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Key points: An eye on nature tells us a lot about how things grow and adapt through various pressures. Models such as the golden ratio and fractals illustrate the splendor of growth and life. What happens to these systems when they are perturbed? How does this relate to our bodies when a state of dis-ease arises from what was once optimal?
As a college student, I had the opportunity to take one of the most influential courses in my education: Fractals and Geology. I grew to appreciate how natural phenomenon can be understood and analyzed and how disruption in growth changes the usual signature.
The Golden Ratio, a mathematical interpretation of a natural observation, possibly had its beginnings with Phidias in 500 BC – 432 BC , a Greek sculptor and mathematician, who applied it in plans that led to the building of the Parthenon. The structure correlates well with the Fibonacci spiral.
The mathematical equation to this follows a pattern of 1,1,2,3,5,8,13,21,34,55 etc. There are many things in nature, I dare say almost everything in nature, that exhibit this pattern, from pineapple structure, sunflowers, pine cones to the nautilus shell and even to the structure of our face and body. It may explain why our appendages have 5 digits.
Fibonacci equation: Fₙ=Fₙ₋₁+Fₙ₋₂, for n > 1
Fractals, in a nutshell, are iterative figures that display self-similarity. These can be created using mathematical equations and most notable of these images is one from the scientist who coined the term fractal – the Mandelbrot set. Once computers were powered enough to handle this equation, they became popular visuals during the late eighties and nineties.
Fractals are on one side finite structures nearing the Euclidean geometric dimensions (e.g. 1 dimension = line, 2 dimensions = square, 3 dimension = cube) but, on the other side, because of the iterations, they are more detailed than our strict understanding of dimensions – they are somewhere in between dimensions. An example would be the scaling effect when trying to measure a coastline. At first glimpse what is linear and finite as measured by a large measuring tool becomes rugged and much longer when you change the tool to an ever increasingly smaller size.
In many ways, the golden ratio and fractals overlap to enhance our understanding of natural patterns. This is in contradistinction to human-engineered structures, in which Euclidean geometry applies.
Mandelbrot equation: F(c) = Z squared + C.
It was in the fractal class, that I became intimately aware of how fractals occur in nature, a new view on things that I sometimes had taken for granted. My project was to measure the fractal dimension of various leaf tracings. The next time you see a leaf on the ground, take a look at how detailed the patterns are. Take notice of the fact that there is a large vein which branches to smaller veins and then smaller veins.
Natural fractals, unlike computational fractals, do not go on ad infinitum. We see similar types of structures when we look at our vascular, pulmonary, lymphatic, neurologic systems and kidney, brain and organ structures.
These structures are not found this way by accident. A number of factors potentially contribute to this growth of these structures in nature and in our bodies. Examples include the specific function of the organ system, the effects of gravity and pressure on the growth, the effect of temperature, the nutritional status and source of the growing structure.
When you look at our lungs, these seemingly simple closed structures are branches upon branches of tubes, arteries, veins and lymphatics – to the cellular level. The main tube, the trachea, branches off into the right and left mainstem bronchi which branch off into multiple bronchioles and then successively smaller bronchioles until we reach the alveoli. The same iterations occur with the venous, arterial and lymphatic systems As the branches become smaller, there is a transition from a structural (moving things in and out) to a functional process (gas exchange and movement of 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) and returns to the left side of the heart.
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 grow using energy obtained and grow to maintain energy efficiency.
Now, put these processes in disarray. If there is a damage to the structure, such as with the lungs from smoking, how does the function change. If there are changes in the pressure around the structure, for instance that which would occur in becoming obese, how does the body accommodate for these changes. If there is a change in what nutrition enters the body, how does the body alter its function and structure. How do these changes affect our bodies ability to optimally function in homeostasis?
To be continued