Is God’s Design Evident in the Fibonacci Sequence?
In mathematics there are a variety of “special” number sequences: Prime Numbers, Odd Numbers (1,3 5,7, …), Even Numbers (2,4,6,8…); Rational and Irrational Numbers. But there is also a very special sequence of numbers called “The Fibonacci Sequence”, after its discoverer, Fibonacci of course.
In mathematics, the Fibonacci numbers, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144….
They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book Liber Abaci.
Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. They also appear quite often in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone’s bracts.
Fibonacci numbers are strongly related to the golden ratio: Binet’s formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity — and which takes on the form of a spiral. This logarithmic spiral, or golden ratio, abounds in nature.
Phi and the Golden Ratio (or Rectangle)
As with other Greek letters, lowercase phi is used as a mathematical or scientific symbol. Some uses, such as the golden ratio, require the old-fashioned ‘closed’ glyph.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Mathematicians have studied the golden ratio’s properties since antiquity. It is the ratio of a regular pentagon’s diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.
Some 20th-century artists and architects, including Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing it to be aesthetically pleasing. These uses often appear in the form of a golden rectangle.
The Fibonacci Sequence is Clearly Shown in Nature
The Bible starts by proclaiming that an all-powerful God created (“bara” – to create out of nothing) the heavens and the earth.
“In the beginning God created the heavens and the earth (the cosmos)” Gen 1:1
That includes the sun, the moon, the stars, the galaxies, and of course the earth, with all of its living and non-living things. Now if the all-powerful Creator and “Master Designer” was the Author of all creation, it shouldn’t surprise us that we would see evidence of His design across all of nature. And indeed we do. Evidence of the Fibonacci Sequence is spread across all of creation, from the design of DNA which resides in all living things, to sea shells, plants and flowers, trees, and the design of human and animal bodies. The Fibonacci Sequence or “golden ratio” is also evident in the spiral nature of hurricanes, and even the spiral shape of galaxies! Here are just a few examples of where this “golden ration” shows up in nature:
The Golden Ratio Appears in the Shape of DNA molecules
Even the microscopic realm is not immune to Fibonacci. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.
These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.
In Seeds and Flower petals
The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five, the chicory’s 21, the daisy’s 34, and so on. Phi appears in petals, since each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors.
The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns. In some cases, the seed heads are so tightly packed that total number can get quite high — as many as 144 or more. And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling (namely one that will not be well represented by a fraction). Phi fits the bill rather nicely.
Many Sea Shells Display the Fibonacci Pattern
Snail shells and nautilus shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider’s webs.
You See the Golden Ration in the Shape of Pinecones
Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a 3-5 cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right.
Fruits and Vegetables
Likewise, similar spiraling patterns can be found on pineapples and cauliflower.
The Fibonacci Sequence is Tree Branches
The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant.
The Fibonacci Sequence is clearly evident in the way the tree sprouts as it grows – from a single trunk, to two great limbs, then three, then five, then eight, and so on. This pattern of branching is repeated for each of the new stems. A good example is the sneezewort. Root systems and even algae exhibit this pattern.
Hurricanes Display the Fibonacci Spiral
The unique Fibonacci spiral is also evident in the pattern of hurricanes. Notice that the Bible mentions how God controls those clouds, and makes that lightening flash:
Do you know how God controls the clouds and makes his lightning flash?
those wonders of him who has perfect knowledge?” (Job 37:14-16)
Spiral Galaxies Also Follow the Familiar Fibonacci pattern
Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees. As an interesting aside, spiral galaxies appear to defy Newtonian physics. As early as 1925, astronomers realized that, since the angular speed of rotation of the galactic disk varies with distance from the center, the radial arms should become curved as galaxies rotate. Subsequently, after a few rotations, spiral arms should start to wind around a galaxy. But they don’t — hence the so-called winding problem. The stars on the outside, it would seem, move at a velocity higher than expected — a unique trait of the cosmos that helps preserve its shape. Is it any wonder that the Bible declares:
“The heavens are telling of the glory of God;
And their expanse is declaring the work of His hands.” (Psalm 19:1)
Bodies, Faces and even Your Fingers Display Its Design
Although every person’s body is different, proportional averages across populations tend to follow the Fibonacci Sequence. It has also been said that the more closely our proportions adhere to phi, the more “attractive” those traits are perceived. As an example, the most “beautiful” smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on. It’s quite possible that we are primed to like physical forms that adhere to the golden ratio — a potential indicator of reproductive fitness and health.
Faces abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself (which follows along a spiral). Photo by Andrea Piacquadio, Pexels.
