fibonacci spiral

Golden Ratio Fractal.

Fractals stabilize all of the energy waves flying through our Universe, and create an efficient and structured energetic highway upon which to travel. Fractals originate as an alignment of repeating energy vectors that provide for a stable interconnectedness of all energy systems in the Universe. Since these Fractals are energetic in origin, and since energy influences matter, they leave their mark in matter by creating repeating patterns seen throughout Nature. These repeating patterns are also found in the human body serving as a reminder that we all originated from the same source, and we are all connected.

Fractals display self-similarity with the ability for objects to exhibit the same type of structure in all scales, large or small. Fractals give Sacred Geometry and snowflakes their structure. You can also find Fractal patterns in the branches of a tree, fronds of a plant, crystals, ocean waves, earthquakes, and even DNA. Not surprisingly, since Fractals originate as energy vectors, they are also observed in coherence patterns of brain function and in heart rate variability analysis. Dark energy existing in dark matter, consists of energy vectors creating repeating Fractals, and is what gives our Universe energetic stability through similarity in structure. On the earth plane, the energetic influence of Fractals is represented mathematically, allowing for the actual measurements of the physical components of these Fractals.

Mathematical expressions of Fractals are seen in the Golden ratio, Penrose tiling, and the Fibonacci sequence. The Golden Ratio is a number found by dividing a line in two parts so that the longer part divided by the smaller part is equal to the whole length divided by the longer part. Roger Penrose, a professor of mathematics and physics, established that a surface could be tiled in an asymmetrical, non-repeating pattern using five-fold symmetry with two shapes based on the Golden Ratio. This pattern named Penrose tiling, and was later discovered to exist in Nature as the structure of quasicrystals. The Fibonacci Sequence is a series of numbers in which each number is the sum of the two preceding numbers, and is represented in Nature by the petals of a flower and the bracts of a pine cone. All structures and processes in Nature are Fractal. 

Logarithmic Spirals of the Nautilus Shell.

The spiral is a common element of Sacred Geometry as well as to all natural development. Spirals in nature tend to follow the Golden Ratio (Phi) or Fibonacci Sequence in their rates of expansion. The key to Sacred Geometry is the relationship between the progression of growth and proportion. Harmonic proportion and progression are the essence of the created universe and is consistent with nature around us. The natural progression follows a series that is popularized in the West as the “Fibonacci Series” where the first two numbers in the series are added to create the third number for a series of number that begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…and goes on ad infinitum. The ratio of the numbers gains great importance as the series continues. By dividing one number by the previous number, the answers result in or come closer to phi: 3/5 = 1.6666, 13/8 = 1.6250, 233/144 = 1.6180. These numbers can be demonstrated with the spiral of the Nautilus. 

The Golden Ratio (phi) is the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion. The ratio links each chamber of the nautilus to the new growth and symbolically, each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage. This geometry of the Nautilus can be found in the spiral patterns of cauliflower, the placement of the leaves on most plants, the arrangement of pattern on a pine cone. The ratios can be retrieved from the shape of our DNA and the measurement of distant galaxies as the Sacred Geometry demonstrates the blueprint of the sacred foundation of all things and the interconnectedness of all the various parts of the whole. 


Fibonacci Sculptures - Part II

These are 3-D printed sculptures designed to animate when spun under a strobe light. The placement of the appendages is determined by the same method nature uses in pinecones and sunflowers. The rotation speed is synchronized to the strobe so that one flash occurs every time the sculpture turns 137.5º—the golden angle. If you count the number of spirals on any of these sculptures you will find that they are always Fibonacci numbers.

© John Edmark

Constructing Reality Pt.3 - Fibonacci and the Golden Spiral

If we want to understand the mystery behind reality, we have to take a look at its patterns. The language of nature gives us a rash of information on how the whole universe moves and grows. The same pattern can be noticed in blooming plants, evolving populations, crowd behavior, artistic and architectural expressions, and even in the movement of whole galaxies. Referring to the pattern that is all around us, Leonardo da Vinci spoke: “Learn how to see. Realize that everything connects to everything else.”

The human mind has a natural sense for artistic harmony, always feeling drawn to a very special kind of proportion. If we have to choose the most harmonic of the rectangles below, we intuitively choose the one based on the golden ratio Phi Φ, a mathematic term for two quantities, of which the ratio of the small part (a) to the large part (b) is the same ratio as the large part (b) to the whole (a+b). However, Phi is an infinite number, beginning with 1,618033…, which means that all visual images can only approach the golden ratio, but never fully reach it.

The golden ratio rectangle is the visual version of a specific numeric pattern. This pattern has been known for thousands of years, first mentioned as mātrāmeru in the Sanskrit treatise Chandahshastra by the indian mathematician Pingala around 400 b.c. Even though it has also been known in ancient Greece, the pattern is named after the italien mathematician Leonardo da Pisa, better known as Fibonacci. The Fibonacci sequence describes an infinite series of numbers, in which the sum of two consecutive numbers results in the proximately next number. Demonstrated and easier understood: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… The connection between the golden ratio and the Fibonacci sequence becomes clear when we continue to construct the golden ratio rectangle, or the Fibonacci squares, into a possible infinity. But again, since Phi is an infinite number, the Fibonacci numbers can only approach but never reach it.

While the Fibonacci sequence and the Fibonacci squares seem to be abstract geometry, the next step will make us comprehend the link to nature and mother earth. The so called Golden Spiral, also known as the Fibonacci Spiral, is the consequent result of the previously created basic pattern. The Golden Spiral is the model for a huge amount of natural designs and developments that exist in our dimension. While the typical Fibonacci Spiral expands its widths in 90 degree sections, another spiral we often find in nature expands its widths in 180 degree sections. Both spirals are golden.

We can see Fibonacci in many plants on our Earth. By following the Golden Spiral, leaves are provided an optimal light saturation and blossoms a promising seed dispersal, as imposingly seen in the Sun Flower. The same double spiral can be seen in the petals of the lotus flower, which is the best example of the nearly perfect Fibonacci creation. We also see the golden 180°spiral in animals, for example in snail and nautilus shells or in the curling of animal tails. Fibonacci does not only appear as the spiral in animals, but also in connection to reproductive dynamics, for example in bees and rabbits, where every generation increases its population by 1,6.
When it comes to humans, our whole body shows golden proportions, from our face, to our limbs and hands and even where we probably don’t expect it – our DNA molecules. DNA molecules spin according to the rules of the Golden Spiral, for a cycle of the double helix measures exactly 34 angstroms in length and 21 angstroms in width. Fibonacci is not only around us, but also inside of us.

Truth is that no visual construct that can be perceived with our senses could fully reach the exact golden ratio proportion, because we create our reality based on boundaries and not on infinite ideas. Yet, the approach to rediscover our own perfect harmony is a part of all of us, when we strive for enlightenment and peace.