fibonacci-in-nature

The Golden Ratio and Secret Geometry in Nature

These wonderfully symmetrical plants show the fractal nature of math, physics and the universe. Could this be evidence of sacred geometry? “Look deep into nature, and then you will understand everything better.” -Albert Einstein

The Golden Ratio, or Fibonacci sequence, is everywhere. It can be found in ancient architecture, in some of the world’s most beloved artwork (such as the Mona Lisa), and most definitely in nature. It’s for this reason that the intriguing sequence, which begins as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on forever, has fascinated mathematicians, scientists, designers, and artists for centuries. 

Leonardo DaVinci, for instance, was known to use the Fibonacci sequence in his masterpieces because the pattern is aesthetically pleasing. Is it a coincidence that the ratio can be seen from a micro to macro scale in all biological systems, and even in inanimate objects? Clearly, there’s much to learn about sacred geometry and inherent order in the universe. 

 Some theorize that the phi ratio (phi = 1.61803…) is evidence that nature is inherently perfect, and that when mankind strays away from the natural law, sickness and imbalance occur. While the Golden Ratio doesn’t account for every structure or pattern in this world and others, it most certainly is a key player.

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 Series.

The Fibonacci series covers the simplest golden section sequence which can be expressed in whole-numbers (the golden section of 89 being 55, and that of 55 being 34, etc.):

2, 3, 5, 8, 13, 21, 34, 55, 89 …

In it each number equals the sum of the two preceding numbers (that is, 2+3 =5, 3+5=8, 5+8=13, etc.).

The sequence approaches nearer and nearer the proportion of the geometrical golden section i.e. the irrational key-number of the geometric mean: the square of every number is equal to the product of the numbers preceding and following it - with the difference of plus or minus 1.

The Fibonacci series embodies the low of natural growth. In the fir-cone starting from the centre, a system of spirals runs in the right and left directions, in which the number of spirals always result in the values of the Fibonacci sequence: 3, 5, 8 and 13 spirals.

A similar setting can be seen on the sunflower, pineapple, chamomile, dandelion, marguerite, cactus, likewise in the arrangement of leaves on the stem and in the horns of some ruminating animals.

Like standard jigsaw puzzles, this puzzle has only one solution, but instead of every piece being a different shape and approximately the same size, every piece is the same shape and a different size. The placement of the pieces is based on the golden angle (≈137.5º), and results in a pattern frequently found in nature, for example on pine cones or sunflowers. The puzzle has 8 spirals in one direction, and 13 in the other.

The Golden Mean was used in the design of sacred buildings in ancient architecture to produce spiritual energy that facilitated connectivity with spiritual realms through prayer. Our reality is very structured, and indeed Life is even more structured. This is reflected though Nature in the form of geometry. Geometry is the very basis of our reality, and hence we live in a coherent world governed by unseen laws.  These are always manifested in our world.  The Golden Mean governs the proportion of our world and it can be found even in the most seemingly proportion-less (active) living forms.