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Applying Fractals to Determine the Structure of Optimal Health

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. Nature exhibits not simply a higher degree but an altogether different level of complexity.”

Benoit Mandelbrot on fractal geometry

What follows is a journey down the rabbit hole of looking at optimal health. I included some of this material in previous posts but thought it would be useful to integrate it as a chapter. This is a “sneak peak” of a health book I am putting together. I intend to share some information on a universal theme and illustrate how it might provide a framework for our health. I hope that you enjoy the material and find it an eye-opening journey.  Please be sure to sign up on the blog for past and future posts.

Christopher M. Cirino, DO MPH   

Founder Your Health Forum

The Mandelbrot set frames the future path toward discovering the mechanism of health and disease

The Mandelbrot Set unravels the mystery of life and how health and disease can be better understand in the science of growth and aging.

Introduction: Observation Meets Scientific Rigor

The Evolution of Scientific Inquiry

Humans have contemplated the mechanisms of nature and the body for thousands of years. Perspectives developed and evolved, which became the prevailing philosophies and practices of the time, including Chinese medicine, Ayurveda, Greek thought related to the theories of Miasmas and the Four Humors, Allopathic medicine, Osteopathic Medicine, Homeopathy, Naturopathy, Integrative medicine, and Functional Medicine. Some of these disciplines, such as Ayurveda and Chinese medicine, evolved their models over centuries, while others developed more recently with the dawn of greater technology, e.g., Allopathic medicine. However, every discipline has an incomplete story, bordering on the limits of our scientific understanding. Even some of them strive to explain broad concepts that get watered down in pseudoscience or are inaccurate “quackery.”

When the germ theory constructs were espoused during the time of Hippocrates and later in the middle ages by Ibn Sina (Avicenna), there was no microscope available to confirm these beliefs to allow these principles to be accepted and disseminated. It took more than 800 years later for a scientist like Louis Pasteur to publish the Germ theory in 1861 after microscopes were refined over the course of a few hundred years. Even this was met with skepticism at the time.

The contributions of allopathic medicine are vast across all specialties. Physicians now use fine-tuned therapies the size of small molecules to affect the cellular signaling in the body for rheumatologic, oncologic, dermatologic, and gastrointestinal diseases, such as Rheumatoid arthritis, breast cancer, psoriasis, and Crohn’s disease. Earlier bulky chemicals came with greater risks of toxicity. People with an otherwise fatal disease, such as HIV, can now take one pill daily and live a normal lifespan. A disease without a cure, hepatitis C, can now be cured in as little as 8 weeks.

Osteopathic medicine has gained greater credibility and traction since its inception in 1874 by Dr. Andrew Taylor Still. At one point, the American Medical Association considered osteopathic medicine a cult. Dr. Still lost three of his children from meningitis in 1864. This may have been the impetus for the intensive study of the human body that he conducted for a decade afterward. At the time, medical practice was a lot less precise than it is now. Procedures like bloodletting and treatments like opium, whiskey, and arsenic were in a doctor’s meager toolkit, none of which had any benefit. The tenets of Osteopathic medicine include 1) the body is a functional, interconnected unit; 2) structure and function are interdependent; 3) the human body has the innate ability to heal itself. These tenets echoed some of the prevailing thoughts espoused by Hippocrates, mainly that the body could heal itself.

Today, the American Osteopathic Association recorded that in 2019, there were 121,006 Doctors of Osteopathic Medicine (DO’s) in practice. This is the highest number in history; there has been a nearly 300% increase in osteopathic medical physicians in the past three decades. What had started largely centered on a concept of musculoskeletal system dysfunction (somatic dysfunction) being the source of disease developed into a full-service profession parallel to allopathic medicine? But, in many ways, both professions are converging.

Complementary and Alternative Medicine (CAM), Naturopathic Medicine, Functional Medicine, and Integrative Medicine are different terms applied to a framework to understand the body holistically and address the lifestyle factors that cause illness. All medical practitioners can agree on these general concepts: that disease simply does not occur in a vacuum; there is a cause and effect. These concepts are not foreign to allopathic and osteopathic medicine. Although the fundamental constructs in which this system addresses chronic disease are sound, the practitioners accept a grab bag of alternative modalities of treatments, such as free radical therapy, acupuncture, reiki, and reflexology, that are either not scientifically supported or have been debased. Attached to office visits often comes a list of products and supplements with a half-attempt to personalize care while profiting.

Toward the Source of Health and Disease

The medical profession inculcates physicians with a skillset to listen and determine the patient’s signs and symptoms. This approach cannot be devoid of the search for or query of a cause. Just as we would not mop up water under a sink without finding where the water came from, so too when a physician addresses a patient with a problem. With future technological advances, just as the microscope literally changed the scope of a physician’s perspective or the stethoscope affected a physician’s auscultation, it is expected that the health paradigm may shift or expand from uncovering greater knowledge of the source and mechanism of diseases through technology. Some concepts regarded as pseudoscience, like the Germ theory at the time, may very well gain recognition as being scientifically based.

Science will continue to be the guide, though it will likely adapt too. New study designs and calculation instruments will likely be employed, diverging from the randomized clinical trials that best address pharmaceutical studies. Since the study of wellness requires an assessment of multiple coordinated systems, considering “the forest for the trees,” new technologies will likely be more sensitive to patterns in complex systems and functional (dynamic) observations. Even without direct physician observation, any person can now screen their sleep or assess their heart rhythm, or someone with diabetes continuously monitor their glucose, all using ubiquitous tools only recently made available.

A look at nature gives us a lot of information on how the environment affects our growth

Photo by Tausif Hossain on Pexels.com

Describing Patterns of Nature

The Golden Ratio

Let us step back for a moment and try to see the forest for the trees – literally. We will circle back to a universal health concept later. I have a fond love for nature. Not many experiences can hint at more about biological structures than a simple walk in the park. Nature provides us many examples of growth and structure, and from it lies an important insight on health, growth, and adaptation.

