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Exploring Design Styles: Fractal Art

Here's an in-depth look at fractal art, a mind-bending visualization of mathematical calculations.

Exploring Design Styles: Fractal Art
Marc Schenker April 22, 2024 · 15 min read

Fractal art sits at the intersection of design and mathematical calculation, which makes it completely mind-bending. This type of algorithmic artwork results from fractal objects (never-ending patterns that are eternally complex and appear similar to the whole image) represented as various visual artforms, such as animation and still images. Think of this as mathematical beauty in visualization.
Part of the broader genre of new media art, fractal art is a trend that took shape in the mid-1980s. During that time, computer aesthetics also began to develop as an art form, as design became more digitized on the road to the 21st century.
Due to the mathematical complexity of these fractals, algorithmic art that incorporates these patterns and shapes is often mesmerizing and, some would say, hypnotic. One thing’s for sure: It’s an aesthetic that you’ll be easily able to identify and won’t soon forget.
Prepare to get your mind blown with this immersive walkthrough on digitized art.

The History of Fractal Art

To figure out where this trend came from, we have to go back earlier than the 1980s. This decade was known for very retro styles and typography, but, due to the then-nascent emergence of computers and the Internet, also for technological inroads in design.
However, as a subset of algorithmic art, the roots of fractal design began with the American computer artist Roman Verostko. His claim to fame is the invention of his proprietary software for creating original art, back in the 1960s. Verostko’s software manipulates the drawing arm of a pen plotter–a machine initially meant for engineering and architectural illustrations. Verostko’s software changed this application to function as an extension of the artist’s drawing hand and arm.
It’s important to note that this was more along the lines of computer-generated art and design, as opposed to fractal art proper, since the computer program was written to tell the pen plotter what to do (instead of the artworks being created inside of computer memory). Still, this is a distinction without a difference because all art created by fractals is based on software created by man (ie, the artist), after all.
To gain a better understanding of this concept, have a look at some fractal shapes that are created by designers:

Between the 1960s and mid-1980s, something very profound happened that gave this design trend its identity and name. This was the coining of the word “fractals†by Benoit Mandelbrot, a French-American mathematician, in 1975.
In reality, though, the concept of fractals has been around since the 17th century, when the German mathematician Gottfried Leibniz mused about self-similarity (possessing the same, statistical similarity at different scales), a key principle in fractals. By the 19th century, another German mathematician, Karl Weierstrass, came up with the first definition of a fractal (a function with a graph) while presenting to the Royal Prussian Academy of Sciences.
Still, we can’t ignore Mandelbrot’s contributions to the actual development of fractal art, which is typically created with fractal-generating software. His work led to several, key evolutions that would popularize fractal design in the 1980s:

  • In 1979, Mandelbrot and IBM programmers came up with the first fractal printouts.
  • In 1980, computer graphics researcher and developer Loren Carpenter presents Vol Libre at SIGGRAPH (Special Interest Group on Computer Graphics and Interactive Techniques), a two-minute, computer-generated movie that included fractally rendered landscapes.
  • In 1983, Acorn User magazine featured a BBC BASIC listing for creating fractal shapes.
  • Starting in 1984, computer games began to render fractal forms in games like Rescue on Fractalus!

Throughout the 1990s and into the 21st century, fractal art has intensified in popularity, thanks to the increasing use of software programs, as well as designers and artists who are willing to experiment with this visualization of mathematical beauty derived from precision algorithms.

The Diversity of Fractal Imagery

The cool thing about this design trend is the sheer number of different approaches to this visualization. In essence, a different mathematical calculation leads to a unique visualization of a shape. Here’s a quick rundown of all the ways that algorithms and even artists and painters can express this style.

Standard Geometry Fractals

This type is based on standard geometry.

Image Credit: Wikimedia Commons

It relies on iterative transformations found on a starting figure, such as a straight line (the Koch snowflake), a cube (the Menger sponge), or a triangle (the Sierpinski Triangle).

Strange Attractors

This is a group of numerical values to which a mathematical system tends to evolve.
It must also have a fractal structure.

Image Credit: Wikimedia Commons

Iterated Function Systems

Iterated function systems are ways to create fractals.

Image Credit: Wikimedia Commons

They’re commonly two-dimensional creations and self-similar.

Newton Fractals

These forms of fractal art created by applying Newton’s method within the plane of complex numbers.

Image Credit: Wikimedia Commons

They are boundary sets.

Fractal Flames

Created by Scott Draves, an American video artist and mathematician, in 1992, fractal flames are part of the iterated function systems class of fractals.

Image Credit: Wikimedia Commons

However, they’re unique in their own right because their color is based on structure instead of density or monochrome.


Mandelbulbs are three-dimensional figures that were created in 2009 by Paul Nylander and Daniel White.

