Patterns and Numbers

From the smallest to the largest parts of Creation, like a ubiquitous phenomenon messaging the fingerprint of God, repeated mathematical precision, patterns, shapes, spirals, symmetries, numbers and divine proportions can be found everywhere.  The appeal of the Golden Ratio is universal.  It is found throughout the world of design.  Generation after generation has been enamored by the phenomenon known as the Golden Ratio.  You may see it referred to by other names, such as Golden Number, Golden Proportion, Divine Proportion and Divine Section.  Whether in land, sea, or air, we see the twin principles of the Golden Ratio and Fibonacci Sequence in play throughout the universe in living and non-living things.  Fibonacci numbers can be seen in the spiral leaf arrangement of plants.  Spiral galaxies such as our Milky Way galaxy follow the Fibonacci pattern.  The geometric pattern is seen in a seashell spiral (e.g. it is echoed in the logarithmic spiral of the nautilus shell) as well as some spider web formations.  We see the spiral in the horns of certain goats and the cochlea of the inner ear, seed patterns seen in daisies and dandelions, the tail of a comet and the tail of the seahorse.  We see the pattern in the body structure and fin placement on dolphins, the flight patterns of the honey bee and the spiral motion of ocean waves.  The Golden Ratio in Creation is guiding the pattern of life.

Fibonacci numbers appear to be like a built-in numbering system throughout Creation.  Fibonacci was an Italian mathematician.  Fibonacci numbers are special numbers in a specific sequence, and they are abundant in Creation.  This special pattern of numbers begins with 1 and 1, as follows, e.g.: 1 + 1 = 2.  1 + 2 = 3.  2 + 3 = 5.  3 + 5 = 8.  5 + 8 = 13.  8 + 13 = 21.  13 + 21 = 34.  21+34 = 55.  34 + 55 = 89.  55 + 89 = 144, etc.  1, 2, 3, 5, 8 and 13 are Fibonacci numbers.  Add the sum to the number that came before it and that’s the Fibonacci Sequence.  The ratio of 2 neighboring Fibonacci numbers is an approximation of the Golden Ratio (e.g. 8/5 = 1.6).  Our universe is a grand Golden Ratio-based universe.  From Golden Spiral galaxies, hurricanes, seashells, the body of a penguin, the design pattern of flowers (e.g. sunflowers, the lily, buttercups, the daisy, marigold flowers, asters, a blooming rose), the spiral growth pattern in pinecones and pineapples, to the beautiful Echinecea flower, all were created with Golden Ratio beauty in mind.  The Golden Ratio is found in the peacock’s feather.  We see the pleasing, divine master design principle of the Golden Spiral pattern repeat all over in Creation.  If you count the number of spirals in a pine cone that are going to the right, then count the number of spirals going to the left, you typically end up with 2 adjacent numbers in the Fibonacci sequence.  Pine cone scales form counter-rotating spirals in a Fibonacci ratio of 8: 13.  The same pattern can be found in many other plant parts (e.g. pineapples, sunflowers, cauliflower florets) and leaf arrangements of many other plants.  The human body again and again illustrates the Golden Section or Divine Proportion, e.g. the length of the arms and legs, compared to the torso.  The ratio of the ideal human forearm to the hand is Phi – 1.618, the Divine Proportion.  The feet have several proportions based on phi lines.  The microtubules in our cells are Fibonacci spirals.  Human skull dimensions follow the Golden Ratio. Various animal bodies, marine creatures and insect bodies often represent proportions with consistent Fibonacci numbers too (e.g. a spider’s body, ants, starfish, sea urchins). 

Branched  pattern formations are abundant in our living domain.  This natural form phenomenon can be observed in countless organic and inorganic worlds, where the same delicate web of branching design can be seen repeated again and again.  Some examples are neurons, the bronchial/arterial structure of the lungs, blood vessels, coral, mineral dendrites, the branching patterns of trees, the vein systems of leaves, ferns and plants.  Snowflakes too emerge in symmetrical branching patterns of endless variety.

