Defining fractal art: A “history” (kind of)

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Defining fractal art


One of human hobbies is to classify everything by giving it names. Nothing can exist without at least a common designation. And so it happens that at some point, probably in the late 1970s, it became necessary to distinguish a novel type of computer-generated images from the sample pages in the catalog of visual things. By then some people had already realized the potential appeal of this kind of pictures, so intriguing and so different than anything that preceded this style, that it was worth coining a unique label for it. Since it was the product of the equally recent field of fractal geometry, it seemed reasonable to call it fractal art.

In his popular book The Fractal Geometry of Nature (1982), Benoît Mandelbrot recognized the emergence of this “new form of art,” and described it as geometric, minimalistic (when close to the scientific models), and having the defining characteristic of self-similarity. To him, this art was prone to acceptance because it was more akin to nature (as fractals were the structures that described a great variety of natural –and artificial– phenomena) than mere abstractions. The whole book, as he expressed, was purported as a manifesto (Mandelbrot, 1982), so we could well say it was, broadly speaking, the first fractal art manifesto in history (though maybe that’s pushing it too much).

In 1989, Mandelbrot referred again to fractal art, distinguishing it from art for commercial intend and art for aesthetic purpose. Fractal art was different because it was “art for the sake of science” (Mandelbrot, 1989, p. 21). He also observed that,

The artist’s taste can only affect the selection of formulas to be rendered, the cropping and the rendering. Thus, fractal art seems to fall outside the usual categories of ‘invention’, ‘discovery’ and ‘creativity’. (Mandelbrot, 1989, p. 24)

With that declaration, Mandelbrot granted significant weight to the technical aspects of fractal art: it relies on fractal algorithms to generate an image, and requires a computer to speed up the calculations. The last component is human input, the one responsible for making decisions as to select the algorithm, pick up the aesthetic sections to further develop, apply some coloring, and finish the work. The first two aspects deal with the fractal, and the last one with the art.

Here is a short list of attributes to define fractal art in the early days… and the clues to exclude what is not. First, it is the production of pictures resulting from the application of fractal geometry and its algorithms. Images that exhibit repeating patterns or suggest infinite details do not classify as fractal art if they are not plotted algorithmically; only the ones generated by iterated computations are potentially the seeds of this kind of expression. Second, a computer with proper software (a fractal generator) is the means to give life to fractal art since this is how the pictures originate; as such, anything conceived by other means do not fall into this category. Third, the skills of a human being to guide the process are a must. This last point establishes a distinction between this craft and any other autonomous method that reduces human intervention to a minimum, as is the case with generative art, with which fractal art shares a bit.

A fractal algorithm, a computer to execute it, and a human to choose from the pool of outputs is what it takes to generate fractal art. Notwithstanding these delimiters, inspiration from fractal theory let some artists outside the field –even in the traditional arts– to embrace complexity, chaos, recursivity and self-similarity, and call their production likewise. After all, aren’t fractal principles applicable to everything in existence? In a similar vein, isn’t everything in the world a fractal, so to speak?

More recent attempts at defining fractal art

In 1999, at the pinnacle of computer-generated fractals, Kerry Mitchell came up with a Fractal Art Manifesto to explain to the laymen what this art is:

Fractal Art is a genre concerned with fractals—shapes or sets characterized by self affinity (small portions of the image resemble the overall shape) and an infinite amount of detail, at all scales. Fractals are typically created on a digital computer, using an iterative numerical process. Lately, images that are not technically fractals, but that share the same basic generating technique and environment, have been welcomed into the FA world.

Mitchell keeps fractal art within the digital medium, though he expands the category to include other computer-generated images with a similar origin but that are not “pure” fractals. By then, post-processing was a thing, and people were applying additional processes to fractal pictures to enhance or alter their original properties. Even several fractal generators had already incorporated graphics editing tools to the software, so those working with these shapes could edit them without leaving their natural workplace. That signaled an evolution of this genre.

The Fractal Art Manifesto limits the scope of fractals to the visual arts because that’s the medium in which its author works. Nevertheless, in 2000, the Fractal-Art-FAQ, a document maintain by Jean-Pierre Louvet, Juan Luis Martínez and Phil Jackson, expands the range to include music, another artistic manifestation in which fractal theory has its influence. They note that “the same recursive principles of fractal imaging have been applied to music to create what has been termed fractal music.” They also add the following observations about the current state of the visual aspect of fractal art:

After a first phase, when the goal was to produce pure self-similar images of mathematical objects using the best possible colors and some other visual effects, now the tendency is to use fractal programs to create abstract images whether they clearly show fractal structures or not. In particular, the current interest in mixing several layers of individual fractals (often unrelated) to create a single complex image is a manifestation of this tendency. Also, many artists use some post-processing transformations on the fractal images, and now several fractal programs come with their own post-processing options. Other artists combine fractal motifs with photographic pictures or with other images created with advanced graphics’ programs. But consider that keeping evident the fractal structures in the image and limiting the graphic effects may be an interesting challenge too. (Section 2b)

The Fractal-Art-FAQ allows a more flexible view of fractal art at the turn of the 21st century, but still recognizes the three defining elements of the 1980s (algorithms, computers and human input) as essential.  A few years later, when Wikipedia added an entry for fractal art, it also kept these general ideas:

Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media. […] It is a genre of computer art and digital art which are part of new media art. […] 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.

Unlike previous definitions, Wikipedia opens the doors to classify non-computer-generated images as fractal art, stating that in the western world it is “rarely drawn or painted by hand,” implying that in other parts of the world some hand-drawn or painted examples of fractal art exist., on the other hand, goes back to basics and offers a more brief definition that limits it to the fundamental points of the genre:

This art form is based on the calculations of fractal objects that are represented as images. Fractal art is created with the use of computer software; it is not art that is rendered by hand. In some cases, non-fractal images are incorporated into the fractal design to create a type of hybrid work.

In summary

All definitions above coincide in stating that fractal art is a creative expression that uses fractal properties as a means to produce mainly images –be it still or animated– and music. The generation process usually requires a fractal algorithm, a computer with proper software, and human input for composition. All these points have been agreed upon since the beginning. Yet, some people have tried to expand the concept to include art created out of repeating patterns in more traditional ways, even without the intervention of technology. By definition, such works shouldn’t be classified as fractal art. A traditional painting depicting a self-similar pattern, or even spirals or the iconic silhouette of the Mandelbrot Set should probably not be classified as fractal art by those same rules.

Now some questions remain: Is there more than one “fractal art”? Have we been using the wrong arguments to define the style, or is it that we’ve been giving it the wrong name? If after almost 40 years of evolution we’re still not clear of what this art is or is not, or even if it’s art at all, what are we missing from the equation? Similarly, what should we call a picture that is based on fractal ideas, but which is not rendered algorithmically? How should we refer to an image that started out in a fractal generator, but went through a series of graphical transformations inside an enhanced fractal generator, or outside in a graphics editor? How should we classify a picture of a natural or artificial structure that exhibits fractal characteristics?

Shouldn’t we simply agree that this art form has evolved to encompass a wider spectrum of artistic expressions? Should we stick to the original definition, or do we really need to classify everything with a fractal structure within the umbrella of fractal art?

Juan Luis Martínez
2017.02.13 (Monday)