The next time you see a leaf on the ground, pick it up and look at how detailed the venation patterns are. Take notice that there is a large vein that branches into smaller veins and then smaller veins. In an elective class in college entitled “Fractals and Geology,” I became fascinated by how these natural phenomena could apply to how the environment affects growth. Although the area that I chose was the application of fractal measurements on leaf venation patterns, it continues to influence my views of health and disease, the concepts of which I will discuss in this article.

Look but don't touch. This nettle's venations fill in a leaf structure as it grows; structure and function are linked

The natural structure has been the subject of wonder, art, philosophy, and mathematics for millennia. Ancient mathematicians described the patterns of growth for thousands of years. What became known as the “Golden Ratio,” a mathematical interpretation of natural observation, had its origins with Phidias in 500 – 432 BCE, a Greek sculptor, and mathematician. His observations were even applied in the plans of the Parthenon. The structure correlates well with the Fibonacci spiral, a pattern pictured below, created from the mathematical equation and the pattern of 1,1,2,3,5,8,13,21,34,55, etc.

There are many structures in nature; I dare say almost everything, which exhibits this ratio of structure and growth, from the shape of a pineapple, broccoli, sunflowers, pine cones, nautilus shells, and even to the structure of our face and body. Aside from some evolutionary variations, why do humans have five toes and sloths have 2 or 3 toes?

The Fibonacci Spiral

The Fibonacci Spiral in its subtle structure captures the pattern of growth

The Fibonacci equation: xn = xn-1 + xn-2; xn is term number “n” xn-1 is the previous term (n-1) xn-2 is the term before that (n-2)


The Concept of Fractals

In 1975, Benoit Mandelbrot coined the term fractal from the Latin fractus, or “broken,” mainly for its broken, irregular nature. A fractal is an iterative structure that displays self-similarity. This discovery filled the gap of explaining natural structures, which Euclidean geometry was unable to characterize. Place a head of broccoli inside a box and observe that it does not fill the box’s space. A box is a three-dimensional Euclidean structure (a cube); living things approach but do not reach Euclidean geometric dimensions (i.e., one dimension is a line; two dimensions, a square; three dimensions, a cube). However, because they are detailed and show scaling, fractals are more intricate than a specific dimension. They are someplace in between dimensions. The term to describe the complexity of a fractal is the fractal dimension (FD). The higher the dimension, the greater the complexity. If the broccoli were broken down by mold, it would become less complex.

Fractals describe natural structures between the second and third dimensions (i.e., FD >2 and <3). Computers have simulated fractal formulas, and the most notable of these images was from Mandelbrot in 1980 (The Mandelbrot Set). Once computers were powered enough to handle these graphic renderings, fractal visuals became an important influencer of pop culture, art, music, and science during the eighties and nineties. Unlike computational fractals, nature’s structures are finite, eventually with the iterations terminating.

They display a scaling phenomenon so that when a tool is applied to measuring them, the results vary depending on the tool’s size. Since fractals are “rough” and not linear, measuring these structures’ perimeters produces increasing lengths as the tool becomes smaller and captures the roughness. Mandelbrot analyzed previous observations of coastline measurement variance and published in 1967 “How long is the coast of Britain?” If you were to measure a rough coastline with a ruler, smaller ruler sizes would measure greater complexity, leading to an increasingly longer coastline.

The Applications of Fractals in Health and the Human Body

Pressure Gradients of Fluid

The human body’s fractal nature hints at mechanisms by which our body sustains life and how disease states unfold. Within the body are cells that form numerous tubes, networks, and pathways that have transporting, filtering, assimilation, and removal functions. The arterial system in the body ensures that every cell receives nutrients assimilated and metabolized in our gastrointestinal tract and oxygen acquired from the lungs. Each cell can discharge the waste and carbon dioxide through the venous system back to the heart.

The blood recirculates through the system again to remove the carbon dioxide in the lungs and become oxygenated again and then is pumped from the heart’s left side through the functional filters of the body, the kidneys, and the liver. In this way, every single cell interacts with the rest of the body through a network. Through this, optimal health starts and ends.

The fractal organization is a necessary condition of complex lifeforms. These structures bestow several characteristics upon the organism: they provide a passageway from the environment to every single cell, they protect each cell from rapid changes in the environment, and they create a dynamic support network for each system and the body as a whole. Our circulatory system relies on the interplay of the blood pressure, the thickness of blood (density), and the vessels’ compliance and diameter, and its structure and function have fractal characteristics.

Ohm’s Law of Hydrodynamics

∆ P = Q X R

Q=Stroke Volume x Heart Rate

Q = Flow through a blood vessel = Cardiac output

∆ P= Pressure difference of two ends of the vessel

R = Resistance of the vessel

The circulatory system, as a tree would of its branches, grows outward from the heart, from the aorta to the microscopic capillary tributaries. The blood returns to the heart from tiny venules to the vena cava. The pressures generated from the heart related to the growth of vessels and the maintenance capacity of the system. Your blood pressure is a measurement of the maximal pressure from the heart, systole, and its most relaxed period, diastole. The pressures gradually diminish from the heart to the peripheral capillaries. The receiving venules relay the flowing blood back to the heart under lower pressures.

Any injury to the system resulting in a vessel break (e.g., varicose veins) alters the blood flow and taxes the system. A narrowed artery (e.g., in atherosclerosis or age-related changes) will require heart pulsation to increase blood pressure. Obesity leads to increase adipose stores, which exert some increases in peripheral resistance. Imagine changing water pressure by putting your thumb over the hose to make it narrow; the heart compensates similarly these conditions exist – up to a point.

Fractal Structure: Passage from Environment to Cell

Every cell in our body requires oxygen, micronutrients, and macronutrients delivered by the circulatory system. During human development, the embryo cells form specific sheets of folded tissues that provide the body with a greater surface area for growth and functioning. To maintain the requirements of each cell, the circulatory system grows within the structures.

When we look at the seemingly simple organs, such as the lungs, the kidneys, and the liver, there are branches upon branches of structural tubes to the cellular level, interfaced with vessels. Air is inspired, runs from our mouth, passes through the epiglottis into the trachea, and then branches off to form the right and left main-stem bronchi. These tubes branch into successively smaller bronchioles until the air reaches the alveoli, where gas diffuses into the vessels.

