Notice that at each stage, between the extremes on each end, there is a high measure of both grouping and symmetry. Above we are seeing the same transition as shown in figure 1, except throughout the transition in fig. 2 the influence of each order is intense, causing the objects to remain grouped but evenly spaced. This maintains the objects in a lattice pattern. In looking at these patterns we can imagine the cooperation of each individual type of order intensely competing against one another. Notice the influence of each side is apparent throughout the transition, as if the invisible influence from the extreme order on each side is reaching all the way across to the other side. Below we see these same two transitions shown together, showing nature has two options when evolving from grouping to symmetry, one where the intensity of each order is very low and another where the intensity is high.

I always use a checkerboard pattern to represent symmetry order however that pattern is actually a limited measure of symmetry order, since each square or circle in the lattice pattern represents a measure of grouping order, meaning that we can divide up each square of our checkerboard pattern into smaller, finer squares and then mix them back together again as a finer checkered pattern.  Each square is unavoidably a grouping of smaller squares. Notice that once the transition above reaches a stage where the objects are spread evenly, they must then divide apart or dilute in some way, necessarily so if the pattern is to continue in the direction of increasing symmetry order or balance. In science this would be called a phase transition. 

Figure 7: Grouping and Symmetry Order with increasing color dimensions.

In figure 7 above we see simple examples of rows, rings, and spiral, in this case portraying colors of light projected on a screen, forming patterns in which we easily see both grouping and symmetry. The first image of each example shows a grouping extreme while the last image shows the light combined together, resulting in a total lack of differentiation and form, yet each is the extreme of symmetry order for these patterns. Of course subjectively one's instinct abhors the notion of loss of form, the thought is almost horrifying to our identification with form, even if the separate forms are becoming the oneness we otherwise sometimes idealize.  In reality we are more apt to see oneness as nothing.  More objectively one's intuition might recognize that what is generally occurring in these transformations is that imbalances are combining together to become a balanced whole.  There are many dualities in nature that balance out to zero, just as there are triads that balance out, and so on. Colors of light are an ideal example, in how the infinity of colors all sum to white light.

Figure 8: A large mass ornamented with symmetries. Orderliness is the product of two orders strongly cooperating.

Fundamentally we know that all identifiable material things are non-zero imbalances. They are made of positives and negatives. And of course the ultimate balance point is always a zero balance.  In science we describe the grouping of matter, stars, galaxies, planets, gases, as order, yet each represents an imbalance in nature.  Here we are discovering that the balance of zero has to be considered a type of order also.  Balance isn't a nothing, at least not in the sense of not existing.  Real nothings are simply balances and uniformities. The absolute zero of physics is the ultimate balance, it is a combination of all times and places and things that collectively form a oneness, making the uniform result appear to be empty of things.  A really amazing fact about the universe is that empty space, and the result of combining everything together into a unified whole, have the same exact qualities.  So how then do we distinguish between the ultimate everything of symmetry order, and the nothingness of empty space? Actually there is no distinction. Even the ordinary empty space that surrounds us is far from empty. It is full. The world of things we exist within is not more than a primordial nothingness, but rather all we know is less than a timeless everything.

Symmetry order is the unifying force in nature.  It is the great attractor, the great point of balance toward which all change naturally progresses.  Symmetry order is the invisible backdrop, the blank canvas, the board on which the game is played.  But acknowledging symmetry order is far more involved than simply recognizing that balance leads to a smooth uniform pattern.  The direction of symmetry order is not merely toward a balance between the objects we see in our universe.  Such is simply what exists at the surface of symmetry order, like waves on an ocean.  True symmetry order involves unification of the world we see with the complete world, the infinity of other worlds, of other times, and other lives, all of which must be in balance in order to not be a part of our world, because our world, the things of our world, are created from imbalances. Parts are removed from what we experience, anti-matter for example. For us to have form, our identical opposite anti-matter selves have to exist somewhere else, creating the imbalances we see as the finite world. And naturally imbalances tend toward balancing out.  That is a universal principle we all recognize.  And of course the final product of balance is the native state of the collective Universe, the timeless whole, the basic nature of existence, the default of being.  In the direction of increasing symmetry, the form of objects of this world are fusing and combining together with the underlying balance of the timeless infinite whole.  The physicist David Bohm called this process enfoldment.

A surprising number of others in the past have constructed similar models of two orders, including Henri Bergson and William Yeats in the early 1900's, but the most recent and most notable was Bohm. Many of these same ideas were introduced by Bohm to modern science in the 1960's.  In an interview with Omni magazine conducted by F. David Peat and John Briggs, David Bohm explained his concept of enfoldment:

Bohm did mean for implicate and explicate orders to replace order and disorder, unfortunately, the mainstream of other scientists didn't catch on to his vision, and Bohm struggled with despair and depression at not being able to convince the scientific community of the scientific value of his discoveries, a struggle I indirectly inherited and share frustration in.  After independently discovering two orders in my own way, and learning to present my own system of seeing the same thing, the same principles, the same process in nature, and then discovering and studying Bohm's work in greater detail, I now believe the only reason Bohm's ideas were kept from having greater impact is that he was led more to challenge how quantum mechanics was being interpreted in his day rather than led to directly challenge the second law's usage of the terms order and disorder.  Although judging from my own experiences I am sure it would have taken years for the challenge to sink in to the often dull collective mind of science.

We are not accustomed to recognizing the simplicity of uniformity and sameness as being properties of an underlying order.  We easily recognize the balance and symmetry in the pattern of a snowflake as being highly ordered.  Yet the same qualities of symmetry and balance pushed to extreme leads to an indistinct sameness that we have no respect or appreciation for because of our identification with finite form.  The funny thing is that when many things become one thing, we see nothing.  We are so attuned to recognizing the organizational properties of grouping order, or the pattern complexity that results of patterns which utilize both grouping and symmetry, that the uniformity of symmetry order in extreme, the order of oneness and wholeness, doesn't seem like anything at all.

We all know that if we mix two or more things together to extreme they become one thing, but when that one thing is everywhere and everything, it looks like nothing at all, so it is difficult to rationalize that the original parts that went into creating the uniform pattern are still there in the uniformity.  There is a similar uniformity and sameness in grouping order when we combine all of one kind of thing into a single object, like many atoms of gold together form a larger body of gold.  But the combinational sum of like things creates a larger object with increasingly distinct and pronounced qualities relative to other things.  In contrast, when all things combine together into one thing everywhere there isn't anything else to relate the sum of all to, so symmetry order is ever less pronounced as various qualities merge together.  Of course this is not how we expect the world to add up.  In math when we add up things the sum gets ever larger and pronounced, not increasingly more invisible.