Editor’s Note: It is always a thrill when one of our authors receives recognition for excellence. Terry Marks-Tarlow and colleagues, Harris l. Friedman, Yakov Shapiro, & Katthe P. Wolf, have had their book, Fractal Epistemology for a Scientific Psychology (Cambridge Scholars, 2020), nominated for the APA Ursula Gielen Global Psychology award. The book has also just been released in paperback, which makes it more accessible. To celebrate both these achievements, we have been given permission to publish the Foreword and Introduction. We have become more aware that the human brain will almost automatically seek to find patterns within things. As psychotherapists, when we work with a life that feels broken, we often find a pattern or shape of what is within the client that can be utilized to generate healing. Fractals are the fundamental underpinning to much of this intuitive perception of patterns and the shapes of things. Understanding more about fractals can only lead us to more understanding of ourselves and the fascinating profession we practice. We thank Terry and the publisher for allowing us to share their knowledge and wisdom.


The Profound Nature of Fractals

Richard Taylor

What do we see in the wispy edges of clouds, in the intricate branches of trees, and in the jagged peaks of a snowy mountain range? For many years, it was assumed that these images were a haphazard mess devoid of any pattern. However, the past fifty years have seen a remarkable revolution in the way we study nature’s scenery, which has brought scientific inquiry and artistic views of nature closer together. At the heart of this revolution lies the discovery of intricate patterns called fractals. Dramatically referred to by many as the fingerprint of life, fractals have been shown to be the basic building block of many of nature’s patterns, ranging from clouds, trees, and mountains through to our brains, blood vessels, and lungs.

No one should be surprised that nature uses fractals so prevalently. The fractal geometry of nature is profound, both in the simplicity of its construction and in the favorable properties that emerge. Fractals repeat patterns at increasingly fine magnifications. Yet, with this simple act, they build a rich and intricate shape possessing a level of complexity that Euclidean shapes such as triangles, squares and circles cannot match.

Mathematicians have studied the exotic consequences of this complexity since the 1860s. However, a century passed before Benoit Mandelbrot realized that nature was using this same pattern repetition to build the world within and around us. Upon his discovery, he struggled to find an umbrella term to unite the earlier mathematical work with that of nature. Marveling at the jaggedness of fractal lighting, he focused on its fractured character and, on a whim, morphed the Latin translation fractus into the now familiar term fractal.

Armed with this quirky name, a new era of understanding nature was welcomed in. Many subsequent studies were fueled by bio-inspiration—the principle of learning from nature’s repetition and applying it to artificial systems. For example, we now have fractal storm barriers based on coastlines, fractal solar panels based on trees, even my own fractal electronics based on neurons. Clearly, the future shines brightly for scientific applications of this building block of nature.

Even more exciting, fractals have the potential to build bridges from the sciences to the arts. Surely, artists and scientists have a shared interest in understanding fractals? For me, the most staggering factor in the story of fractals is that artists have been creating fractal patterns in their artworks long before these recent scientific breakthroughs. Examples include Leonardo da Vinci’s drawings of turbulent rivers, Jackson Pollock’s epic organic paintings, and M.C. Escher’s mind-bending prints. Pollock’s fractals have even been shown to reduce people’s stress-levels, perhaps explaining that magic feeling of awe that many people experience when facing one of his creations (Taylor, 2006). This deep resonance between the observer and their fractal world is not a new discovery. Experiments from the 1980s show that hospital patients recover far more quickly from major surgery when given a room with a view overlooking nature (Ulrich, 1984).

This effect is called fractal fluency—our eyes have become fluent in the visual language of nature’s fractals. In a sense, we are “hardwired” to appreciate fractals. The theory for fractal fluency pictures fractals as being embedded deep in our psyche, perhaps forming the basic structure of the Jungian collective unconscious. Another theory builds on the fact that our eyes trace out fractal motions when searching for visual information.

Similar to the eye hunting through images, many animals undergo fractal searches through their terrains when foraging for food. Ongoing research looks to see if people’s daily journeys similarly follow fractal patterns. This prevalence of fractal searches triggers a flood of more profound questions related to our human behavior. In terms of creativity, perhaps our minds exploit fractal searches when exploring the landscapes of our imaginations? If so, perhaps our minds use fractals to drive many emotional, cognitive, and spiritual aspects of our lives?

Such human questions might surprise those who associate fractals with their mathematical origins. However, as Galileo is often quoted, “the book of nature is written in the language of mathematics.” In fact, a number of defining studies on the road to Mandelbrot’s discovery foreshadowed the potential of fractals for exploring questions of humanity. Mandelbrot’s work evolved from Lewis Richardson’s 1950s work attempting to develop models of why nations go to war. Even earlier, Ralph Elliott’s research from the 1930s pictured the stock market as following fractal up and downs, a phenomenon latter proposed to indicate that society exhibits a collective fractal mood.

In the future, we might well conclude that fractals are the essence of being human, not just in the building of our lungs, our nerves and our bloodstreams, but in our individual and collective behaviors. This is the brave new world for fractal researchers. “A Fractal Epistemology for a Scientific Psychology” belongs firmly to this exciting world and its quest to bridge the personal with the transpersonal will broaden the scope of fractal thinking. In my discussions with Mandelbrot, he was delighted to see fractals venture from their mathematical shell and shake the world. He would have been delighted to read this book.

Taylor, R.P. (2006). Reduction of physiological stress using fractal art and architecture. Leonardo, 39, 245-251.
Ulrich, R.S. (1984). View through a window may influence recovery from surgery. Science, 224(4647), 420-421.

Go to the February 2021 issue for the main article Towards fractal foundations for transpersonal science
by Terry Marks-Tarlow, Harris l. Friedman, Yakov Shapiro, & Katthe P. Wolf

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