The chest wall might measure 20 inches long by 15 inches wide by 7 inches thick. The lungs may measure 12 inches long, 6 inches wide, and 3 inches thick. However, within this compact size is an incredible surface area. Imagine if you took these paths and placed them end-to-end. The length would be approximately 1500 miles, the distance between New Orleans and Boston. At the end-of-the-line, the alveolar sacs, which number 300 to 500 million in the lungs, all the diffusion of oxygen and carbon dioxide gases.

Fractals Have Scaling 

When you look at a fractal, you see the same components when you magnify it when you reduce it. This relates to its scaling properties. Building a body composed of building blocks that are only 20-30 microns in size (1 x 10-6 meters or one-millionth of a meter) requires a conduit that can bring the nutrition and oxygen needs to each cell. The conduit, which is itself composed of cells, either requires a system by which casting of prior cells or their secretions can create an uncirculated, denser substance (for example, cartilage, bone, and fibrin – think trachea, teeth, nails, hair, bones) or that tiny blood vessel systems be incorporated throughout. Similar iterative structures occur in the venous, arterial, and lymphatic systems of the body.

The organs are composed of specialized cells that allow a mixture of venous, arterial, and tube-like canals to carry out the basic function or filtering (lungs, kidneys, liver), assimilating (small intestines), and disposing of (kidneys, large intestines). In general, smaller branches transition from a structural (passages for in and out) to a functional process (gas exchange and nutrients from the blood). The alveoli are principally where gas exchange occurs from the air sacs to the intricate vessels where the arterial and venous systems meet — from the pulmonary arteries to the air sacs (carbon dioxide-rich blood allow carbon dioxide to escape) from the pulmonary veins (oxygen binds to hemoglobin in the blood cells), then returns to the left side of the heart.

However, these structures are not found this way in living organisms by accident, the exact mechanisms by which life self-organizes is still not completely understood. It likely is driven by molecules, chemicals, and hormones that turn on genes for protein production. At the underpinnings of structural determination lies the interplay of genetic guidance and environmental influence. Several factors influence both the growth and genetic expression, thereby influencing the development of structures. Examples include endogenous (internal) hormone production or other internal/external chemical signals, gravity, pressure, temperature, nutrition.

Bronchiolar Patterns Illustrate How Fractals serve the purpose of maximal function

The same process is occurring throughout our body to allow proper oxygenation of tissue (our vascular system), detoxification of our blood (liver and kidneys), drainage of fluid outside of our blood acquired in injury and infection, etc. (lymphatic system), and sensation and movement (nervous system). The systems are developed to maintain energy efficiency.

What happens when this process is in disarray? If there is damage to the structure, such as the lungs from smoking, how does the function change? If there are changes in the pressure around the structure, for instance, what occurs in obesity, how does the body accommodate these changes? If there is a change in what nutrition enters the body, how does the body alter its structure and function? How do these changes affect our bodies ability to function in homeostasis optimally?

The human experience requires the proper function of a series of organ systems, constructed by cells and their products. These systems allow us to sustain and adapt to our lives as terrestrial animals. Effectively, we are a universe of water-immersed microscopic cell sheets organized into tissues and organs, with bacteria on the “outsides” of our bodies – and then some. Our bodies are likened to an internal ocean, with water comprising 64-83% of each system. Even the hardest part of our body – bones – are far from devoid of water – consisting of 30% water.

The process of fractal organization from primordial single-cell organisms to the macro-systems that continue to evolve, requires a code to the structure which is imprinted in our DNA. What are some of the benefits that afford multisystem organisms, such as animals, a greater ability to adapt to various environmental pressures that are encountered? The writing will expound on the possible benefits of cell community and how understanding fractals can create greater insight into how structure enables complex organisms’ function. It is with hopes that through this exploration, we can understand what makes us uniquely human and what is health.

Fractal organization allows Scaling Up.

Before we begin the journey, it is important to mention that any attempts to understand the process by which complex organisms have emerged require some degree of hopeful connection in our retrospection. Things just happened as time unfolded, and it would be more than naïve to say that humans could be capable of understanding all of the variables. We assume that they were guided by numerous evolutionary selection pressures in the environment, such as gravity, sunlight, ambient radiation, food and water resources, and otherwise unknown survival pressures.

There are also countless examples of how evolution has occurred in more recent times (e.g., the bubonic plague, the peppered moth, and the industrial age). However, I can’t say that a “flap of a butterfly wing” didn’t have a role in our evolution – the so-called butterfly effect. We are merely just observers in the confines of scientific reasoning. Consequently, some of what we describe as “benefits” may be more creative or speculative in nature. I do not subtract the possibility of divine nature in this seemingly random and impossible series of events.

What about the intestines: Stretched out, they would measure 10 to 20 feet. If the large intestines were measured out, the length would measure approximately 5 feet. Kidneys: Each kidney contains approximately 1 million nephrons measuring 1-2 inches long. If you added the total amount of nephrons in the body and their average length, you would have 2,000,000 inches or 31 miles! What do these numbers mean?

The body is a universe of tissues which are designed to fulfill the body’s needs – from getting oxygen to every cell of our body and adjusting it on-demand – as in our respiratory and circulatory system, to disposing of gas, liquid, and solid waste through expiration, micturition, and defecation, and absorbing the nutrients from the environment that we consume and detoxifying any harmful forms of foods including sugar (digestive and hepatic system) and adapting to stressors and producing hormone precursors (endocrine and metabolic systems).

Fractal Growth, Health, and the Organization of Natural Structures

Many of us recall the whimsy as we looked at natural structures growing up as children. Just picking up a fallen leaf during autumn, as it did in my life, brings the questions of what leads to the shape of the leaves, their venation patterns, how color changes occur in the leaves, and what ultimately causes them to become fragile and dry out. When we visualize the complexities of our bodies, we can apply the same questions. The questions intrinsically require some degree of hypothesis to answer them and accept that the answers may not be inclusive of all the variables.