Image Credit: Wikimedia Commons

They were created with spherical coordinates.

L-System or Lindenmayer Fractals

Initially, a parallel rewriting system, the L-system or Lindenmayer system can be used to generate self-similar shapes.

Image Credit: Wikimedia Commons

They’re also helpful in modeling the morphology of different organisms.

Fractal Landscapes

As the name implies, these are surfaces generated via algorithms meant to create fractals that copy the look of natural terrain.

Image Credit: Wikimedia Commons

They are created by random fractal processes.
The final type of fractal art is something called fractal expressionism. This is even more special than the shapes we’ve discussed up to this point because these fractals are created completely by the artists themselves, as opposed to mathematical calculations or computer generations.
For this type, we have the American painter Jackson Pollock to thank. His famous painting style–which involved poured paintings and the kind of random wildness typified in other design trends such as action painting–has been called both organic and natural by critics.
Fractal expressionism implies that artworks exhibit a straightaway representation of nature’s pattern in their creations.
For some more inspiration, check out these fractal illustrations created by designers for designers:

The Design Characteristics of Fractal Art

By now, you’ve had a good, in-depth look at the intricate, mind-bending formations of this digitized style of art. Here are the common bonds that will always be present in any design that incorporates this style:

  • Self-Similarity — A mathematical concept where an object will always be precisely or just about similar to any part of itself. In visual artwork, this means that a smaller part of the entire design will look very similar to the whole and vice versa.
  • Psychedelia — This is a reference to altered consciousness and designs that attempt to recreate this mental state, such as surreal elements and distortions.
  • Intricate Patterns — A characteristic tied into the aforementioned self-similarity, this intricacy is seen in the sheer level of detail and complexity of any fractal pattern, given the magnitude of repetition of the shapes.
  • Mathematical Beauty — The premise on which all fractal art is based, mathematical beauty refers to the aesthetic enjoyment viewers get from the abstract, pure, and simple organization of math.
  • Patterns in Nature — Fractals are naturally found in nature in many formations, such as clouds, shells, mountains, trees, coastlines, and snowflakes, to name just a few. Ergo, when admiring algorithmic art, you’re seeing the natural world represented in a digitized form.
  • Vivid Colors — Perhaps the most striking feature of these shapes is the color with which they’re displayed. Whether in manmade fractals (ie, Jackson Pollock paintings), natural patterns in the environment, or in digitized software, splendid colors are always a hallmark of this design trend.

Now that you can identify this style wherever you spot it, let’s talk about the interesting techniques at work behind the scenes when you’re beholding these awesome formations.

The Techniques Behind Fractals

For starters, the majority of this artwork comes from algorithms and computer-generated software, with the brilliant colors mentioned above being intentionally added for pure, aesthetic effect. In the vast majority of cases, it’s never drawn or painted by hand, though some of the notable artworks from Jackson Pollock are the exception.
Fractal-creating software is typically the starting point for this fractal art, following this sequence:

  • Establishing the parameters for relevant fractal software
  • Calculating the potentially time-consuming algorithm
  • Assessing the outcome

In the post-processing phase, additional software may be utilized to further change the images, and there may even be some non-fractal shapes thrown into the mix, based on the artist’s decision.
These days, everywhere you look, you’ll see fractals as the basis for various kinds of animation and digital art. They’ve also found application in various fields like:

  • Plant-growth simulation
  • Landscape generation
  • Texture generation

If you’d like to try your hand at creating your own fractal masterpieces, there are various programs, both free and paid, that you can use:

  • Apophysis — For Microsoft Windows systems, this is an open-source IFS program.
  • Chaotica — This is a commercial IFS program specifically for Windows, Mac OS, and Linux. It is free for non-commercial use.
  • Electric Sheep — This is open-source, distributed screensaver software that lets you animate and evolve fractal flames, for display as screensavers on networked computers.
  • Terragen — A generator for fractal terrains, Terragen produces animations for both Mac OS X and Windows.
  • Ultra Fractal — Ultra Fractal is an app for generating and rendering fractals. First available in 1999, it’s since become one of the more popular pieces of software for experimenting with these digitized shapes.
  • Wolfram Mathematica — This modern technical computing system empowers you to create fractals.

Examples of Fractal Art

These mesmerizing patterns and shapes abound all around us, whether in nature, created by algorithms, or as tangible structures created by man. Here are some very noteworthy creations.

Manmade Structures

Main Dome of the Selimiye Mosque

In Edirne, Turkey, sits the Selimiye Mosque, which is on the UNESCO World Heritage Site list. If you visit it and check out the interior of the mosque’s main dome, you’ll see stunning Islamic geometric patterns, which are very similar in design to the repeating sequences of fractals.

Image Credit: Wikimedia Commons

The more you look at the intricate forms and shapes, you begin to realize that they share the self-similar trait so characteristic of fractal geometry.

