in Slovakia 4. about the possibility - how to use dynamical web pages in creating Your own "piece of art"

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What is webMathematica? WEBMATHEMATICA ENABLES THE CREATION OF DYNAMICAL WEB SITES THAT ALLOW USERS TO COMPUTE AND VISUALIZE RESULTS DIRECTLY FROM A WEB BROWSER. All of the computational power in Mathematica is available to build special calculators and problem solvers that are delivered over the web or over your corporate intranet to the specific intranet site. The development process is so simple that most Mathematica users can proceed through it without having to go through long development cycles or needing the services of dedicated developers. In many cases, all that is required is adding the Mathematica commands and a couple of simple tags to a web page.

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The web interaction of webMathematica is provided by a Java web technology called Java servlets. Servlets are special Java programs that run on a web server machine. Support is provided by a separate program called a servlet container (or sometimes a "servlet engine") that connects to the web server. One of popular servlet container is Apache Tomcat. Essentially all modern web servers support servlets natively or through a plug-in servlet container. Closely related to Java servlets are Java Server Pages (JSPs); both servlets and JSPs integrate very closely with webMathematica. The computation and visualization engine for webMathematica is Mathematica. What is webMathematica?

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And now for artists - simple and more useful webMATHEMATICA allows a site to deliver HTML pages that are enhanced by the addition of Mathematica commands. When a request is made for one of these pages, the Mathematica commands are evaluated and the computed result is inserted into the page and delivered to the client browser. What is webMathematica?

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And now for artists - simple and more useful How it works ? 1. Browser sent requests to webMathematica server. 2. webMathematica server acquire Mathematica kernel from the pool. 3. Mathematica kernel is initialized with input parameters, it carries out calculations, hand returns result to server. 4. webMathematica server returns Mathematica kernel to the pool. 5. webMathematica server returns result to browser. What is webMathematica? webMathematica technology

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We can demonstrate the real application running on one part of Lindenmayer turtle graphics. What is webMathematica?

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1st step Browser sends request to webMathematica server. You can write to the web browser YOUR own Axiom, Replacement rules, Number of iterations and Angle of rotation. How to choose these parameters is explained on all created webMathematica pages. How it works in real ? explanation for artists on example of Lindenmayer systems What is webMathematica?

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2nd step webMathematica server acquires Mathematica kernel from the pool. Don't understand? Never mind! This server activity is realized automatically, without any needs from user. Fractals - Lindenmayer Systems How it works in real ? explanation for artists on example of Lindenmayer systems What is webMathematica?

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3rd step Mathematica kernel is initialized with input parameters, it carries out calculations, hand returns result to server. Don't understand? Never mind! This server activity is realized automatically, without any needs from user. LSystemWithF[axiom_, (* initial sequence *) rules_, (* replacement rules *) iterations_, (* number of iterations *) \[Delta]_ (* angle of rotation *)] := Module[{minus, plus, fastRules, last, direction}, (* computation of the two rotation matrices, for "right" and "left" *) minus = {{ Cos[ \[Delta]], Sin[ \[Delta]]}, {-Sin[ \[Delta]], Cos[ \[Delta]]}}; plus = {{ Cos[-\[Delta]], Sin[-\[Delta]]}, {-Sin[-\[Delta]], Cos[-\[Delta]]}}; (* we rewrite the replacement rules in a form that is faster.*) fastRules = rules /. {(a_ -> b_) -> (a :> Sequence b)}; (* Initial position and direction *) last = {0, 0}; direction = {1, 0}; (* - multiple application of the replacement rules using Nest - interpretation of F, + and - using Which. If "only" the direction direction is to be altered, the result is...;, i.e., Null - add the initial position using Prepend - sort out all "non - motions" - i.e. Null using Select *) Select[Prepend[(Which[# == "F", last = last + direction, # == "+", direction = plus.direction;, # == "-", direction = minus.direction;]& Nest[(# /. fastRules)&, axiom, iterations]), {0, 0}], (* select all points *) # =!= Null&]] How it works in real ? explanation for artists on example of Lindenmayer systems What is webMathematica?

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4rd step webMathematica server returns Mathematica kernel to the pool. Don't understand? Never mind! This server activity is realized automatically, without any needs from user. How it works in real ? explanation for artists on example of Lindenmayer systems What is webMathematica?

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5th step webMathematica server returns result to browser. Do you want see it in practice? Look at... How it works in real ? explanation for artists on example of Lindenmayer systems What is webMathematica?

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real webMathematica pages What is webMathematica?

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Do you want see it in practice? Look at... What is webMathematica?

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The beauty of plants has attracted the attention of mathematicians for centuries. Geometric features such as the bilateral symmetry of leaves, the rotational symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most extensively. Beauty is bound up with symmetry. In case we want to understand the beauty of flowers from the mathematical point of view, it is need to analyze two separate look in for that prolem. The first is the elegance and relative simplicity of developmental algorithms. The second is self-similarity. When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. Lindenmayer systems - Mathematics and beauty plants

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In 1968 a biologist, Aristid Lindenmayer, introduced a new type of string-rewriting mechanism, subsequently termed L-systems. L-systems are applied in parallel and simultaneously replace all letters in a given word. Lindenmayer systems - Mathematics and beauty plants

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Lindenmayer systems - Mathematics and beauty plants

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Lindenmayer systems - Mathematics and beauty plants

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Here are results produced by turtle walking (Lindenmayer systems) See also (gallery or create Your own) Lindenmayer systems - Mathematics and beauty plants

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Here are results produced by turtle walking (Lindenmayer systems) See also (gallery or create Your own) Lindenmayer systems - Mathematics and beauty plants

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Lindenmayer systems - Mathematics and beauty plants

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Other applications In the next picture there were generated a random walk and rotate a modified version of this walk around the starting point. Simple algorithm based on three pseudo-random numbers were used, in which presents the number of direction to go, presents number of copies and number of line segments of one line.

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Other applications The next examples were taken a curve given in the form of line and reflect parts of this curve on some randomly selected segments of list of points. Both of these objects were created randomly with webMathematica pseudo-random generator.

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Other applications These objects were used also for art inspiration look as follows. Young artists from School of applied arts J. Vydru from Bratislava created several photo-montages based on webMathematica random concept during the Scienar meeting in Kremnica.

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Other applications One of the main concepts in randomness was used Koch's snowflakes. Here the various iteration stages for a single curve are stacked on top of each other.

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Other applications T. Šufliarska, webmathematica a Scienar, 2010

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Other applications T. Šufliarska, webmathematica a Scienar, 2010

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And the real art application? The following application were created by Slovak students of School of Applied Art, Other applications

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catBirch tree Other applications

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Starting with such an image, and creating mirror images to the left, below, and lower left, we get an image that is typical for a kaleidoscope. Art application inspired by webMathematica application Other applications

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We take a curve given in the form list of circles and their parts and reflect parts of this curve on some randomly selected segments list of points. Other applications

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11th International conference Aplimat This year was organized 11-th international conference Aplimat and as a part of this international event was organized also the special section dedicated to Math and Art, to connections between scientists and artists.

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Other applications

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Final art workshop Kremnica – On September 14-18th, 2011 we organized the final Workshop in Kremnica, in the place of Academy of Fine Art in Kremnica. There were presented several lectures dedicated to main areas and to the main concepts from this project and students from Academy of Fine Art and Design and School of Applied Art presented their works

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Thank You very much and You are welcome on Altering server

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