Aging and Decay occur nonuniformly and segmentally probably as a reaction to changes in nature

Changes in this Leaf Occured Nonuniformly. Was this triggered as a local response to the micro-environment (sunlight, heat, etc) in these areas?

Likewise, when we turn around the processes and attempt to explain how disease occurs, we can gauge how the system would likely function in an optimal setting. Studies can help understand the disease process since pathologic specimens provide a structure and clinical changes suggest a functional change. In many ways, we are in the age of holism as we gain a greater understanding of these biological structures. Our interpretations of the likely functions become less guesswork and more probable as the results can be assessed in more detail, analyzed, and reproduced.

We look toward fractal-like natural structures with curiosity and an analytical mind, with fascination seeking an explanation. Fractals come to be seen as a necessity of natural structure, organic and inorganic, and the interplay and adaptation of these structures from the changes intrinsically tied between internal and external. Changes resulting from a “dance” between the structure itself and nature – between organization and entropy.

Similarly, dysfunction can emerge from both external and internal forces. How do we begin to tackle this exploration of the factors that prescribe a recipe of fractal structure – that helps us journey “down the rabbit hole” of enlightenment? Looking at a tree and its roots and leaves, we see a scaling phenomenon, not unlike the structure that we see in our various organs, such as circulatory, nervous, and respiratory systems – our entire bodies!

The circulatory system’s mechanics rely on a pump generator, the heart, and how it propels blood through our body, ultimately to reach every cell of our body with nutrients and oxygen. The nervous system follows similar tracks, linking the brain with every micrometer of our bodies. The kidneys and liver tissue have a series of tubes and vessel beds that allow for filtering – not unlike the alveoli in the lungs.

Fractals patterns allow for a buffer between the cells and the environment. A single-cell organism meets its fate by even a slight perturbation of solute content, such as too much salt, sugar, or hydrogen (acid) in the environment. For this reason, substances such as these are used as preservatives to prevent spoiling of food. These solutes will cause a cell to lyse, or break down, as its water inside is released outside as an attempt to balance the environment.

Entodinium protozoa

Entodinium protozoa, smallest protozoa in the rumen

Many layers of cells protect a larger organism, such that only after a significant poisoning would it succumb to these solutes. Many cell layers and systems protect the organism from environmental circumstances. The body is a synthesis of systems that have grown together during development. The systems work in concert to provide an optimal state of metabolism, circulation, respiration, digestion, excretion, movement, and sensation. When one system is compromised, it affects other systems.

Although a disease process may manifest seemingly as one dysfunction, all the systems in some way are affected.

the changes that contribute to aging occur at a molecular level and appear as wrinkles

Fractal Applications in health, aging, and disease

Jeanne Calment of France, the oldest person, lived until 122 years, 164 days. Those that live past 100 years are known as supercentenarians – and she lived a generation further. Think of the body as having a set endpoint, maximal life expectancy somewhere around 122 years. Now visualize your life as a train that will meet its doom when it encounters a cliff at the end of the tracks. We may not be able to control that fate, but we can control the train’s velocity. This is where lifestyle factors, including healthy food and clean water, stress factors, injuries, environmental exposures, and habits, come in. These behaviors either impair or buffer the structure and function of your body on the genetic level. Negative exposures can reduce life expectancy; positive ones can increase it.

Our bodies go through changes that are subtle enough to escape our immediate noticing. As adults, about every 28 days, our skin layer (epidermis) is replaced; as we age, this slows down to every 45 to 90 days at an advanced age. With aging, there is an increased deposition of fibrin and calcium, and other minerals into our tissues at the cellular level within our vascular system. These changes alter the structural integrity of the tissues. An alteration in structure leads to an alteration in function.

Ultimately, functional changes increase the risk of other disease processes and lead to a downward spiral that we see with aging. Remarkably, supercentenarians exhibit a low incidence of vascular disease, in the least associating preserved vascular integrity with a longer life expectancy.

Since fractal structures are found in all living things, they can be useful in analyzing quantitative structural changes in aging. A fractal dimension is a tool that measures the degree of complexity and iterations of a structure. It lessens when structural changes in aging and disease diminish the degree of iterations. For example, as chronic obstructive pulmonary disease (COPD) worsens in lung disease, there is a decrease in functioning alveoli. Airways fractal dimension (AFD) has been inversely correlated with lung disease, with more severe disease associated with a decreased AFD.

Whether the disease is associated with a behavior, an injury, or an infection, changes ensue that decrease our complexity and reduce our function (Bodduluri, S, et al. 2018. Journ of Clin Invest. Airway fractal dimension predicts respiratory morbidity and mortality in COPD). Optimal health requires maintenance of complexity.

Other examples of fractal dimension changes with aging:

A decrease fractal dimension reflects • Age-related changes of the brain in Brain MRI analysis (Aliahmad, 2014)

• Smits et al. showed a gradual decline in EEG complexity with normal aging compared to significant reductions in complexity in those with Alzheimer’s dementia.

• Specific changes in the fractal dimension of retinal images may be predictive of a future stroke (Reishofer, 2018),

The Science of Complex structures: The Fractal Law of Nature

The Structure of Health

Take the information from the previous sections covering fractals and apply them as we address health. From nature, we gather an understanding of life and how our environment affects us. We develop insights or “laws” – of gravity, entropy, and heavenly bodies through the observations we make in the world around us. At its essence, a law is a concept that is simple, universal, and expected. If I dropped my cellphone as I was trying to put it into my pocket, I would expect that it would fall down – not up. The same goes for any sized object and from any height.

For a law to exist in health, we would expect that it would be, at its core, an explanation that could be applied to any living organism with consistent results. Even as we gain a greater understanding of the molecular structure and other chemical signals that interface with health and disease, a law would be further enhanced through these discoveries, not broken.

