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

One of humanity’s favorite 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 sometime between the late 1970s and mid 1980s, during the advent of personal computers—, 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 recognized the potential appeal of these pictures —so intriguing and so different from 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 influential book The Fractal Geometry of Nature (1982), Benoît Mandelbrot hints at the emergence of this new aesthetics, describing it as geometric, showing a certain restraint particularly when close to the scientific models, and having the defining characteristic of self-similarity. To him, this imagery was likely to gain acceptance because it echoed nature —since fractals were the structures that described a great variety of natural and artificial phenomena— than with mere abstractions. The entire book, as he stated, was intended as both a casebook and a manifesto (Mandelbrot, 1982), so we could regard it as the first fractal geometry manifesto in history… though not necessarily of fractal art.

In 1989, Mandelbrot referred to this new art form again, distinguishing it from art created for commercial intent and that made for purely aesthetic purposes. He argued that it 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 (the formulas) to generate images and requires a computer to speed up the calculations (the rendering). The final component —consisting of the selection of formulas and the cropping— rests in human deliberation, the constituent responsible for choosing the algorithm, selecting the aesthetic sections to refine, applying color, and polishing the near-complete work. The first two phases, taken together, focus on fractals as mathematical models, and the third on artistic choices, highlighting the shift from a mechanical computational process to creative human input. While Mandelbrot’s intention appears to have been to emphasize the scientific function of fractals, the last step, set apart as secondary from his perspective, actually requires creativity and intentionality, underscoring the importance of the human role in transforming mathematical output into expressive, visually meaningful art.

Here is a short list of attributes that defined fractal art in the early days… along with clues to exclude what is not from that reference:

  • First, it is the creation of images resulting from the application of fractal geometry and its algorithms. Therefore, pictures that exhibit repeating patterns or suggest infinite detail do not qualify as fractal art unless they are plotted algorithmically; only those generated through iterated computations are the seeds for this form of expression.
  • Second, a computer equipped with appropriate software (a fractal generator) serves as the means to give life to fractal art since this is how the images originate. Consequently, anything conceived by other means does not fall into this category either.
  • Third, the skills of a human being to guide the process are essential. This point establishes a distinction between fractal art and other autonomous methods that reduce human intervention to a minimum, as is the case with generative art, with which it shares many features.

Thus, a fractal algorithm, a computer to execute it, and a human to choose from the pool of outputs: these are the elements required to generate fractal art. Despite these defining parameters, inspiration from fractal theory let some artists outside the field —even in traditional media— to embrace complexity, chaos, recursion and self-similarity, and label their production accordingly. After all, aren’t fractal principles applicable to everything in existence? In a similar vein, might we say that everything in the world is 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 laypeople what this art form 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 had become common, and people were applying additional processes to fractal images to enhance or alter their original properties. Even several fractal generators had already incorporated graphics editing tools into the software, allowing users to modify their creations without leaving their natural workplace (absolving of any outsider’s sin in the process). This signaled an evolution in the genre.

Yet, the Fractal Art Manifesto limits the scope of fractals to the visual arts because that’s the medium in which its author works. However, in 2000, the Fractal-Art-FAQ, a document maintained by Jean-Pierre Louvet, Juan Luis Martínez and Phil Jackson, expands the scope 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 offers a more flexible view of fractal art at the turn of the 21st century, yet it still recognizes the three defining elements from the 1980s —algorithms, computers and human input— as essential. A few years later, when Wikipedia added an entry for fractal art, it preserved 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 classifying 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. ArtHistory.net, on the other hand, goes back to basics and offers a more concise 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 the definitions above coincide in stating that fractal art is a creative expression that uses fractal properties to produce primarily images (visual works) —whether still or animated— and music. The generative process typically requires a fractal algorithm, a computer equipped with appropriate software, and human input for composition. All these points have been agreed upon since the beginning. Yet, some people have tried to broaden the concept to include art created out of repeating patterns in more traditional methods, even without the intervention of technology. By definition, such works should not be classified as fractal art. A traditional painting depicting self-similar patterns —or even the iconic silhouette of the Mandelbrot Set— would probably fall outside the scope of fractal art under those original guidelines.

Several questions remain: Is there more than one type of “fractal art”? Have we been relying on the wrong criteria to define the style, or have we been using the wrong term? If, after almost 40 years of evolution, we’re still uncertain about what this art is —or even whether it’s art at all— what might we be missing from the equation? Similarly, what should we call a picture that draws on fractal ideas but isn’t generated algorithmically? How should we refer to an image that began in a fractal generator but then underwent a series of graphical transformations, either within an enhanced fractal program or in an external graphics editor? And how should we classify a photograph or illustration of a natural or human-made structure that exhibits fractal characteristics? Aren’t all these examples part of fractal art?

Can we simply agree that this art form has evolved to encompass a broader spectrum of artistic expressions? Should we adhere to the original definition, or is it necessary to classify everything that incorporates fractal properties under the umbrella of fractal art?

Juan Luis Martínez
2017.02.13 (Monday)

References

Revision history
  • 2025 April 18 for precision.
  • 2025 August 17: Heavily edited the fourth paragraph and did some minor changes throughout the second half of the writing for clarity.
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