What is a Fractal?
For a 3-minute visual journey of Fractals click on this YouTube video!
If Fractal patterns strike a chord of familiarity—it is because they appear everywhere. Fractals patterns show up in so many areas of life that some say they actually model a fundamental life principle. They are order within chaos.
Fractal patterns take many different forms: they can be identified in pine cones, sun flowers, snow-flakes, plant structures and bone structures and blood vessel networks. Fractals can be identified in the swirls that occur when cream is dripped into coffee, oil is dripped into water, and the path that smoke takes when blown into the air. They can be identified from the airplane window within the winding crevices of huge land masses like the Grand Canyon. Fractal patterns can be said to show up in phenomenon as small as sub-atomic particles and as large as the fluctuating chaos of galaxy clusters.
Many mathematicians and scientists believe that Fractals serve as one of the best metaphors for the way life arranges itself in all of its dimensions and multi-faceted-ness.
Fractals are complex, self-similar shapes that repeat fundamentally similar patterns at ever-increasing and decreasing scales. That is, when you magnify a segment of a fractal pattern, you will discover a microscopic version of the larger pattern. Magnify a still smaller section, and the same pattern will again emerge in infinite complexity with self-similar fidelity. Conversely, zoom out, and you will see the same patterns emerge. Each aspect of a Fractal shapes and is shaped by every other aspect.
Fractals as Trees
At the base of a tree are the roots, which come together in a trunk, then branch out into smaller and smaller branches, then split off in to twigs, and finally separate into stems with leaves or perhaps fruit. We often perceive a twig or one part or a branch of the tree, yet don't necessarily see the "big picture" of the entire trunk or the entire tree. Another way to think of this is that we see the tree but don't perceive the entire forest.
Fractals as Architectural Structures
An talented and experienced architect is able to see and understand the complex Fractal structure of a building very well. As such, they can determine aspects of that structure that need adjusting in such a way that the structure improves in its strength and integrity. The simple process of "tapping" on the walls to determine where the nails (studs) exist is part of the diagnostic process that yields optimal understanding of what is needed to strengthen and improve that structure.
Fractals as Weather Patterns
Scientists specializing in weather systems are trained to examine the Fractal patterns in those weather systems to predict the daily and weekly weather, in addition to examining the effects of global warming and its potential impending threats to our well-being.
Fractal as an Elephant
Consider the well-known parable of 3 blind men who have never seen, touched or experienced an elephant. They encounter an elephant and are asked what they think this object is. One blind man feels the leg and declared that this "elephant" is a tree trunk. Another blind man feels a tusk and argues that is a shiny, weapon. Another blind man feels the trunk and insists that this "elephant" is a like a hose used for putting out a fire.
In this parable, each blind man experiences one part of the elephant and each does not yet comprehend the whole elephant. Fractal patterns provide a useful way to, like the video above, to see and conceptualize the parts that make up the whole.
Fractals as Interconnected Disciplines
Fractals can be a useful metaphor for understanding the complex relationship between the disciplines (or subjects) of mathematics, science, history, language, literature, and the arts. Skillful curriculum design results in learning that reveals themes and principles which is at essence of all disciplines and thus elucidates the "big picture" or “main ideas”.
So often we read or hear that all disciplines/subject are interconnected by conceptual bridges. Here is an example of part of my interdisciplinary curriculum that shows one paragraph on how this interconnection is demonstrated:
“Just as the prevailing winds are caused by planetary spin, so the swirling currents of history have definite courses and times, guided by the great movements of the Earth, and governed by the nature of number and geometry, on which all things are built. It is popular to claim that History repeats itself; rather, it seems in some sense that History rhymes!"
Fractals as Road Maps that Provide Perspective
Fractal patterns provide insight into the laws and design principles that govern the way our lives unfold, which are subsets of the laws that govern the way the world and universe operate. Contemplating Fractals can help provide road maps for gaining insight into our lives. For example, as we determine/perceive the entirety of the fractal pattern or fractal system, understanding it leads to having a greater facility with and mastery over the system. As we understand the system we have more choice in how to shape the system and it becomes more flexible and malleable, allowing us to adjust it in such a way that we more easily reap results and rewards.
Fractals in Body Work
When the Fractal of the body system of bones, muscles and veins is adjusted through massage and/or chiropractic techniques, a greater sense of flow occurs which enhances health and vitality in that body system. Talented medical doctors are able to diagnose the problems in the body in the same way that an expert in physical structures/system can diagnose the problems in a structure or system. The more aware they are of the Fractal and all of its components, the better chance they can help with healing.
Fractals in Psychology and Counseling
A talented psychotherapist or counselor is able to work with the "Fractal of the emotional constellation" of the individual and thus optimize the sense of healthy flow of emotional expression in that individual. Like the detective carpenter/architect who tests for the nails in the wall, a very observant and skilled therapist/counselor, along with certain key questions or inquiries at the optimal time, help to unconceal the "nails" in that individual's psyche and thus allow for the kind of treatment that contributes to a sense of psychological wholeness and healing for that patient.
Fractals in Organizations: Dynamic Systems and Adaptive Leadership
Fractals are used as metaphors to understand the complex, dynamic systems that play themselves out in any organization. When the Fractal nature of an organization is deeply understood and comprehended by a consultant or leader, he or she has the capacity to give feedback to other members of that organization so as to increase effectiveness.
Top leaders in organizations understand that their organization is more complex than their employees, or even they, know or can know. They understand that their organization is analogous to a complex Fractal. With this complexity comes twists and turns that are difficult to anticipate. Knowing how difficult it is to anticipate, they practice what Harvard Kennedy School of Government professor Ronald Heifetz calls “adaptive leadership.” A leader who exercises adaptive leadership is adaptable and flexible in ways that help their system--their organization--to thrive.
Using Fractals/Complexity in Teaching, Counseling, Coaching and Consulting
In my teaching I use Fractal metaphors not only to empower students in understanding the complexity with disciplines (such as History and Math) but also between subjects. In this sense I’m an interdisciplinary specialist; the focus of my doctorate program at Columbia Teachers College is Interdisciplinary Studies. Working with complexity in a classroom also involved understanding the complexity with the group of students in terms of their variety of learning styles and cultural backgrounds. Their academic intelligence is intertwined with their emotional and social intelligence; as such, students need their teacher to be cognizant of the complexity of their various forms of intelligence. When consulting with schools and learning organization I use complex models to help organization see their blindspots like the example of the elephant above.
I empower members of schools and learning organizations to gain greater perspective on their own complexity and, upon understanding this complexity, to exercise greater adaptive leadership at all levels of their organization. I do this through lecture, seminars, workshops, and individual and group coaching. You can read academic papers about this process here.