We are at a crossroads in our understanding of health, which I believe will take us to a time where more people will realize better health and enjoy a long and productive life. Can our understanding of “healthy” form a basis for constructing health promotion and disease prevention efforts? After all, it is better to determine a patient at risk for a stroke than for s/he to have one and offer therapy afterward.

Although many doctors already see patients with behavior challenges in their clinics, those who continue to smoke or harm themselves and want to change are competing with the brain’s safety net. They simply cannot stop because the brain does not want to. We already know that our current health system is “problem-focused” and limited in scope since addressing disease is a palliative effort compared to preventing it and assisting in behavior change. Pharmaceutical companies spend millions on research toward developing more medications that treat depression, diabetes, heart failure, and erectile dysfunction – all for treating conditions that result from behaviors.

Da Vinci's Vitruvian man drawing

Da Vinci’s Vitruvian man drawing captures the golden ratio

What is healthy, and how do you know it when you see it?

The motif of nature and the four seasons and how it resonates in understanding our lives has been the subject of much writing and poetry. As a seed germinates, we are born and then develop and ripen to our sweetest and most active forms before we begin to diminish, wither, and die. Nature is also a biologic mirror to the story and structures of our bodies…which takes me to a contemplative walk in the park to think of these questions.

Does nature provide lessons to us about our health? When I am out in the park, I take a look at the oak trees and think about their components from most peripheral to most internal: the leaves, the branches, the trunk, the bark, and the roots. In the spring, I look around and see the trees and their outstretched branches with blossoms in full bloom and small leaf buds starting to develop and grow into what will become full leaves in summer.

Each leaf has a complex vein network with patterns not unlike the branches of the tree itself. The leaf identifies the tree and vice versa. Using a magnifying glass, I see how complex the patterns are. I realize that each leaf is fulfilling a role for the entire tree. Is optimal growth and functioning a clue to what it is to be healthy as humans? Our respiratory system reminds me of the trees and branches that I see outside on my hikes.

If you were to take the segments of our lung airways and place them end-to-end, it would measure 1500 miles! That is a lot of detail inside our chest. The characteristic of branching patterns that display self-similarity is the definition of a fractal. This complexity seems inherent in what it means to be healthy. It also interesting and not coincidental that our lungs represent the pathway of oxygen into the bloodstream. Simultaneously, the leaves are the surface, in which carbon enters the tree and oxygen exits.

Health is the state of constant adjustment and prediction to the outside world

Health is the Constant Predictive and Reactive Adjustment to the Outside World Photo by Samuel Silitonga on Pexels.com

An Organism is a Dynamic Dance of Outside with Inside

How does the outside interact with the inside? What are the points of entry?

With a tree, there are at least three routes from the immediate outside: the leaves and branches adjust to location of sunlight and temperature, the leaves working in an integrative way with the growth of the tree; the network of roots that connect the outside soil to the trunk, branches, and leaves and send and receive water and nutrients from the soil and glucose synthesized; the bark and outer layers react to wind, gravity, and warmth and grow in a different manner to maximize survival.

The trunks of some trees that I see have either small knobby areas or oval-like structures known as a callus. It occurred when something happened to the tree that disrupted the bark. The tree heals like what would happen if we had an injury to our skin – our skin heals with a scar.

In animals, the route that the environment affects the body’s boundaries typically occur in 4 ways:

  • Injury and injection of the skin (examples include burns, trauma, and injection by biting/sting insects, animals, or drugs)
  • Inspiration into the lungs (examples include oxygen and smaller particles aerosolized in the air (including virus, toxic vapors/fumes, tobacco, drugs)
  • Ingestion  in the mouth and through the gastrointestinal route (food, drink, toxins, microbes)
  • “Inside Job” includes Interpretation and Imagination generated from our brains for safety, prediction, and resilient narratives. To some degree, we all face interpretations of traumatic experience or other chronic stressors that can alter the body’s chemistry (neurotransmitters, neurohormones, and hormones) and affect the immune system, growth, and maintenance of the system, and predispose to disease. This also includes how we adjust our lifestyle and how it may help or harm our health (exercise, sleep, habits). Neurotransmitters and neural pathways regulate these.

My mother was diagnosed with diabetes when I was in medical school. It was at that time; I was learning that in diabetes, the blood in her circulatory system becomes thickened by too much sugar hyperglycemia, which induces cellular injury, as insulin production diminishes (which, in turn, is injured by increased insulin demands in a high sugar diet) and adipose tissue renders insulin less effective. In this setting, the higher sugars reach the entire system and cause molecular injury via the circulatory route and affect vision, kidney function, and sensation.

What initially arrives in the gut can impair the body’s homeostatic system and, via the circulation, lead to damage to the body as a whole. We really are what we eat. So, health seems to relate to our body’s natural design and how it adjusts to the outside environment. Our gastrointestinal system serves the purpose of our bodies’ root system by breaking down the food we eat and absorbing the micronutrients and macronutrients (proteins, sugars, and fats) in food. The transition point to the systemic bloodstream is via the portal system and liver, a filter system that allows for detoxification of the blood. The body can secrete substances with bile in the intestines. Bile consists of salt and other acid components that have natural antibiotic and detoxifying properties.

How can we see the health of the trees and our bodies from the outside in?

When I look at nature and analyze the trees, I notice that some trees don’t look completely upright or healthy. What happened in the lives of those trees? I see how leaves change color in the fall; the color changes occur adjacent to the areas of the venations or are initially small areas where chlorophyll pigmentation has altered. Just as we see can determine a tree’s health by examining the leaves, bark, and the fruit – giving us an idea of the sunlight, the soil, and the water – so too can the things we are influenced by show up in our bodies.

I sometimes notice overweight people (as I had been) and wonder what is happening in their bodies to cause them to gain weight. I wonder whether it is just a question about what types of food one is eating, leading to this weight gain. Maybe it is like a plant that deals with a specific type of soil nutrient – it continues to work, even if the soil may not be right until it can later improve. In this case, we as humans are affected by the environment we imagine, train ourselves to create, or are forced to endure (e.g., parenting) – obesity is a maladaptive state of coping with this.

