rain forrest

Rain Forest, St. Lucia


Photo Credit: Robert Gendler

The Orion Deep Field
A Stellar Nursery


Appalachian Trail
Western Maryland



















The Mandelbrot Set
A fractal of limitless complexity and great beauty



Seahorse Tails in the Mandelbrot Set





































Photo used by permission of Gary Meisner
The Golden Ratio In the Design of the Human Body
The central incisors form a golden rectangle. The ratio of the widths of the central incisors to the lateral incisors is Phi. Notice the Phi ratio in the distance from the center of the lip to the corner of the mouth.


Photo used by permission of Dr. Eddy Levin

Phi in the design of a leaf. The Golden Mean Gage demonstrates the golden ratio in the spacing of the leaflets.

Click HERE to see a video showing how the golden mean gage can be used to design well-proportioned furniture. To buy plans for making a golden mean gage from Wood Magazine, click HERE.



















Photo used by permission of Dr. Eddy Levine
Logarithmic Spirals in Sunflower Seed Head

pine cone

Logarithmic Spirals in Pine Cone

This pine cone has eight spirals in one direction and thirteen in the other. Both numbers are in the Fibonacci series.
















Universal Concepts of Beauty

Humankind's appreciation for beauty is universal despite national, ethnic and cultural differences. This is because it is God that has created beauty and the elements that contribute to beauty. He has given man the ability to appreciate the beauty in what He has created.

When the creation was finished, God evaluated His work and said that it was very good.

Genesis 1:31 And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.

The universe was designed to support life. Man was given an environment that was harmonious, stable, self-renewing, and it was beautiful. Even now, when the creation is less safe, supportive and benign than it was at the beginning, we can all appreciate the beauty of the earth and the heavens. It is difficult to find a landscape devoid of beauty if it has not been devastated by a natural disaster or ruined by the hand of man. Most of us need beauty in our surroundings. God anticipated and provided adequately for this need. When He said that what He made was good, He undoubtedly meant that a part of its goodness was its beauty. The Fenton translation of the Bible renders Genesis 1:31, "And God gazed on all that He had made and it was very beautiful". This page discusses how God made His creation beautiful.

How do we determine what is beautiful and what is not? God must have written this into our DNA in a kind of firmware that is transferred genetically. We do it without analysis. Its an inherent ability we all have. We see beauty, we recognize it, we appreciate it. It is an ability God has shared with us.

Creating beauty is a matter of design. There are seven principles of design:

      • Scale and proportion
      • Symmetry
      • Balance
      • Rhythm
      • Emphasis
      • Variety
      • Unity

Successful designs incorporate these principles in varying degrees. I don't want to discuss all the principles, but rather, focus on two that are extraordinary. These two are cosmic in their use in the design of natural things. The two principles are scale and proportion.

Repetition Of Patterns In Many Scales

Perhaps you have noticed an unusual property of some plants--similarity on many scales. Ferns are an example of this design feature. In the picture below, notice that each leaflet of the fern branch is similar in shape to the entire branch. The component pieces of each leaflet are similar copies of the leaflet, but on a smaller scale.


In this example, there is similarity on three scales. The use of this design element creates a degree of complexity that the eye finds appealing. The fern leaf is a "FRACTAL", that is, a geometric shape that exhibits similarity on many scales. Fractals appear everywhere in nature. Fractal shapes are found in clouds, in mountains, coastlines, trees, vegetables and even in the structure of lungs and circulatory systems of humans and animals. The pervasiveness of fractal structure in nature is discussed by Benoit Mandelbrot (who coined the term, "Fractal") in "The Fractal Geometry of Nature" and by Michael Barnsley in "Fractals Everywhere".

The fractal structure of the fern is rather simple, being only three levels deep. It is possible, with very simple mathematical equations, to create extremely complex fractals, having similarity on an infinite number of scales. If you would like to create some stunningly beautiful images with you computer, download the computer program, "Fractint".

The image below was created by Fractint. It is a small portion of a vastly complex shape called "The Mandelbrot Set".


If you study this picture, you will notice that similar shapes appear at many scales. The dome shape resembling a jellyfish is repeated dozens of times. Another fascinating recurring theme is the double seahorse tail that descends to infinity in a logarithmic spiral. This spiral shape will be important in the discussion of proportion. Magnification of this image (can be done in Fractint) would demonstrate that the theme of the pattern is reproduced in smaller and smaller scales to the limit of your computer's ability to crunch numbers.

God has used fractals to add interest and beauty to nature. He has somehow encoded the equations necessary to create fractal structure into the DNA of living things. He has created natural processes that produce fractal shapes in inanimate matter. Without fractals in our surroundings, our environment would appear bland and dull.


Since ancient times, it has been recognized that proportion contributes to beauty. The Greeks knew that one particular ratio was especially pleasing. They used this proportion in their art and architecture. It is known as the GOLDEN MEAN, the GOLDEN NUMBER or the GOLDEN RATIO. This ratio gives rise to the GOLDEN RECTANGLE, a shape that has aesthetically pleasing proportions.

A golden rectangle can be constructed in this fashion: First, draw a square.


Next, bisect the square.


Draw a diagonal from the middle of the base to an opposite corner.


Create an arc with a radius equal to the diagonal, its center at the midpoint of the base, extending to intersect the line of the base.