“Thank you for making me so wonderfully complex!
Your workmanship is marvelous—how well I know it”.(Psalm 139:14 NLT)
It’s in the very design of your fingers! Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the value of the golden ratio.
In the Way Life Reproduces
One also sees the Fibonacci Sequence in the way life reproduces. For example, the honey bee follows Fibonacci in interesting ways. The most profound example is by dividing the number of females in a colony by the number of males (females always outnumber males). The answer is typically something very close to 1.618. In addition, the family tree of honey bees also follows the familiar pattern. Males have one parent (a female), whereas females have two (a female and male). Thus, when it comes to the family tree, males have 2, 3, 5, and 8 grandparents, great-grandparents, gr-gr-grandparents, and gr-gr-gr-grandparents respectively. Following the same pattern, females have 2, 3, 5, 8, 13, and so on. And as noted, bee physiology also follows along the Golden Curve rather nicely.
It’s Evident Even in the Flight Patterns of Birds
When a hawk approaches its prey, its sharpest view is at an angle to their direction of flight — an angle that’s the same as the spiral’s pitch
God’s Workmanship is Clearly Seen in Nature!
God speaks to us through general revelation His creation, and well as through His special revelation, the Bible. When you look up and behold the sun, moon and stars, He speaks to you about His divine nature and power:
The Bible emphasizes that God has made His divine nature and godhead plain, by the things which are clearly seen:
For what may be known about God is plain to them, because God has made it plain to them.
For since the creation of the world God’s invisible qualities,
His eternal power and divine nature, have been clearly seen, being understood from His workmanship,
so that men are without excuse. (Rom 1:19-20)
The Fibonacci Pattern is Nature: By Accident, or Evidence of Design?
The fact is that the Fibonacci Sequence shows up in nature, and is clearly “seen” – from the smallest life forms to entire galaxies.
There are two views about such a pattern of numbers “showing up” in nature. Those that believe in evolution, the notion that all things that exist today in nature were produced by natural selection acting on random mutations in organisms over a long period of time, will tell you that you are only seeing the “appearance of design”. That there really is no intentional design, or Designer. Its all just a product of blind chance.
The other view is that there really are patterns of design in nature, and that they reflect the handiwork of an all powerful Designer acting through creative processes to produce this design pattern across all of nature – from the smallest plants and animals, to the design of entre galaxies. When you look at a beautiful lace curtain, you picture a curtain designer. An intricate watch speaks of a ingenious watchmaker. Its patently obvious that where there is a design, there is a designer. These things just don’t happen by accident.
Which is a more reasonable conclusion, based on the evidence? The these patterns all across nature are the product of blind chance evolution, or the product of an all-powerful, all-knowing, Creator Designer working through the natural processes He started and continues to work through? You decide.
Watch and Listen to John Kostik on The Fibonacci Sequence:
John Kostik’s presentation “The Divine Proportion”, on YouTube
How Would You Like to Meet the Original Author and Designer?
If the Creator and Designer of the universe wanted to communicate to us what He is like, how could He show us more clearly than by becoming one of us? If He wanted to communicate to us the seriousness of breaking His moral law, how could He show us more forcefully than by demanding that the most valuable thing in the universe be forfeited as a penalty? And if He wanted to tell us how much He loves us, how could He do it more dramatically than by dying for us? Consider John 3:16 …
“For God so loved the world
that He gave His only begotten Son, that who so ever would believe in Him should
not perish, but have everlasting life”.
Do you have a personal relationship with the Master Designer of all creation? If you do, then you have everything to look forward to – in this life, and in the life to come. You were made for a purpose, and believing that Jesus is the Christ, and receiving the Lord into your heart and walking daily with Him will help you come to realize His purpose in your life and fulfill it. If you don’t have a relationship with your Creator, you can! Don’t put it off! Here is a link to Billy Graham’s web site that can show you how…
Invite JESUS into your heart! Steps to Peace with God ==> http://www.billygraham.org/SH_StepsToPeace.asp
Wikipedia: Fibonacci Numbers – https://en.wikipedia.org/wiki/Fibonacci_number
Wikipedia: Phi, and the Golden Ratio – https://en.wikipedia.org/wiki/Golden_ratio
John Kostik – YouTube: https://youtu.be/Rz_iybqYHCs
Gizmodo: 15 Uncanny Examples of the Golden Ratio in Nature, By George Dvorsky – https://gizmodo.com/15-uncanny-examples-of-the-golden-ratio-in-nature-5985588
The Bible – https://www.blueletterbible.org/