Using Fractals In Biophilic Design

Fractals and the Human Experience

Fractal designs are found everywhere in nature and have permeated the human experience of the world. They are found in artwork by Van Gogh and Botticelli, architectural feats like the Eiffel Tower and in structures from ancient Greek, Egyptian and Aztec civilizations. Fractals in biophilic design are infinitely complex patterns that are self-similar across all scales, micro to macro.

Figure 1: The Koch snowflake is a fractal curve that starts with an equilateral triangle. Each iteration removes the inner third of each side, building another equilateral triangle at the location where the side was removed. Iterations zero through four shown.

Naturally occurring fractals can be found in fern fronds, waterfalls, tree branches, leaf veins, mountain ridges and so much more.

The appeal of fractals for humans appears to be innate rather than learned. Preferences for fractals are seen in children as young as three (Robles, 2020). The ability to effortlessly detect and process fractal patterns is fractal fluency. Our ability to easily grasp nature’s complex sense of order frees up our minds for cognitive tasks such as evaluating threats or problem solving (Trombin, 2020). One could argue that humans are instinctively drawn to fractals for survival.

Human beings evolved in sensory rich fractal-laden environments, as opposed to our modern built environments, which are intrinsically Euclidean — rectangles, lines, right angles, etc. This separation creates an opportunity for designers to use fractal-inspired elements to align humans with our innate needs and preferences.

The Study of Fractals in Biophilic Design

The practice of using fractals in biophilic design is beautifully researched and documented by Terrapin Bright Green, a sustainability consulting firm specializing in biophilic design research and education. Terrapin reviewed 500 publications on biophilic responses to create their groundbreaking study entitled “14 Patterns of Biophilic Design“.

Fractal geometries are a biophilic pattern described as “Complexity and Order.” A space with thoughtful “Complexity and Order” is engaging but not overwhelming, soothing but not boring (Browning, 2014).

In 2020, Terrapin released a deep-dive on Complexity and Order conditions entitled “Working with Fractals” by Rita Trombin.

The study includes a toolkit for designers wishing to incorporate fractals into their daily work. Trombin’s eight insights into designing biophilic fractals may influence your next design project:

  1. The best opportunity for incorporating fractals may be to create visual or physical access to the outdoors where fractals occur naturally.
  2. Determine how fractals help in telling the design story. Question which design problem the fractal solution is solving.
  3. Target a medium range of fractal complexity. Overly complex fractal geometries or overuse of fractals can induce discomfort.
  4. A biophilic fractal feature has an impact on the space around it. Fractals increase the complexity of a minimalist space or add order to a complex space. Consider the fractals within the space they will occupy.
  5. Pay attention to scale – fractal designs on a bedroom wall will be experienced differently than fractal designs in a multi-story art installation. 
  6. Place fractal designs in locations where the most people will benefit from them. 
  7. Fractal experiences can be multi-sensory —visual, tactile, auditory, continuous or fleeting, spatial or organizational. 
  8. Computer generated fractal designs are simple to generate but can lack the warmth and randomness of nature. Start with nature before technology.

Case Study – Relaxing Floors by Mohawk

Mohawk Group is one of the world’s largest flooring manufacturers with a reputation for forward-looking strategies (Smith, 2020). Following the trend of biophilic design, Mohawk created a line of carpet tiles inspired by fractals. The Relaxing Floors line was a collaborative effort between Mohawk, 13&9 Design, scientist Richard Taylor and the University of Oregon.

This team started the process of creating a fractal-based flooring design by looking at how the human eye observes a landscape. The eye moves around the landscape, focusing on areas of interest in much the way a bird flies around a landscape looking for food. These patterns create a fractal trajectory map as shown in Figure 2(a).

In Figure 2(b), the team adds “seeds” or dots at the locations between trajectories. In Figure 2(c), remove the trajectories, and in Figure 2(d) the seed sizes scale to reflect the length of the trajectory to reach them. In the flooring pattern, replace the circular seed shapes with lines and triangles. The result is a grouping of carpet tiles that can be cut and arranged randomly but still retains its fractal quality.

Mohawk Group Relaxing Floors Collection

As you see more people and places adopt biophilic design, additional studies will bring a light to the use of fractals. And while this article serves as just a brief overview of what fractals are, there is no better way to learn than from your real life experiences. So the next time you are out servicing client accounts, take a look around and see what kinds of fractals can you spot.


Browning, W.D., Ryan, C.O. & Clancy, J.O. (2014). 14 Patterns of Biophilic Design: Improving health and wellbeing in the built environment. New York: Terrapin Bright Green.

Robles, Kelly E., Nicole A. Liaw, Richard P. Taylor, Dare A. Baldwin & Margaret E. Sereno (2020). A shared fractal aesthetic across development, Humanities and Social Sciences Communications, 7:158.

Smith, Julian, Conor Rowland, Saba Moslehi, Richard Taylor, Anastasija Lesjak, Martin Lesjak, Sabrina Stadlober, Luis Lee, Jackie Dettmar, Mark Page, Jeanette Himes (2020). Relaxing Floors: Fractal Fluency in the Built Environment. Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 24, No 1, pp. 127-141.

Trombin, Rita (2020). Working with Fractals. New York: Terrapin Bright Green.

Mehgan Laveck is the owner of Rocky Mountain Living Walls, a biophilic design company based in Fort Collins, CO. Mehgan started RMLW in 2016 after a long career as a project management professional in construction and IT. Green walls are an outlet for her innate creativity and her passion for biophilic design. Mehgan grew up with a strong appreciation for nature, riding horses with her family in the mountains of Asheville, NC. She moved west to pursue graduate studies in theoretical math at Colorado State University and never looked back. These days, you can find her trailblazing in her industry – sharing the benefits of living walls, preserved moss walls and other biophilic design trends

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