Form a new rectangle with its base extended to the point of intersection.


This is a golden rectangle. The ratio of its width divided by height is an irrational number, 1.61803... . This is the proportion that the human eye finds most pleasing. Pleasing design incorporates the golden mean in its dimensions. For a full explanation and many examples, visit the Golden Mean Gage site.

Nature is full of designs incorporating the golden ratio. Also know by the Greek letter, PHI (Ø), this ratio is found in the design of plants, animals and of the human body. Phi is found, for example, in the widths of human teeth. When dentures are made, the ratio of the width of the lateral incisor to the central incisor must be 1.618 if the teeth are to look natural. The ratio of the joints of the fingers and of the hand to the forearm also approximate the proportion of Phi.

The human face is constructed using the proportion, Phi. The most attractive faces conform to a mask or template created by plastic surgeon, Dr. Steven Marquardt. This template locates the position of the facial features with respect to each other in proportions of Phi. The more closely a face conforms to the mask, the greater its beauty. This mask is universal in its application. It works for all races and both genders. It demonstrates that beauty is a universally accepted standard that transcends race, gender, time and culture.


Images used by permission of Gary Meisner, Golden Number Website

For more information on this fascinating subject, click HERE to visit Dr. Marquardt's site.

We have seen how the golden ratio, Phi, can be generated geometrically. It can also be generated numerically using a string of numbers know as the "Fibonacci Series". The Fibonacci Series consists of the numbers, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 and so on. Each number in the series is the sum of the two numbers preceding it. There are many interesting properties of this series of numbers and many natural phenomenon arising from it.

The ratio of any two successive numbers in the series is 1.61803, or Phi. For example, 377 / 233 = 1.61803. Ratios of the larger numbers in the series more closely approximate Phi. If we calculate the ratio of 8 / 5, for instance, we have 1.60000.

Phi appears in nature in countless ways. Flowers usually have a number of petals that is in the Fibonacci Series. Seed heads of flowers and pine cones have seeds arranged in spirals radiating outward from the center. The number of spirals is in the Fibonacci Series. As plants grow, putting out leaves and producing seeds, they rotate in order to produce the most efficient packing. The angle of rotation is based on Phi . The angle of rotation = 360° x 1 / Ø, or 222.49°. Learn more about this at Dr. Ron Knott's website.

The spiral structure that we see in seed heads of sunflowers and in pine cones is a design theme that is based on Fibonacci numbers and is found throughout nature. This logarithmic spiral can be constructed by tiling squares having dimensions that are Fibonacci numbers.


When the corners of the squares are connected by arcs, an approximation of the logarithmic spiral is produced:


These spirals are found on vastly different scales throughout the universe.

two spirals

Photo Credit: Brian Lula

Hurricane Isabel appears to be about 1200 miles wide in this picture, while the Whirlpool galaxy is 50,000 light-years in diameter, an extreme example of the fractal structure of things and the recurrence of sprials in nature.

Logarithmic spirals are also found in mollusk shells.  This cutaway view of a nautilus clearly shows the graceful spiral structure of this creature’s shell.


  The human ear is a logarithmic spiral too.


There is a remarkable vegetable that is designed with both fractal structure and logarithmic spirals - Romanesco Broccoli.


This vegetable has been described as “visually stunning”.  It is grown in Italy and Switzerland.  If you would like to try your hand at growing it, you can buy seeds from
Seed Savers Exchange. Ordinary broccoli and cauliflower are fractal and cauliflower has spirals too, but the effects are not as dramatic as those in romanesco.

Lasting Beauty

God has created beauty.  He has defined the rules that create aesthetics. His brushstrokes, fractals and spirals, can be identified all over the universe. He has shared His sense of beauty with humankind and has allowed us to perceive beauty as He does and in the things He has made.  God has endowed humans with beauty, using the same rules to design our bodies that He used to design other objects of beauty in creation.  Indeed, God has fashioned us after the design of His own body, honoring man by making us in His own image. 

There is a final aspect of beauty that the Christian must consider.  God’s plan is to make man after His own likeness of character, not only His outward appearance.  God's character is beautiful. The book of First John tells us this:

1JO 1:5 This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all.

Light is a metaphor for everything that is good, that is true, that is enlightened, that has beauty. There is no darkness in God. He has no hidden motives, no character flaws, no evil intent, no selfish desires. God has brought forth the beauty we can perceive from within Himself, from His nature. The things He has made are an expression of His own beauty of mind, heart and Godly character.

Godly character: That is the true and hidden beauty that Christians must have.

1Peter 3: 3  Whose adorning let it not be that outward adorning of plaiting the hair, and of wearing of gold, or of putting on of apparel;  4  But let it be the hidden man of the heart, in that which is not corruptible, even the ornament of a meek and quiet spirit, which is in the sight of God of great price. 

The outward beauty of the physical creation will age and fade, but the hidden beauty of character which God values will last forever.  In a sense, creation is an on-going project of God’s.  Creation’s work will not truly be done until all men have developed Godly character.  God will make mankind truly beautiful—from outward appearance to indwelling character.

God, the Creator of beauty is going to make man beautiful--every man and woman who has lived will have a chance, ultimately, to develop Godly beauty in his or her character. God has a plan to make this happen. To find out how, click HERE.

To download a sermon about beauty of character, right click HERE and select "Save Target As".