The quantification of art and fractals, by William Wang

When we consider art, specifically visual art, the term can conjure a variety of images. For most people, art can be represented by classical art: drawings and paintings, such as the Mona Lisa. But with the development of technology, visual art begins to encompass new mediums and styles. An art student might begin by learning drawing and composition, then proceed to develop skills in charcoal or watercolor. Computing transforms this paradigm altogether. Digital artists today can paint through tablet interfaces, or illustrate with vectors.

However, works created in such a manner merely utilize computers as a tool. Ultimately, analog mediums can produce visually identical results. To truly use computers as a medium, we must marry two seemingly contrary traits: the creativity associated with art, and the strict logic associated with mathematics and programming. In school we are taught that these are complete opposites: some people are “left-brained” and logical or “right-brained” and intuitive. But computer art demands we abandon such overgeneralized schemas.

Yoko Ono, Painting for the Wind, 1961

Yoko Ono first demonstrates this combination in Instruction Paintings, wherein she paints by sending instructions to a third party who paints solely in accordance with the instructions. This foreshadows the emergence of coded art, which today ranges from Java-based Processing to the consumer front-end of the internet: websites presented using HTML and CSS. In coded art, the artist does not create using any tools in the way a painter or logo designer use theirs. Unlike these tools, they do not operate in a “what-you-see-is-what-you-get” (WYSIWYG) environment. In many ways, artists using code as a medium delve one level of specificity deeper than the digital illustrator.

For the artist using Photoshop, for example, they draw with a mouse or tablet, and the computer translates that interaction with the tool into an image. The artist might draw a horizontal line across the canvas, and the computer must interpret this command to produce the result our intuition predicts. Meanwhile, the coder must specify and quantify all of the details: the color, opacity, thickness, flow, etc. of the line, as well as the exact pixels at which the line begins and ends. While the pen tool might create smooth Bezier curves in Photoshop, the coder must calculate the precise angles and anchor points.

This bears the question: why bother? Don’t these digital tools just make life easier for the artist? For the artist seeking to use the computer as a tool, this is mostly true. Creating a painting with code is simply more tedious and difficult than painting through Photoshop. But discarding the tool also provides us with more power. The coder can introduce complexity and precision to visual art the human mind cannot feasibly manage.

This results in fractal art. Unlike traditional art or its simulations thereof in the digital medium, fractal art is impractical in analog mediums. This algorithmic art involves mathematical calculations that produce fractal objects, which are translated by the computer into visual images. In other words, the artist is not imagining a result and producing it. Instead, the artist devises a clever set of rules or definitions, inputs the parameters, and uses the computer to manifest the work the same way Yoko Ono used a third party to paint according to her instructions.

Mandelbrot Set

Two of the most famous types of fractals are the Julia Set and Mandelbrot Set. They epitomize the usage of computers for static visual art: without a computer to interpret the rule set created by the fractal artist, these beautiful works would not be possible. It just goes to demonstrate that “left-brained” logic and “right-brained” creativity are not mutually exclusive. If anything, they might be more interdependent than pop psychology would lead you to think.

Julia Set