Numerical Patterns in Nature Part 1: Fibonacci Sequence

sunflower fibonacci

Nature offers beauty, from towering trees to tiny droplets of water, deserving both attention and adoration. Each component, no matter how small or seemingly inconsequential, becomes a masterpiece when examined more closely. Complex configurations actually construct the mundane, resulting in a world of diverse and limitless abundance. It is our responsibility to perceive, understand, and feel grateful for the divine intricacies which decorate our collective home.

red cabbage fibonacci

A well-known numerical occurrence in nature, the Fibonacci Sequence, results in aesthetically pleasing patterns; These numbers eventually form the shapes seen in pinecones, flowers, insects’  wings, and plants.

bee fib

Upon adding the two previous numbers in a series in order to find the next, Fibonacci’s succession surfaces; 0,1,1,2,3, 5, 8, 13, 21, 34, etc. (0+1=1, 1+1=2, 2+3=5, 3+5=8, etc).
pinecone

                 The quantity of flower petals, location/number of branches and stems, and mechanism by which plants expand distinctly follows Fibonacci. Trees maximize sun exposure and maintain balance naturally as they mature; this feat depends upon certain orientation of branches reaching up to the sky. Nature adopted a pattern that works every time.

fibonacci-tree.png
   
(Photo credit: https://botanicamathematica.wordpress.com/2014/04/01/fibonacci-tree/)

             All flowers possess a quantity of petals synonymous with the Fibonacci Pattern: 1, 2, 3, 5, 8, 13, 21, 34, 55, or, 89 (and beyond!). While rare, there are a few species exemplifying the beginning of the sequence: The White Cala Lily has one petal, Euphorbia has 2. It is more common for flowers to have 3 petals (Lily, Iris), or 5 (Buttercup, Wild Rose). 8 petals can occur (Delphinium), as with 13 (Corn Marigold), 21 (Chicory), 34 (Plantain), 55 (Daisy), or 89 (Sunflower). Each of these values belongs in Fibonacci, which dictates the flowers’ development.
daisy

Notice the similarities between a pinecone, sunflower, daisy, and bee’s wing: the mode of growth is consistent.

Formation of plants in this way can be visually represented; As Fibonacci numbers continue, another shape inevitably forms, which resembles a rectangle. The Rectangles are assigned based on the values determined in the sequence (0+1=1, 1+1=2…). As values increase, the formula remains; A predictable equation presents itself, and strategic blossoming can be mapped in accordance with the sequence.
fib rectangles

Another important geometrical pattern emerges within the Rectangles, revealing the secret of the Fibonacci numbers.

A spiral can be traced within the Fibonacci Rectangles, which represents the recurrence of a specific value.

fibonacci spiral

If Fibonacci constituents are reduced to ratios, (adhering to the Fibonacci scheme by calculating the ratio of each preceding value; 1:0, 1:1, 2:1, and so on), then the same answer resounds. Dividing any number in the series by its antecedent value inevitably produces like outcome.
The solution always proves to be a ratio of roughly 1.618, indefinitely, gaining accuracy as the numbers in the sequence balloon.
shell fib

*As Fibonacci progresses, the ratios hiding therein oscillate slightly above and below 1.618, more closely matching the number with each new addition to the sequence.* 

 As the numbers increase, the resulting ratio reaches ever-closer to 1.618: Phi, or the Golden Ratio
phi

What is the significance of 1.618, and how does it relate to these omnipotent patterns?

Learn about Phi and its association with divine perfection in our next original article…Coming soon!

fib flower

Please stop by our other pages for the rest of the series and other original articles like this one!…

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s