Fractals patterns are all around us.  Constructed by repeating a basic pattern again and again but on a smaller scale, beautiful, intricate, unique fractals appear all over Creation.  Even the simplest fractals are self-similar, whereby small pieces are same as the whole (i.e. they look the same no matter how big or small they are).  A fractals’s pattern gets more complex as you observe it in larger scales.  Clouds can be fractals.  The arrangement of beach sand can be an example of fractals.  Cell biology evidences fractals.  Fractal structures appear in soils.  Other examples of fractals include coastlines, tree branching, ocean waves, shapes of leaves and flowers (e.g. Queen Anne’s Lace), river deltas, rock formations, mountainscapes, lightning bolts, and the branching design of our lungs.  Another example is Romanesco broccoli (a hybrid between broccoli and cauliflower that grows in a Fibonacci fractal pattern or a golden spiral, a pattern based on the Golden Ratio).  Such interesting and appealing, intricate self-similar repeating patterns of different sizes enlarge a surface area and dampen vibration.

In botany, phyllotaxis is the arrangement of leaves on a plant stem.  It is an organizational pattern found in the Fibonacci spiral, which is based on the Fibonnaci Sequence of numbers.  Phyllotaxis is a quintessential example of self-organizing in plants.  Explicit mathematical ordering principles can be clearly seen in the operation of intricate spiral patterns in phyllotaxis (otherwise referred to as “leaf ordering”).  About 80%  of the 250,000 varied species of higher plants (higher plants generally have distinct roots, stems and leaves) display a spiral phyllotaxis formation (from Greek phyllon “leaf” and taxis “arrangment”).  Phyllotaxis has a hidden mathematical pattern. Scientists believe this process is controlled by a chemical mechanism – plant hormones that influence this process.  Here are some well-known construction patterns as to how leaves are arranged on a stem: distichous pattern (e.g. coleus; corn); decussate pattern (e.g. mint); whorled pattern and spiral pattern (helically arranged leaves – opposite and alternate arrangement, these leaves follow a Fibonacci spiral pattern in how they radiate out from the center).  The spiral arrangement ensures the leaf receives maximal rain and sunshine, delivers moisture to the plant’s root system, and allows for optimum positioning for insect pollination.

There are few things quite as remarkably beautiful as a male peacock’s fantastic exhibit of fully unfurled multi-colored feathers. Underlying this breathtaking display is a mathematical phenomenon having to do with the Fibonacci Sequence, whereby the spread radiant feathers create a complex pattern involving pairs of complementary spirals appearing in opposite directions.

Art forms of Creation are all around us.  Detailed patterns and markings everywhere provide a visual feast of wonders.  Creation abounds with an endless appealing variety of vibrant flamboyant colors, shapes, patterns, textures, fascinating spots, inventive stripes, elaborate markings and deep designs.  Growing and shifting formations can be found throughout the heavens and detailed intricate patterns are visible on the earth in living and non-living things (e.g. insects’ segmented bodies).  From distant spiral galaxies to seashell shapes and the patterns observed in flocking birds, Creation is alive in form and beauty.  We have abundant examples of bilateral mirror symmetry (e.g. beetle markings).  The stunning plumage art of bird feathers delight us with displays of brilliant unexpected color combinations.  Consider the myriad interesting markings of certain animals such as zebras, tigers, leopards and giraffes.  The vast array of gorgeous butterfly wings is a treat for the eyes.  Nothing compares to the awesome, striking, luminous, semi-circular fanned out ornamented tail feather train of a strutting peacock.  Marine life is rich with plentiful fish featuring dazzling iridescence, alluring colors, decorative stripes, and eye-catching patterns of every sort. The exquisite designs, fanciful colors and lovely scents offered in the lavish variety of beautiful flowers and leaves that plentifully drape the earth can leave us breathless.

How mysteriously mystifying are the shifting ripple and ridge patterns of wind-blown sand.  Equally intriguing are the many shapes and facets of crystals.  Snowflakes provide inexhaustibly amazing examples of interesting structures, each curiously unique from all others.  Many delicate patterned seashell exoskeletons can be considered artistic sea sculptures – each a distinctly beautiful complex formation.  Arithmetical arrangement is found repeatedly throughout Creation.  Hexagon is a prevalent shape.  A hexagon shape occurs in the beehive.  The hexagon shape is a great shape for bees to store items like pollen and nectar, as the hexagon makes for a strong shape.  Hexagon is the predominant shape seen in snowflakes.  Spirals are a common design feature that can be seen in the cosmos (e.g. spiral galaxies) yet it also is evidenced in abundance in plant structures like petals and leaves.