"The greatest impediment to scientific innovation is usually a conceptual lock and not a factual lock" -- Stephen J Gould
To say that patterns in nature are ordered seems to state the obvious. The concept of order permeates all other characteristics that describe patterns because patterns in nature are manifestations of and clues to an underlying order. What makes "order" such a fascinating and important subject is that it touches upon the processes and dynamics that define structure and pattern. Any discussion about order includes both the architecture of a pattern (form) and the ongoing dynamic processes (function) that are taking place within that architecture.
The universe is an elaborate ordered structure. Many basic patterns and processes recur on widely different scales. Some things that are very different from each other contain the same underlying order. This section provides an overview of the concept of "order". Here, we lay the groundwork for the discussions on connectivity and symmetry.
Western science operates on the fundamental assumption that nature is ordered. The concept of order has been around since the medieval times when science adopted the Biblical worldview that one God created an ordered world. But, the idea of order became a paradox in the minds of scientists. Our world clearly exhibits order in many forms. The daily rising and setting of the sun quickly comes to mind as one simple example.
But, disorder also surrounds us. Consider the turmoil of the sea's surface during a storm -- all while there is the regularity of the ground swells. Or weather, or the stock market. There seems to be a tendency for disorder within the context of order.
The potential for disorder is sometimes called "entropy" -- the tendency of a system to head toward a disordered state. The idea of entropy is embodied in the second law of thermodynamics which states that isolated systems with no influences from the outside world will exhibit increased disorder over time.
This idea of entropy seems to be in direct conflict with the ordered trend of pattern formation we see in nature -- living systems in particular. Instead of becoming disordered, living systems develop into highly complex and ordered structures. Their processes are ordered. Living things take in food and air. They dissipate heat and waste products. Unlike the isolated systems described by the second law of thermodynamics, living organisms are not closed systems. They are not isolated!! Instead they are highly connected to their environment which includes living and non-living systems. Unlike closed systems, these open systems are constantly exchanging matter and energy through conduits of connectivity.
In contrast to living systems, a dead organism does not take in and dissipate matter and energy in the same way as a living system. We can see the effects of this as a body decomposes. The dead body demonstrates an increase in entropy -- an increase in disorder. A dead body falls apart. It undergoes structural transformations that result in less order.
The key point is that order is achieved because a system that is manifested by patterns is connected with other patterns. Connectivity is an essential and intimate component of order. Order cannot be fully understood unless both a structure and its "connectedness" are considered.
We now examine a (seemingly) simple example of order. The common sphere is a simple geometric object in three-dimensional space -- like the shape of a bubble. Of all the shapes in our geometric inventory, a sphere has the smallest surface area for a given volume. The sphere is a manifestation of order for any natural process that seeks to contain the greatest volume for a fixed surface area.
A bubble is a good example of a naturally ordered sphere. A bubble's spherical shape is caused by surface tension. Surface-tension is the connection between the liquid's molecules caused by various intermolecular forces. In the body of a liquid, each molecule is pulled equally in all directions by neighboring molecular forces resulting in a net force of zero. At the surface of the liquid however, the molecules are pulled inwards by other molecules deeper inside the liquid and are not attracted as intensely by the molecules of air (or another liquid) that surround the bubble. Surface tension causes the bubble's surface to form the smallest area for the given volume of whatever is contained.
The order caused by the connecting forces of surface tension creates a pattern -- in this case a sphere. Many natural objects have shapes that are very close to that of a sphere. 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. An interesting example of this ordering is hot mud being thrown up into the air at the Mud Pots at Yellowstone Park. Note that the mud has a tendency to form spheres as the airborne liquid is separated by the hydrothermal forces.
The center of a sunflower is an ordered collection of natural objects called florets. There is a definite structural order in the placement of the florets as they describe spirals proceeding both left and right from the center of the flower. This is called the Fibonacci Spiral which is based upon a sequence of numbers called the Fibonacci numbers. The ratio of any two consecutive numbers in the Fibonacci sequence is constant and is called the Golden Ratio -- often referred to as "Phi". Phi defines the constant angle that a floret defines with its preceeding neighbor. Phi is ubiquitous in nature. In addition to sunflowers, we see Phi and its resulting spiral arrangement in a myriad of nature's patterns including DNA, snail shells, and the solar system. Generally, the connecting forces are both physical and chemical in nature. Learn more about order as it is related to Fibonacci numbers.
A view of barren cottonwood trees hardly seems to be a picture of order. But yet it is. To define that order, one needs to move from the world of simpler natural objects like bubbles into the realm of complex patterns that are described by "fractals".
Wikipedia describes a fractal as "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity". The term "fractal" was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
One of the key characteristics of all fractal objects is "self similarity". The tree is an approximate fractal because a cropped picture of one small segment of the photo reveals a pattern that is approximately the same as the original photo. In general, when changing the size (called "scaling") of a fractal, the image looks approximately the same.
The same order or pattern exists at every scale. It is said that a fractal object is "scale invariant" because it looks the same at every scale of magnification. The scaling process of a fractal object can be described as a single number called a fractal dimension which stays the same no matter what level of magification is being viewed. It is this fractal dimension that defines the order of a fractal object and its relationship within itself.
Fractal order is very common in nature. Examples include plants, mountain ranges, lungs, lightning strikes, and clouds. Learn more about Fractals and self similar patterns.
Fish schools, bird flocks, animal herds are three of many examples of order that emerge from within self organizing systems. The resulting patterns displayed by the system as a whole are called "emergent behavior".
The self-organizing order that shows emergent behavior operates without a leader. Instead, each individual within the system behaves according to a fixed set of rules executed from limited knowledge of local information only. The result is a systematic behavior that the individual alone could never accomplish.
A well studied example of order resulting from self organization is fish schools. In the early 1980s, Brian Partridge and others performed studies on fish visual abilities and their pressure sensing lateral lines. They showed that fish can sense and keep a distance from their nearest neighbors. In 1986, Craig Reynolds developed computer simulations of bird flocks and fish schools that mimicked the behavior of real self-organizing biological systems. Later, David Hooper developed Cool School, a realistic simulation of fish schools and their interactions with predators.
Both the live experiments and the simulations showed that order at a system level can result from the order of individual behavior as a simple set of common rules are followed. Reynolds describes the three necessary rule sets for each individual with respect only to its nearest neighbors to be keeping a defined separation, aligning in the same direction, and maintaining a cohesion. The connectivity within the school, or a flock, or a herd comes from behavioral interactions between individuals and not physical relationships.
Scott Camazine notes that the distinguishing features of all self organizing systems are large numbers of individuals within the system, large numbers of individual interactions, simple individual rules of interaction, decentralized control, and emergent properties.
Perhaps the most complex example of order is represented by the human being and other living organisms. They represent an extrememy intricate and elaborate hierarchy of other patterns along with the conduits of connectivity that link these structures. In examining these examples of complex order, one also realizes that all that persists is the pattern of organization itself. The actual physical structures (water molecules, skin cells, nerve pulses) change every millisecond. The "connectedness" of these dynamic structures is contained in the organization plan. In this context, the definition of order is in the information carrying content.
Appreciating the concept of order in nature's patterns is fundamental to beholding nature and achieving an understanding of the patterns that emerge. All forms of order involve connectivity because the flow of some form of energy within a system is essential to the sustenance of the patterns that we see.
We now move on to look at other characteristics of patterns in nature including a more detailed look at connectivity and symmetry.
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