The Ratios of Nature ~ Cash Mattock


This series is about some ratios that are found in Nature and how they inspire me when I create. I think that everyone should have a good understanding of these ratios because they help give us a deeper understanding of the universe.

When I create my portraits I take inspiration from the nature and structure of matter. This energy/matter connection spans everything in our universe. This series is a short dissertation of my thoughts on this subject. I honestly don’t think that I we’ll be able to settle on a consensus on this in my lifetime but I find solace in keeping these concepts alive.

I think the best place for me to start is to quote a passage from my book, Esoteric Theories of Flora, Fauna and the Universe…
“The nature of the particle vortex is to draw mass-energy together to make more complex structures such as atoms and molecules. The fractal motion of the particle-string-vortex, combined with all the forces, creates a wake. This fractal wake echoes through atoms and molecules. The influence of this wake is very weak but its combined influence is the slight of hand in the fractal nature of our universe. It is the secret ingredient to the organization of matter. Everything from our DNA to solar flares are fractals. On an atomic level we don’t consciously connect the energy behavior of a particle-string to the growth patterns of a tree but they are related. There are even recent studies that compare the shape and behavior of our brain cells to the expanding galaxies in the universe.”

Our universe doesn’t just have some mathematical properties. It only has mathematical properties. Everything is composed of a variation of self similarity. Fibonacci is renowned as the most important mathematician of the Middle Ages. He discovered a sequence of numbers using simple addition that has a direct correlation with Nature. These numbers became known as the Fibonacci Sequence.

The concept of the Fibonacci Sequence is fairly easy to understand but it applications can be quite complex. The sequence starts with the number 1; 1 plus 1 make 2 and then each number following is the sum of the two preceding numbers ({1}+{1}={2}, 1+2={3}, 3+2={5}, 3+5={8}, 5+8={13}, 8+13={21}, 13+21={34} or in short… 1 ,1, 2, 3, 5, 8, 13, 21, 34, 55 and so on). The astounding thing about these numbers is how often they appear in Nature. As this calculation is repeated a ratio emerges which is approximately 1.618. This ratio is an irrational number which is number that cannot be written as a simple fraction therefore the numbers in the decimal go on forever. This ratio is known as the Golden Ratio or Phi. The proportions of our bodies follow this ratio. Growth patterns found in plants like the number of petals in a flower are Fibonacci numbers. All of the notable Renaissance artists recognized and religiously followed this ratio in their creations. Geometrically this ratio has been taken a step further to what’s known as the Golden Spiral. A Golden Spiral is a logarithmic spiral with a growth factor of Phi. In Nature these spirals can be found in sea shells, our inner ear, hurricanes, galaxies, just to name a few. A fractal is an object or quantity that displays a self similarity so therefore the Fibonacci Sequence and the Golden Spiral relate to fractals. Everything in our universe can be compared to fractals. The Golden Ratio has to play a part to unlocking the secrets of the universe.

The Fibonacci numbers also appear in music. A major chord is made up of the 1st, 3rd, 5th and 8th (including the octave). If the root and the octave are included there are 13 semitones that make up an octave. If we count the semitones for all these intervals in the same way (including the root note) then the 3rd is 5 semitones and the 5th is 8 semitones. If the Golden Ratio is applied to frequencies in the color spectrum the color combinations are always pleasing. Of course there are the obvious 3 primary and 3 complimentary colors.

There is correlation between sound and color that is often overlooked. Everything in the universe has a vibration therefore everything is a wave. You and I are waves with a very small wavelength so we can deduce that sound and visible light, which are obviously waves, would have a connection. There are 7 notes in a scale with the 8th being the octave. There are also seven dominant colors in the color spectrum that we are all familiar with which are red, orange, yellow, green, blue, indigo and violet. A major chord is made with the 1st, 3rd and 5th notes in the scale which similarly correspond to the primary colors.

Pythagoras was an Ionian Greek philosopher and mathematician who’s best known for the Pythagorean Theorem. He developed the Pythagorean Scale in music which eventually led to the equal temperament system that we use today. He felt that the 5th and the 4th intervals in his scale were perfect and divine. He even believed them to have positive physical and psychological effects. The color correlation to these intervals is red, green and blue (RGB). This color mix is used in analog photography and is still being used in digital photography, smart phones, computer monitors and TV’s. The 4th isn’t a Fibonacci number but if we count the semitones from the 4th up to the octave in the same way as before there are 8 semitones.
Not as clean of a relationship as the others but I like to think of the 4th as a “sleeper” correlation. Some of the color combinations using Phi aren’t as pleasing as others as well but like I said I think that Phi is only one part of the puzzle. This brings us to another irrational number. The number Pi.

Pi is one of the most random numbers and it is used to calculate the circumference of a circle which is one of the simplest shapes. Pi is the ratio of a circles circumference and it has been calculated to over 10 trillion digits. It goes on forever and it never repeats itself is any constant manor. There is a sequence of six nines that begins at the 762nd decimal point that’s known as the Feynman Point which I find interesting but in my opinion there’s really nothing more notable than that. The Golden Ratio reflects the width and the length of any section of the DNA helix but we need Pi to calculate the circumference. We also need Pi to calculate the ripples of waves or the circumference of our observable universe. Pi plays a part in Heisenberg’s uncertainty principle which helps us understand the fundamental structure of the universe itself.

I created this image by using relationships between Phi, Pi and the theories from my first book. Some of the connections are very interesting. I will explain these correlations in a book that I’m currently writing that’s based on my El Drama de Aly series. There will be three more series before I’m finished. The book will focus on my art and where my inspiration comes from. This is all a preview of what is to come. Thank you to Magaly Avila and everyone else at El Drama de Aly for inspiring me to do this.

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