“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.”

Benoit Mandelbrot

Introduction: Fractal Patterns 

I am going to start this article with an admission: I am a fractal geek. After a whirlwind course in my fractal-virgin mind in 1993 entitled “Fractals and Geology,” I have never seen the world the same since. When I finished college, I entered Osteopathic medical school with the naïve ambition to “help the world and make it a better place.” It is a common one that medical students start with, only to get then blasted with a dose of reality during their training. However, it does not have to be abandoned.

After my training, I realized fairly abruptly that healthcare was not cut out to actually helping patients out of the behavior cycles that led to the manifestation of disease in them. Ultimately, I began the course over the last four years that brought me to where I am today. I began by writing the message out to interested readers and reaching out to a greater audience in a way the clinic cannot allow.

What does healthcare have to do with fractals? Let me begin by writing the first assumption: we are all fractals! In fact, every living thing is a fractal structure. Even non-living natural processes possess fractal structures.  What isn’t a fractal? Although crystals form into geometric shapes, variances in the temperature, saturation, and formation process are fractal-like. Anything humans engineer from natural resources, including buildings, cars, and even the processed food we eat, is not fractal. Therein lies an important lesson of life. In this article, I will summarize the concept of fractals and how the quality of our lives depends on understanding their significance in health and disease.

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The Human Scientist, Patterns and Mathematics

Whatever you call it, our eyes are susceptible to detecting patterns in the natural world. When we walk outside, immersed in nature, and look around at the trees surrounding us, our eyes capture structures that aren’t quite spheres, triangles, squares, circles, or lines. Our brains look at the roughened margins of these structures. They screen them for any inconsistencies and predict the oncoming shapes as we continue along the path. There is a natural tendency for the brain to find patterns, even when there aren’t any to find.

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Science, in its essence, is about learning to predict and make inferences from observations. The earliest scientists were the naturalists and astronomers, predicting weather patterns and seasons, looking up at the stars, and recording the position of heavenly bodies.  They used mathematics to model the observations of the world around them. Theories came from observations. Some of these became predictable laws. Anyone can predict that if they let their wallet drop, it will fall down and not up.

Pattern perception is an intrinsic attribute of all human beings, but it requires priming with experience. To predict a pattern, the brain calls on short and long-term memory, the senses, and the ability to organize and interpret that which is seen and match it to prior experience. The brain scans a new object with a repertoire of images, to which it actively compares. This concept is known as the Theory of Prototype.

An example of this is when you see a car model for the first time. The senses process the object; the brain receives input of the frame, doors, windshield, and wheels and compares it to an image bank in the long-term memory, deducing that it is a car. The brain then actively predicts and interacts with it, receiving new input updating its catalog. For more information, I have attached an excellent article by author Youguo Pi et al. that goes into pattern recognition in great detail.

Let’s put your pattern detection to a test. Find the next numbers to these sequences:

1. 1,2,3,4,5,6,7,____
2. 1,3,5,7,9,11,____
3. 1,4,1,8,1,16,1,____
4. 1,4,9,16,25,____
5. 1,5,9,14,19,24,30,36,42,48,____
6. 1,6,16,36,76,158,___

I am sure you were able to determine most of the missing numbers for the above sequences.  The final three were more complicated equations: problem 4 used square roots of successive numbers starting with 1, then 2, then, etc.; problem 5 used the equation add numbers successively starting with 4 for a successive number of times starting with 2; problem 6 used 2(x + 2), where x was the current number.

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From Observational Science to the Scientific Method

The scientific method has provided researchers with an invaluable tool to measure the variance between experimental and control groups. Using these concepts, scientists have successfully treated HIV with one tablet, changing it from invariably fatal to a chronic, controlled disease, cure hepatitis C with a short 3-month regimen, and prevent COVID-19 through vaccination (and hopefully halt the pandemic).

The practice of medicine not only benefits from the scientific method but also through clinical observation. Doctors recognized the patterns of multiple patients diagnosed with unusual diseases, like Kaposi’s sarcoma,  Pneumocystis pneumonia, and Cryptococcal meningitis, to alert health authorities, leading to the detection of HIV. Clinicians in China had to alert public health authorities after a series of patients developed severe lung processes, leading to the discovery of the COVID-19 outbreak.

This is not a new phenomenon. Systems of medicine (e.g., Chinese and Ayurvedic medicine) were developed over centuries of clinical observation and experience. Although these practices have various terms and theories, they attempt to create a system to predict the function of the human body through inputs and outputs. For example, Chinese medicine explains heartburn as being caused by emotional upset and eating the wrong foods. Reflux is generated by “rebellious qi,” surfacing up instead of flowing downward.

Whether we call it “qi” (chi) or the “reflux of hydrochloric acid in the setting of impaired lower esophageal sphincter function and dietary instigators,” the risk factors of emotions and food intake as causing reflux are either known or are being studied further. Chinese medicine may provide treatments for certain complaints of chronic disease. Still, it cannot be used to discern the underlying disease etiology of the signs and symptoms or to detect less common disease states.

The Chinese medicine model probably dated back to at least 23 centuries and was developed through observation. It wasn’t developed as a way to exploit people and get them to buy various herbal concoctions. The terms describe the concepts that were predicted through understanding patterns. Whether described as “chi” in Chinese medicine, “prana” in Ayurvedic medicine, or the “four humors” (blood, yellow bile, black bile, and phlegm) in Hippocratic medicine, physicians in those times attempted to characterize the body and conditions in the settings of limits of understanding. Nevertheless, they bring forth concepts emerging or are still explainable, such as meridians, the importance of rhythmic movement exercises (Tai Chi), and breathing on health.

