Although known as the four "chaos attractors," they are really the opposite - they are Cosmos Attractors that balance chaos. The four "Attractors" bring order out of Chaos. They are part of a basic law of four - a "fractal of four." The Universe has a fundamental pattern of fourfoldness throughout all scales of magnitude. When applied to Nature, including Man, the Law of Four manifests as the four attractors. These attractors balance entropy, providing order from out of chaos. When applied in the microcosmic level "the four" manifests as the four basic energies or forces: electro-magnetic, gravity, and the strong and weak forces. In human consciousness its the four functions of sensing, thinking, feeling and willing. Understanding how the Attractors work in the meso-cosmic world can help us make sense of our world, and make sense of our consciousness functions.
Everywhere we see a hidden order and similarity over scales, such as is that shown geometrically by the Mandelbrot and Julia sets. This hidden order is based on one of the four Attractors, the Strange Attractor. It governs the fourth dimension of space-time reality. The other three attractors, which likewise bring hidden order out of Chaos, follow the first, second and third dimensions, the line, plane and solid. They are called the Point Attractor, the Circuit (or sometimes Cycle) Attractor and the Torus Attractor. As humans living in the fourth dimension we are at our best when we avoid their influences and follow the spontaneity and freedom of the Strange Attractor. Only in this way can we live autonomously in the moment, in tune with what the Chinese call the Tao, the Way, the flow of forces in the fourth dimension.
The four attractors act on all levels of reality to form Cosmos out of Chaos. They make up a newly discovered Wisdom Law fundamental to making sense of what is happening in the real world. The world is not really totally ordered as previously believed. It is fundamentally disordered, chaotic, but it contains forces or attractors of cosmos that create patterns of order over time. They are anchors of order in an otherwise stormy sea. Full understanding of the Attractors requires a new understanding of space and time. As to space, we need to understand how space is the original force - in Sanskrit called Brahman, in Chinese Wu Chi, in Peruvian and Japanese Ki - which creates the world through the point. Real insight into this only comes from direct experience of Ki. A new understanding of time entails realization that time is not really defined by the clock, but by intensity and rhythms. In the fields of the four attractors it is time which makes it possible for order to appear from chaos.
In the computer the electric current automatically creates the iteration. With Man it is not so easy, we ourselves have to return to Zero - Awareness - to start a new iteration. Awareness is sacred space (called "Wakan" by the Native American Lakota tribe; "Mana" by the Polynesians) which you connect with as soon as you attain the center of your true Self, called by the Japanese - Hara. Thus the difficulty which many scientists have in understanding Chaos is not mental, but existential. Their consciousness based on the Cycle attractor of analytical thinking refuses the Strange attractor, which means total individual responsibility. They cannot ground themselves in Zero and experience the true meaning of space and time. As they cannot find their inner core - Awareness/God - they can only see Chaos from the outside. They cannot make the jump from knowledge to Wisdom, to inside the black. Without this anchor they lack the experiential insight - and the confidence and Wisdom this brings - needed to live on the edge where great discoveries are made. They only see isolated Cantor sets and miss the pattern which only comes from awareness of the whole, the Mandelbrot fractal.
The Point attractor is the simplest way to bring order out of chaos. Its home is the first dimension of the line, a collection of an infinite number of points. With the Point attractor in play a person is invariably drawn to one particular activity, or repelled from another, like the positive or negative poles of electromagnetic energy. There is also sometimes a point just in between attraction and repulsion, the saddle point, when the energies are in balance, just before one force becomes stronger than the other. With the Point attractor there is typically a fixation on one desire, or revulsion, and all else is put aside until it is satisfied or destroyed. With the positive attraction force all roads seem to lead to the same destination; with the negative repelling, all lead from the same place. A positive magnet drawn to negative, a pendulum slowing down with friction and air resistance, or more graphically, a young male dog around a bitch in heat, all demonstrate the workings of the point attractor. It is a black-white, good-bad, single minded attractor, except in the rare instances of the saddle point. Its analogy in consciousness is the feeling function, with its likes and dislikes.
With the Cycle attractor a person is drawn first to one thing and then to another, like a circling magnet, first attracting, then repelling, then attracting again. Its home is the second dimension of the plane, a collection of an infinite number of lines. Under this Attractor you cycle back and forth from a set of two or more activities. Although not as simple and direct as the Point attractor, there is still regularity and simplicity to the cyclic events. An example is a desire to sleep at the end of a day, which when gratified naturally leads to a desire for activity at the beginning of a new day, followed much later by a desire to sleep again, etc. In Nature it can be seen in many ways; for instance, the predator prey systems where the respective predator prey populations cycle up and down in relation to the other.
The Cycle attractor is more complex than the simple attraction or repulsion type Point attractor. Its analogy in consciousness is the thinking function. Like objective thinking the Cycle attractor recognizes both sides and tends to include a third; for example, the synthesis coming out of the thesis and anti-thesis.
With the Torus Attractor there is complex cycling which moves forward and so is different while it repeats itself. Its home is the third dimension of the solid, a collection of an infinite number of planes. With the Torus Attractor there is a high degree of irregularity and complexity in the pattern, particularly when compared to the Circuit or Point attractors. But unlike the Strange attractor, predictions can still be made, the pattern is fixed and finite. Mathematically the Torus is depicted in the shape of a large donut or bagel as shown above. It is made up of a spiraling circle on many planes which may, or may not, eventually hook up with itself after completing one or more full revolutions. Its analogy in consciousness is the sensing function. The complexity of sensations and sensuality.
An example of the Torus attractor at work would be a more complex set of attracting events which occur to a person on many levels over a course of a year, and repeat again, year in and year out. For example, a desire to golf each summer, hike each fall, and eat and drink too much on holidays. In Nature it is shown for instance by the complex interaction of a number of interdependent species: the population of one predator species relates to that of the prey of its prey. For example, the size of the insect population effects the size of the frog population, which effects the size of one of their predators, the trout, which in turn effects their predators, the pike. Unfortunately, most humans are also subject to the complex but predictable influences of the Torus attractor, or the even more simplistic influences of the Cycle or Point attractor.
We need to escape from the deterministic influence of the point, circuit and torus attractors into the unpredictability of the Strange Attractor. This attractor is the basis of Self Organization. There is no apparent order at all to the actions of the Strange attractor. On the surface it appears to be pure Chaos, but nevertheless there is order of a subtle kind which only appears over time when looked at in the right perspective. Its analogy in consciousness is the willing function.
Yet, when tied to Awareness - the Zero - it is spontaneous, unpredictable. It appears to be chaotic, yet it has order of a subtle, fractal kind.
The Strange Attractor can take an infinite number of different forms. All of them are fractal and demonstrate infinite self similarity. The best known fractal driven by the unpredictable Zero - the Strange Attractor - is called the Mandelbrot Set. It is shown in static and zoom magnification form all over these webs. Another is the Lorenz Fractal shown above. Still another important Strange Attractor that appears in odd places throughout Nature is called the Feigenbaum fractal. It is shown with one recursive self similarity pointed out.