Hindu Temples

Another famous, manmade creation that bears a striking resemblance to this mathematical artwork is the Hindu temple. Due to their penchant for repeating patterns and shapes across the entire, gigantic structure, these temples contain a lot of designs that can be considered self-similar, which is the calling card of fractal illustration and design.

Image Credit: Wikimedia Commons

Since the smaller parts of these temples resemble the whole structure, or even fit numerous times inside the entire whole, they are said to be fractal in nature.

Algorithmic Fractal Art

This is the “true†and more well-known application of this style when we speak of this trend. The product of algorithms, computers, and programs, this approach to digital art is truly breathtaking and almost limitless in its creativity. Here are some of the most memorable creations we could find.

3D Fractal Ball

Looking like a veritable cover from a Tool album, this digital artwork was created in Apophysis, the renderer and editor of fractal flames that’s available on both Mac and Windows.

Image Credit: Wikimedia Commons

If you look closely, you can see that all of the tiles that are on the black ground are similar to the entire presentation. Even the series of spheres in the center of the composition displays properties of fractal art, thereby making this creation extremely self-similar.

Random Fractal

Created with the Chaotica program for Mac OS X, Linux, and Windows, this random fractal shows what an artist can do with software that includes the selective randomization of form parameters.

Image Credit: Wikimedia Commons

In essence, it lets the artist give up a certain degree of control in the creation process. Note how this fractal is less symmetrical or balanced that some of the other fractal-based illustrations that we’ve shown you so far. In spite of this, you can still appreciate how the various lines, forms, and patterns relate to each other and to the entire composition as a whole.

Electric Sheep Fractal

Here’s an image of one of the many created through the Electric Sheep project. It shows a figure that’s self-similar, based on the question mark squiggles in the foreground being the same shape as the same squiggles farther off in the background.

Image Credit: Wikimedia Commons

In addition, the larger, overall image is made up of many, smaller squiggles that seem to go on forever.

Multi-Layered Fractal

Depending on the mathematical calculations used, a fractal may be more or less complex. In this case, a multi-layered fractal is one that exhibits extra depth and complexity for the viewer to behold.

Image Credit: Wikimedia Commons

Made with the Ultra Fractal software app, this example of fractal art showcases the immensely gorgeous colors that are possible with this approach to art. Amid the swirling yellows, pinks, reds, and purples, you also get to see the intricate patterns and spiral shapes seem to stretch on limitlessly. In fact, the left side of the composition displays more complexity than does the right side of the frame, which is dominated by more regular forms.

Sterling Fractal

Created in the Sterling computer program, this specific fractal is a great example of what artists can do with vivid, mind-blowing colors. Featuring mainly cooler colors, this shape calms in a very serene fashion.

Image Credit: Wikimedia Commons

From the standpoint of geometry, the composition is also a treat, as it features a plethora of curves, swirls, vanishing points, and other aesthetically pleasing forms.

Patterns in Nature

The cool thing is about this style of art is that you can see it in nature, too, without the interference of man. In other words, nature has been creating these wondrous fractals since the beginning of time–well before our digitized culture started creating fractal art from the mid-1980s onward.
Here are some of the most staggering shapes that nature has to offer.

Nautilus Shell

Not only does the nautilus shell show off an intricate and interesting pattern, but it also demonstrates a logarithmic growth spiral. Put another way, the self-similarity that’s a key factor in fractal art is evident in the development of the shell itself.

Image Credit: Wikimedia Commons

Note how the smallest shapes at the very center of the shell bear a striking resemblance to the growing and larger patterns toward the outside of the shell.

Namib Desert Sand Dunes

The self-similarity of this design trend doesn’t just have to be present in natural objects that are self-contained. They can even be present in the environment, where outside forces act on the landscape itself. Case in point: the sand dunes of the Namib Desert of southern Africa.

Image Credit: Wikimedia Commons

The sand patterns are ever-changing because they form based on how the wind blows. However, both the ripples on the surface of the sand and the crescent-shaped dunes themselves reform whenever there are appropriate conditions (read: when the wind blows effectively enough).

A Design Found in Algorithm Art and Nature

Though this digitized art first appeared in the mid-1980s, you can convincingly argue that it’s been around forever due to its uncanny presence in nature. Indeed, perhaps in no other design trend is the nexus between computerized influence and natural inclination so strong as in this one.
Whether digital or straight from nature, one thing’s clear: The self-similarity concept of this approach to art is mind-bending and wondrous. It’s also the basis of this fractal art, which ensures these timeless, unique designs will continue to inspire awe in viewers around the globe.

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About the Author
Marc Schenker

Marc is a copywriter and marketer who runs The Glorious Company, a marketing agency. An expert in business and marketing, he helps businesses and companies of all sizes get the most bang for their ad bucks.

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