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Fractals: A Better Way to Explain Synchronicity?

Humans and nature sometimes repeat patterns as fractals.

Key points

  • Patterns repeat, sometimes as fractals, in all of nature including humans, animals, and plants, and geographically.
  • Meaningful coincidences are composed of two or more patterns repeating together in time.
  • Fractals are characterized by being self-similar and recursive, curving back on themselves.

As Sigmund Freud made very clear, human beings are compelled to repeat patterns—the repetition compulsion. Patterns laid down early in life are propelled forward to recreate the familiar that can be beneficial or problematic. Most varieties of self-help including psychotherapy focus on identifying those maladaptive patterns to find ways to change them.

This human pattern repetition has been reified in memorable aphorisms like the following:

  • Those who do not learn history are doomed to repeat it.
  • Neurosis is doing the same thing and hoping for a different outcome.

Meaningful coincidences, which include synchronicity and serendipity, are based on our recognizing repeated patterns. A pattern in the mind is repeated in the environment.

Pattern repetition also occurs in our natural environment. Many of these patterns take the form of fractals.


The classical Euclidean geometry taught in high school does not fit the patterns of nature. Though cylinders and rectangles may be great for modeling the shapes of technology, there are few regular shapes to be found in the natural world.

with the gracious permission of Dr. Terry Marks-Tarlow
Fractal Shapes
Source: with the gracious permission of Dr. Terry Marks-Tarlow

Most natural objects—and that includes people—are composed of many different types of patterns woven into each other and replicating everywhere in our human body. Replication of shapes and formations characterize all our organs including lungs, kidneys, heart, arterial system, and brain. Patterns repeat in the growth of a human life from conception to embryo, to fetus to newborn baby to child, to adolescence to adulthood. From DNA to cells, to tissue, to organs and systems. Replication marks the evolution of a life from birth to death.

According to psychologist Terry Marks-Tarlow, fractals constitute a meta-level of patterns in the universe—they are the patterns of patterns. They appear at the quantum level and in natural landscapes like coastlines and fault lines. Snowflakes are built on endless varieties of the same basic shape. We see the branching fractal in tree branches and roots, rivers, the arteries and neurons of our bodies.

Fractal geometry is a new branch of mathematics, dating back to the 1970s. From the field’s inception, discoverer/inventor Benoît Mandelbrot recognized the relevance of fractals for capturing complicated natural shapes. The hallmark of a fractal, self-similarity, means that the pattern of the whole is reflected in the pattern of the parts. Self-similar patterns occur across multiple scales, whether in space, time, or across imaginary, symbolic realms. Self-similar spirals, for example, recur in the growth of nautilus shells, in the spiral flower of the sunflower, or as spiral galaxies. As the nautilus grows, the shell’s curve retains the same relationship between part and whole. This is the essence of identity everywhere. Though our parts may change, they retain a vital relationship to the whole: You are still yourself, even though all the cells and fluids in your body or the ideas in your mind continually change. Always changing, yet ever the same.

Fractals are called "fractals" because they exist in fractional dimensions between our standard geometrical dimensions of 1 (a line), 2 (a plane), and 3 (a solid). A line fits perfectly in one dimension. A plane (like a piece of paper) fits in two dimensions and a solid (like a ball) fits in three dimensions. Fractals fit in between a line and a plane (or in the real world, between two and three dimensions). Consider trees. Because they are so complex, with huge numbers of smaller and smaller branches, trees never quite reach three dimensions. If you put them in a box, there will always be some space left over.

Fractals differ from ordinary patterns. Unlike a pattern on a shirt that can be reproduced by machines, fractals are generated by “seed algorithms” that are recursively applied. To be recursive is to curve back on itself, just as the heart pumps blood into circulation and then back into itself or the mind uses thoughts to think about thoughts. Fractals can originate endless numbers of individual self-similar patterns by feeding back on themselves. They feed back on themselves to generate variations in scale and time of the original pattern.

Synchronicity and fractals

Boundary permeability seems to be the key characteristic that fractals share with meaningful coincidences. Simultaneous independent discoveries and shared dreams (Gilhooley and Toich, 2020, p. 9) illustrate boundary permeability between people. The fractal jagged coast of England appears to be a discrete boundary. However, measuring its length depends on the detail of the measuring instrument. The finer the measurements, the longer the coastline, making the separation between land and sea increasingly less distinct (Mandelbrot, 1967).

with the gracious permission of Dr. Terry Marks-Tarlow
Source: with the gracious permission of Dr. Terry Marks-Tarlow

As described by Marks-Tarlow, a fractal epistemology holds that an objective reality exists outside of our minds (Marks-Tarlow et al, 2019). This belief stands in stark contrast to consciousness theorists who believe that our personal consciousness is the same as external reality. From Marks-Tarlow’s perspective, the fractals of external reality merge (synchronize or come into synchrony) with the fractals of our internal reality. Fractals emerge in the boundary between order and chaos, which is consistent with the observation that meaningful coincidences are increasingly likely to happen during destabilizing life situations like stressors, high emotion, and need. Like synchronicities, fractals can be rhythmic, poetic, and inspiring. To view Dr. Marks-Tarlow discussing fractals and synchronicity, please click here.


Among the proposed explanations for meaningful coincidences like randomness, God/universe, and quantum physics, fractals offer a compelling alternative. They promise a more practical perspective than the rational, logical Euclidian lens through which most of us now view reality. It also promises a mathematically-based foundation for understanding reality and an acceptance of an objective reality with which we are deeply involved. The fractals of external reality are, under the right conditions, able to synchronize with those of our internal reality by which we can discover how we may all be connected.


Gilhooley, D. & Toich F, Psychoanalysis, (2020) Intersubjective Writing, and a Postmaterialist Model of Mind: I Woke Up Dead. Oxford, UK: Rutledge

Marks-Tarlow, T., Shapiro, Y., Wolf, K. & Friedman, HT., (2019) A Fractal Epistemology for a Scientific Psychology. New Castle, United Kingdom: Cambridge Scholars

Mandelbrot, B.B. (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension Science: 156, 636-638)

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