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In an attempt to synthesize and to simplify, much has been said about the idea that patterns in nature can be formed by simple physical laws. Certainly, this idea has appealed to mathematicians, physicists, and others who adhere to the reductionist world view. It is certainly true that physical laws play an important part in pattern formation. But, physical forces are not the entire story as the honey bee demonstrates.

This page looks at physical laws and how they work with bee behavior to form the common hive pattern. But, the story starts with water drops.

Of all the shapes in our geometric inventory, a sphere has the smallest surface area for a given volume. A common drop of water is a good example of a naturally ordered sphere that is shaped by the influence of physical forces. The spherical shape is caused by physical laws associated with surface tension.

Each water molecule in a body of water interrelates with neighboring molecules by way of by various intermolecular forces that results in the molecules being attracted to each other. In the body of a liquid, each molecule is pulled equally in all directions by neighboring molecules, resulting in a net force of zero. But, at the surface of the liquid, the molecules are pulled inwards by other molecules deeper inside the liquid because the surface molecules are not attracted as intensely by the molecules of  air (or another liquid) that surround the water drop. This net difference in attractive forces is called surface tension.

This surface tension at a water drop's surface results in the formation of the smallest area for the given volume of whatever is contained. The resulting shape is a sphere.

So, the physical forces associated with surface tension create a pattern -- in this case a spherical water drop. Consider raindrops, the beading of rain water on the surface of a waxed automobile, or a stream of water slowly running from the faucet -- the stream breaking up into drops during its fall. Gravity stretches the stream, then surface tension pulls the stream into spheres. The sphere has resilience caused by surface tension. This resilience takes place because the surface tension pulls the surface of the sphere equally in all directions.

A bubble is sustained as a result of the balance between the internal gas pressure of the bubble and the forces associated with surface tension. The internal pressure that tends to push the sphere apart is counteracted by the surface tension acting around the surface of the sphere to provide a net force that pushes inward.

Foam is a collection of spheres (bubbles) ordered in some way. The weight or gravitational forces that act upon a collection of bubbles causes them to "pack". A two dimensional packing of foam bubbles results in three bubbles whose walls meet at 120 degree angles -- forming roughly hexagonal cells. The physics of this phenomenon is described in detail in the references noted below.

If the bubbles are of unequal diameter, the hexagons are unequal. But, if the bubbles are of equal diameter, the hexagons are of equal size -- taking on the appearance of a honey comb.

Using their bodies as a template, bees make each close packed wax cell cylindrical, like a tube. Like glass, beeswax becomes increasingly fluid as it is heated. The mobility of one wax particle with respect to another changes significantly at specific transition temperatures. The bees raise the temperature of the wax to 37-40 degrees Centigrade permitting the wax to have more malleability . At this temperature the cells take on their hexagonal shape due to their compression by the six closest neighbors in the packed arrangement of cells.

The entire process of creating a honeycomb pattern in a hive, therefore, comes from a combination of physical laws and bee behavior that takes advantage of these laws. The pattern of bee behavior is just as important as the pattern of physical laws that is employed to create the comb structure.