I learned, with my mother and the many patients I have seen with similar challenges, that, despite the education and understanding of the disease process, she, like many others who have diabetes, could never completely optimize her health to improve it. This was the “inside job,” the effects of the disease and the brain in perpetuating the diseased state. In some ways, a disease state is like a “strange attractor” (albeit I use the term more as an illustration) or orbit, where a complex system cycles to propagate and repeat similar behaviors. It takes a thrust outside of this cycle to break the inertia.

Question: Is there an optimal weight range for the body’s functioning?

A tree makes its own food source through photosynthesis using the light of the sun, chlorophyll, and water. As the tree’s food is created, it is directly used in the growth of the tree. Any unused sugar is transported from the leaf through the phloem to be stored in the trunk or roots as starch in the roots and trunk. It can then be converted back to sugar for growth during the next spring.

This process is not unlike what is planned in our bodies with the excess sugar. We take in food – sometimes in disequilibrium as to type, utilized for the body’s maintenance and functioning. Any excess sugar will be stored in the adipose tissue as triacylglycerols to be used for growth or in a state of starvation (such as in between meals). The process of storage in adipose tissue continues providing there is a trigger – and it comes in the form of excess carbohydrates in the diet.

Insulin’s role is to shift sugar out of the bloodstream to be used as energy – including energy storage. This leads to deposits of adipose tissue and weight gain. A reduction in carbohydrates can help a person reduce these stores and lose weight. Excess adipose tissue can create an impedance in the function of our pulmonary and vascular systems. It can also make it harder to get around. Someone who is obese may tire more easily. The body is not functioning optimally.

But the body adapts to weight gain to a point. When my father was diagnosed with high blood pressure, his doctor told him that it might get better with weight loss. He fueled himself with a mostly plant-based diet at one point and lost weight. Even with as little as five to ten pounds, blood pressures improve. The changes seen in weight normalization are far greater than the activity of any pill.

Photo by mali maeder on Pexels.com

Question: How does our food intake affect our health? I wondered how these leaves and other vegetables are so complex and whether that is the way our food should be – more complex in structure. Look at the foods above: the one is Romanescu broccoli, and the bottom is sliced bread. Compare spinach leaves’ inherent complexity, cauliflower, and cabbage with tubers, such as potatoes and cassava, or processed foods.

Processed foods are essentially natural foods that were changed from the original form to a shape closer to Euclidean geometry. This processing releases some of the most important food constituents – the fiber – and reforms it to a geometric shape – the square piece of bread, the round cookie or biscuit; foods composed of simple and complex carbohydrates. These types of simpler foods are the wrong ones for our complex bodies.

The foods are held by loose bonds that break after entering our mouths. There is no further digestive component needed, and the sugar is absorbed into the portal bloodstream through the jejunum. The liver meets it head-on and attempts to detoxify the substance. Insulin shifts the sugars to be stored as glycogen and fat in the liver, and once a critical threshold is met, complexed sugar spills out into the bloodstream as triglycerides. These trigger inflammation in the blood vessels and otherwise get stored in adipose tissueThatht taken from the outside is incorporated and then affects our circulatory, which affects our entire body. Eating more complex structures like vegetables is the most optimal diet for our system and brings important factors that keep us healthy and free of disease.

How about getting older? As we grow older, our structure changes – we shorten in stature because our bones demineralize and desiccate (dry up); our skin wrinkles, and fingers and toes get colder; we can’t see or hear as well as our eyes and ears change. My patients remind me that even our ability to taste decreases – and might lead some to choose sweeter foods.

Do these changes represent the tip of an iceberg about what is happening in our entire bodies? When we look at autumn – when the leaves start to dry up and change color. A close look at a leaf with a magnifying glass reveals that these changes in color and appearance of the leave occur in small fragments congregating around the leaf’s venations before the confluent color change. Similarly, the skin changes – a decrease in collagen production – that produces wrinkles occur over time as we move toward a phase of wilting.

Question: Are there ways to reduce the process of aging in our bodies? Depending on how warm the climate is, the leaves on some trees stay viable toward December, while the trees in colder climates are bare of leaves by then. It also reminded me of experiments with Protozoa, single-celled organisms. As a child, I remember a class experiment with Paramecia. We put a dropper full of concentrated saline (salt) solution into the fluid where the Paramecia were swimming around. Immediately, they swam away in the opposite direction from where the solution was coming.

Does our body have a way to protect itself from these changes? The acid-base buffering system of our body is an example of how dynamic our bodies are. If there were ingestion of acid (like poisoning of aspirin, causing metabolic acidosis), our body would be able to balance that effect without killing us – up until a point. It would not be the same with Paramecia – they would die with a little perturbation. Our bodies can adapt to the environment, and that dynamic ability is a picture of health.

Think about how our heartbeats – is it like clockwork? It actually is not. The system adapts to changes in position, respiration, and other stimuli to allow for dynamic sinus arrhythmia. Studies have found that when pulsations are less dynamic, there is an increased risk for mortality.

Sinus arrhythmia a healthy response to changes of movement and inspiration

Sinus arrhythmia, a health response to fluctuations of pressure received by the heart

Question: Is the “climate” in our bodies something we can control – and can this extend the time of our healthy years?

It reminded me of my grandfather, who a lot of people thought was younger than his age. You and I have seen people in the gym, thriving, working out, and keeping up with others, decades younger, and the looks of disbelief when they reveal their age. Think about the natural cycle of nature – starting with the blossoms and leaf buds of the spring, proceeding to the fully developed leaves of the summer, then with the leaves’ changes and eventual death during the autumn and the slow state of the tree during the wintertime.

Question: Do we also become less complex as we go through this process of dying? What is health, and how can I tell it when I see it? That brings us back to the first question. I observe what is happening in front of me, though it proceeds as it has for decades and centuries. Trees stay alive even during the winter – the main structures that die are the leaves, only to grow back next spring. Even this process is happening in our bodies, as we shed hair, skin, and cells in our gut – up until a point – some of which is programmed and some of which is modifiable.