It’s incredible to imagine that early “researchers,” thousands of years ago, correctly determined that the bark of the cinchona tree (containing quinine) or the wormwood herb (containing artemisinin) could be used as a treatment for malaria. In 1972, Chinese chemist Tu Youyou isolated the active antimalarial compound artemisinin in wormwood, leading to its synthesis and distribution as an anti-malarial drug.

Modern medicine relies on technology to advance knowledge and discovery. The paradigm shifted from primarily observational to the research model. Greater visualization of a disease process improved scientific understanding. It began with anatomy, then with increasingly more powerful microscopes, and later through advancements in radiology, such as the radiograph, CT scan, ultrasound, and MRI. More recently, genomic research enables scientists to detect disease, even without direct visualization, and treat it by informing pharmacologic and vaccine discovery.

I am grateful to the scientists and doctors for how far we have understood COVID-19—search COVID-19 on Pubmed. You will find 127,950 articles- a disease that was only recently discovered in December 2019. However, we have yet to find a treatment for severe covid-19 more effective than one discovered in 1955 (prednisone). Developing technologies may effectively target and inactivate the virus (e.g., monoclonal Ab against the spike protein). Scientific discoveries on a safe and effective treatment for household exposure or a way to turn off the inflammatory cascade to prevent severe disease are promising.

And what of the paradox of chronic diseases in the setting of highly developed societies? With all of the tools that modern medicine provides for diagnosis and treatment, we cannot cure these chronic diseases with medications. An ounce of prevention is better than a pound of cure.

A Better Science?

Neither observation nor scientific design can effectively capture the whole picture of what is actually occurring in health and disease. Observational studies lack the detail of the kinetics of potential risk factors. Randomized control trials (RCT’s) focus on how one element (e.g., medication) affects subjects compared to control, but it cannot safely assume that bias has not entered the design, recruitment, and interpretation. Nor can it predict how the intervention will affect a specific person.

As we develop newer techniques to visualize a process in greater detail, we compromise how that process interacts. How will scientists continue to explore conditions anatomically (to the atomic level) to aid in understanding a disease process more clearly? Or can we glean enough information from understanding the basic concepts that fuel disease and coach our patients toward health?

This conundrum reminded me of some of the theories in quantum mechanics. The Observer Effect posits that an electron’s observation (or measurement) alters the ability to determine its distribution. And Heissenberg’s uncertainty principle states the more precisely you know the position of a particle, the less precisely you can simultaneously know the momentum of the same particle. The understanding of a process requires the predictive interaction with that process. We need to see more of the pattern before we can best predict it.

I recently paged through a medical physiology textbook that current medical students are using. Comparing this to my physiology classes in medical school, the book is replete with terms for molecules that at one point were just grouped as a category (“signal transduction” versus naming the component molecules, e.g., individual toll-like receptor proteins).

Ultimately, science aims to explain better the reality that exists within us and without us. Can scientists ever determine the reality of the human body? What about discovering how the body adapts to its environment? Another paradox comes up (this came up in the book Zen and the Art of Motorcycle Maintenance): since scientists are making discoveries that, in turn, fuel more questions, when will there come a time when we have answered all of these? Here is an example. As we descend closer into the atomic world, our lens captures an increasingly detailed universe. The world expands as we magnify it.

We also learn that there is a greater power as we explore with greater magnification- a genie in the bottle. I don’t need to go into further detail than write the terms “nuclear physics” and “genetic engineering.” These are two examples of scientific exploration that led to significant contributions, the implications of which were not completely understood at the time.

From the observational standpoint, we see the disease on the surface, the skin texture, nailbeds, pulse, appearance of the urine, the odor of the breath, and color of the sclera (e.g., icterus). Technology allows us to analyze the blood and urine and image the abdomen and pelvis. In more cryptic diseases, we essentially have to use techniques to take the disease out and look at it under the microscope or use more sophisticated analysis. We can take biopsies of tissue and send special diagnostic tests using genetics (e.g., shotgun metagenomics).

But the process that we observe is one fueled by a cascade of events of dysfunction, beginning on the atomic and molecular level. No doctor, let alone any human, is capable of seeing in the molecular range. Physicians develop predictive knowledge, a way to see patterns. They must fine-tune this skill from the cognitive distortion that simultaneously confounds their interpretations.

How can we advance the understanding of the structure of health with objective measures and predictive tools?

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A Fractal Model of Health and Disease

I have explained fractals, a term coined by Benoit Mandelbrot, in previous articles on the website. I grow hopeful in future applications on this concept. Fractals are patterns that can be measured using mathematical tools. And just like the microscope enabled scientists to see the invisible, computers are being used to handle massive amounts of data to calculate patterns that would have previously been impossible.

Fractals, by definition, are iterative objects that display self-similarity. I can predict what the smaller subunits look like when I look at the whole, and vice versa, i.e., predicting the tree with the forest and the forest with the tree. Fractals seem to transcend a rift in science: a way to predict the detailed with the general,  microscopic with the macroscopic.

We can gain a greater understanding of a system’s environment by how it can grow. We look at the structure and can predict a function. In disease states, the structure is impacted, resulting in a loss of function.

In the next post on this topic, I will explore these concepts further and propose how fractal models can be increasingly incorporated into medicine to understand health and disease, specifically in chronic diseases. I will describe the utility of engineering machines to quickly assess the structure of one’s body and predict a state of health or disease.

…To be continued