In Optimizing Health, we are interested in what is modifiable. We can’t change that we will die. As I see it, health is a state that is far from static – it is the ability of an organism to withstand the environment, to harness it, to grow and maintain itself, and even to thrive despite it. We have organs similar to a filter system or a root system that allow us to take in nutrients needed for growth and metabolic operations and use what is in the environment. Just like when you cut a tree, you don’t see the soil inside it, so too does our blood work with what is absorbed after the liver detoxifies it – up until a point.

Our bodies represent the interaction of inside with outside – like an inner ocean. The single cells in our bodies are equally bathed by nutrients, water, and oxygen, some of which are gained in the air we breathe and some of which are gained through the food and drink we ingest.

A person with diabetes may have numbness in their legs; a person with high blood pressure may have swelling in their legs; a person with a bad liver will develop jaundice. As our bodies change, our structure changes, and inherently our function changes. We do have some control over this.

I am reminded of some of my patients, after being diagnosed with diabetes, who started an exercise program and began to eat healthy food: they could lose a significant amount of weight and reduce or stop insulin and other diabetic medications.

Ultimately what is in play is a shift from our more complex, functioning, dynamic lives to one where complexity diminishes, either slowly, from the blunting and structural changes in aging, or more rapidly, with the damage that occurs with disease. The change in complexity to simplicity reaches a plateau when we die – and even then, our bodies further disintegrate into the various chemicals that were holding our lives in place.

Health through a Holistic, Fractal Lens: The Parable of the Five Blind Men and the Elephant

We are shortsighted in our understanding of health and disease. The parable of the elephant and the five blind men captures the limitations of a disease-centered, reductionist view. When examined in its components, the elephant has a rope-like tail, a tree-trunk limb, a snake-like snout, spear-like tusks, and fan-like ears. But it is all of that and more.

A problem-focused view on illness often looks at health with a myopic lens. If someone has high blood pressure, medication is recommended if it reaches too high of a value. Someone with fluid retention may be given a diuretic. A person who has diabetes may be given a pill and/or insulin. In using medication for each condition, a false sense of security is shared between provider and patient, as if the condition may improve because of the medications. A person may construe this as “keep calm and carry on” with unaddressed behaviors to further fuel the problems.

With a holistic approach to the above conditions, obesity can be understood as the common link. When the United States saw an obesity epidemic beginning in the 1980s, this condition wasn’t even regarded as a disease. It was considered a risk factor and consequently wasn’t addressed as such in most medical schools. The dogma of “eat less and exercise more” was commonplace. Meanwhile, the food industry removed the fat from food and marketed sugary foods as “low-fat.” Nutella (candy spread) became “part of a complete breakfast.”

Missing in all of this was a true understanding of how the body builds adipose tissue through excess sugar and how obesity is largely preventable – and much more difficult to treat when present. A holistic view on health and wellness We can start with the World Health Organization’s definition at the beginning of this chapter.

We can all agree that health is certainly more than not having a “dis-ease.” It is a state of greatest ease or well-being. Think of what it would be like to have all of your organs, tissues, joints, and senses performing at tip-top function. I am sure many of you are probably thinking about a time in your life when you were closer to this state – and much younger! Although health is in that optimal state, the body is anything but a static system.

Think of fractals and all the body structures — the liver can release glycogen stores into the bloodstream in between meals, and adipose tissues diminish during a lengthier period of fasting and enter the bloodstream as triacylglycerol or “ketone bodies.” It is a state when all levels function at maximal efficiency – as needed for increased capacity or energy-conserving during resting times.

On a system level: >The heart smoothly receives the blood in coalescing veins from the body and propels it forward to the lungs. On the left side, the oxygenated blood returns to be propelled forward to the brain and the rest of the body, free from any significant resistance. The size of the heart and pressures in the receiving lung and system allow the blood to flow efficiently and are not too high to cause the heart to have to grow and increase pressures. The heart is functionally prepared for any increase in aerobic stress.

>The brain is functioning in a focused manner, receiving oxygen-fresh, nutrient-rich blood to fuel it. The brain receives signals from the senses and every part of the body to allow signals to flow to and from it to optimal performance. Neurotransmitters are not over-triggered and are stable, as one is free of excessive anxiety and other distractions. Any external perturbation is processed, and a response is applied to maintain a calm, steady state.

>The lungs are not faced with any resistance mechanically, easily expanding to allow for the maximal intake of air. Oxygen transfers into the alveolar sacs with ease, as there is no trapping of air from scarring (because of smoking, pollution, or other contaminants) or spasm (asthma). The blood flows freely to and from the lungs without any significant resistance.

>The kidneys are optimally filtering the blood, retaining salt if needed, or removing it along with balancing the amount of water needed for the blood volume. All of the harmful ingredients are being secreted out into the urine. The kidneys produce an optimal amount of erythropoietin to activate the bone marrow to produce enough red cells.

>The GI system: The esophagus functions well with normal motion, and acid production in the stomach stays there to help digest the food as it churns it. The small intestines absorb all of the nutrients from the food and traffic them to the portal circulation to be metabolized in the liver. The pancreas secrets the ideal amounts of insulin and enzymes as the food is fiber-rich, vitamin-rich, and mostly plant-based, free of inflammation-provoking substances (e.g., concentrated sugars, salt, and saturated fats). In the liver, glucose is metabolized by insulin, and fats and amino acids are prepared to be used by all of the body’s cells. Sugar is packaged into glycogen in the liver to be slowly released in the blood between meals by a glucagon signal. Triglycerides and fatty acids are produced at a safe level to be transmitted to the rest of the body.

>The Neurotransmitter and Endocrine systems: The body responds with an appropriate release of hormones, including those used for the autonomic systems (epinephrine, norepinephrine), for motivation (dopamine) and positive behaviors, and a state of joy (serotonin, norepinephrine). Cortisol secretion is at an optimized basal rate, not driven to excess production, as the brain can adapt to any real or perceived stressor. The sex hormones persist at a normal level, not blunted by sleep issues, like sleep apnea, diabetes, or alcohol.

>The Integumentary System: Skin is smooth and producing oils and anti-microbial peptides to an appropriate amount to prevent folliculitis. The skin cells are free of injury caused by sunburn or wounds that can lead to skin cancer risk. Muscle mass is preserved and functioning to complete needed tasks, prevent falls, and protect the joints. Tendinous insertions are free of significant scarring damage and calcium buildup. The joints are well preserved and can handle tension when needed.

>The Immune system: white blood cells (neutrophils) are signaled in the small intestines to neutralize harmful pathogens in the Peyer’s patches and other centers. Other white cells, macrophages, circulate around the blood and vascular tissue to control inflammation and capture pathogens. Other immune mechanisms such as skin antimicrobial peptides, complement, and other proteins in the natural immune system are serving as the initial defense in the skin, tissues, and blood. B cells are producing antibodies that are turned on when bacterial invaders trigger the humoral immune system. A person may develop an infection but is at a lower likelihood of more severe disease or complication. There are no triggers that could result in inflammation and auto-immune conditions.

On a molecular level: Proteins are being translated from messenger RNA in the mitochondria of cells in an optimal formation to fulfill each tissue type’s needs. Telomere lengths are being relatively conserved (not shortened) as chromosomes are read and proteins are encoded. Autophagy is optimally functioning to clear proteins, organelles, and lipids.

So too is what is occurring in the body – all of this, but much more! Now combine these systems into a dynamic, flowing process and picture what it might be to have a fully functioning body, free of any impedance. That is health and wellness.

What are Homeostasis and Allostasis?

All living organisms have systems that work in concert to maintain stability and limit the impact of external or internal perturbations. This process is known as homeostasis. Whether it is the acquisition of energy through food or the body’s ability to adjust to the threat of physical harm, or “fight or flight,” the body can accomplish and optimize its function to allow for maximal effect. From a single-celled organism to advanced animals, an organism’s ability to adjust becomes a multi-systemic process.

While a single-celled organism could die (“lyse”) if it came across too much alcohol, sodium, or sucrose (table sugar) in its environment, an advanced organism has a multi-cellular system to buffer the direct effects of these substances up to a point. What might be poisonous on a cellular level, in an advanced organism, multiple cells lining its digestive tract can begin to manage these substances and reduce the direct harm. The process by which the body adjusts to stressors to return to homeostasis is Allostasis.

The liver receives substances absorbed from the intestines, and it metabolizes the blood’s toxins to less harmful products. For example, alcohol is broken down in two steps by alcohol dehydrogenase and its product aldehyde by aldehyde dehydrogenase in liver cells to form acetate, converted to carbon dioxide (exhaled) and water (urinated).

  • For alcohol, the lethal dose 50 (LD50 = a calculation of a dose in which a level is expected to kill half of the population) is blood alcohol between 0.35 and 0.40 percent, which constitutes about 17 beers in 1 hour for a man weighing 180 pounds.
  • For sugar, a potentially LD-50 for the same adult would approach 5 lbs – or more than 250 pieces of “fun size” Halloween candy (20,000 calories). That’s a lot of candy corn! For salt poisoning, a more common event with drowning survivors or drinking seawater if stranded at sea, it is estimated that as little as 25 grams of sodium (around 4 tablespoons) at one time for an adult and 7-13 grams for a child could be lethal. It is definitely not a wise decision to conduct a salt-eating challenge to boost your social media followers.

The greater the perturbation in the system, the less compensated the adjustment and the more harmful or life-threatening the consequence. The body’s shift from a “compensated” to an “uncompensated” or “diseased state” can occur rapidly, such as from poison or drug ingestion or insidiously, such as the long-term effects of high glucose levels on the tissue of the kidneys, eyes, and nerves. At this crossroads, a patient may present with symptoms or have signs of developing dysfunction.

I am always amazed when I see a patient with severe anemia from a slow-bleeding colonic tumor presenting with no more than gradual fatigue and weakness to the point. If a patient were to develop an acute, significant gastrointestinal bleed from a stomach ulcer, s/he might suddenly become weak and dizzy – and probably pass dark, tarry stools or even blood in the stool. At a much higher blood count than the patient with a slow-bleeding tumor, their systems decompensate.

Our body makes similar functional adjustments as one gains weight through time. The adjustment process can become more severe as weight gain occurs, leading to a breaking point when the health effects of weight impact life quality. Many people may have noticed early signs and symptoms of these changes, including fatigue, body aches or fibromyalgia symptoms, and sleep disorders. They may have already sought out providers or tried different medications or used substances to treat the problems with a temporary effect. A person may take ibuprofen for back pain or body aches. He or she may drink caffeinated beverages for an energy boost. They may take sleeping pills for sleep apnea. They may take herbal or homeopathic medications and potentially delay the recognition of the underlying problem.

Take-Home: Applying Fractal Wisdom  

1. Exercise conditions the heart and the vascular system and refreshes the body “engine flush” – all organ systems, including the brain, will receive greater oxygenation and ability to repair. This will also allow for neuro-hormonal adjustment and conditioning.

2. The food and drink we choose each meal are important for the body’s functioning, storage, and capacity. Choose wisely. A diet high in cellular fiber (plant-based) is recommended. Hydration is critical in system functioning and should be water.

3. Sleep is an important tool for the body and brain for restoration. Ensure that you are getting sleep at a consistent time and duration.

4. Complex systems require strong muscular and skeletal frames to protect from injury and maintain internal structure and function. Life requires movement and blood flow.

5. Celebrate yourself and share your unique attributes with others! Create a family that welcomes your creativity and allows your expression. No one has the same narrative, experience, background, or gifts to share.


This is only a brief bibliography of the information

  •  Aliahmad et al. Zone Specific Fractal Dimension of Retinal Images as Predictor of Stroke Incidence. 2014. Scientific World Journal. Article ID 467462.
  • McEwen BS, Wingfield JC. Allostasis and Allostatic Load. 2007.
  • Reishofer G et al. Age is reflected in the Fractal Dimensionality of MRI Diffusion based Tactography. 2018. Scientific Reports).

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