A seemingly endless amount of information can be derived from a simple formula, Z_n+1 = Z_n² + C. This alone may be the most important point. An idea can often produce very complex results, or inversely, a very complex system may be based on a simple idea. Any cosmology that describes a conceptual reality should be simple if it is to allow a large number of results. Interestingly, those results may be unique depending on how the simple idea has been applied, but they are always constrained by the rules governing the operation 0of the simple idea.

In the Standard Cosmology, individual Selves have self-determination, but that self-determination is constrained by the rules governing the operation of available energy, and those rules are based on the worldview of the source of that energy. In this way, we can do as we wish, but we cannot violate local natural principles and our decisions are biased by a sort of imperative we inherit from our creator entity.

1. Formation is the result of attention on imagination with the intention of forming an object of reality. An "object of reality" is anything, including a person (Self), an idea or a thought.

2. The simple formula, Z_n+1 = Z_n² + C, might be considered the basic element of energy in imaginary reality. A "given" in the Standard Cosmology is that there is a fundamental form of energy that is universally present in reality. The behavior of this energy is governed by rules so that the presence of the energy implies the presence of the rules governing its operation. A parallel can be seen in set theory, in which the rules of math govern how the equation must be calculated (operated) to produce a result.

3. In set theory, fractals represent regions in the number set which are stable. In a similar way, there appear to be loci or regions in reality in which the rules of formation permit more complex and longer lasting objects of reality. They represent regions such as the physical aspect of reality that contain many opportunities for experience operating under the same rules of formation. Smaller loci may be as simple as a thought form or even an idea.

4. In set theory, a fundamental fractal seems to be present with many satellite but lesser instances of that fractal. Reality appears to have major regions or realms in which many similar venues for experience exist. There appears to be many lesser loci for creation in which less substantial venues for experience may exist. This may be compare as the physical and near physical as a realm and personal realities within that realm. Again, this is not an exact one-to-one correspondence. It is a anology.

1. Expanding on the idea that an individual point on the real number plane can be compared to a unit of energy, the point can also be compared to a set of initial assumptions, which would be a person's worldview as he or she embarks on an experience. In this case, the number of iterations that can be applied to the basic formula would be compared to understanding gained from the experience.
   
   In other words, any point x + yi could be compared to my lifetime and the initial understanding and inclinations I came into this lifetime with. It can also be compared to the worldview I have as I enter into a lifetime experience, such as a work experience. The number of iteration the calculation can be taken to before it reaches some limit would represent the understanding I gain in these experiences.

2. Movement in imaginary space is not movement from "here" to "there," in the same sense of changing locations. Movement is accomplished by selecting experiences (initial assumptions or x + yi) that provide the greatest opportunity for increased understanding. These experiences increase in complexity and value to our learning experience as we improve our ability to select helpful initial conditions for experiences because of our increasing understanding. In that way, we are "attracted" to the fractals, which represent some region of stability, such as the physical or the astral universe but not necessarily the final objective.

3. The set of initial conditions represented by a fractal has only energy and a common set of rules governing how that energy can be used in formation. In order to manifest as an object of reality, the rules of formation must be applied to an image held in the mind of a creator entity. Here, it should be noted that imaginary space is an environment in which Self must exist. Imaginary space constrains how Self may move about and behave, but it is also managed by Self. As an individual Self gains sufficient maturity through gaining understanding about the operation of reality, it is more able to move about.

4. The Mandelbrot Set does not suggest a mechanism by which a Self might initially come into existence. It is just an illustration suggesting the basic nature of the cosmology, but it does suggest behavior once the journey has begun. If you assume that a Self is an aspect of a creator entity sent into reality to gain understanding about the operation of Natural Law by experiencing its operation in certain venues, then you  must also accept that Self is preoccupied by gaining that understanding and returning with it to its creator entity. So, imagine that Self is cast out to the farthest reaches of reality, which in this model, are the regions in which an initial assumption will take the calculation to infinity very quickly.
   
   Self has the urge to gain in understanding and can only do so by testing different initial assumptions. Once tested, the resulting experience must manifest as understanding, and so, the initial assumptions may be tested many times, or all of the adjacent assumptions may be required before understanding does occur. Once understanding is reached, think of this as gaining spiritual maturity, Self is able to move on to the next set of initial assumptions, which are venues for experiences. Self cannot go further than understanding allows. In effect, Self is energetically in agreement with the set of initial assumptions it is testing and cannot move on until it changes the nature of its energy--its understanding or worldview. As such, Self cannot return to its creator entity until it has achieved sufficient spiritual maturity to be energetically in agreement with the aspect of reality its creator entity inhabits.

5. A creator entity may exist in one of the more substantial fractals, and itself be an aspect of another creator entity occupying an even more substantial fractal. As such, Self may be one of many Selves working their way back to the same creator entity, and the creator entity may be one of many working their way back to yet another creator entity. In this cosmology, their might be many rounds of aspectation Self must deal with before it is finally reunited with its prime creator.

Closing Comments

A cosmology is just a hypothesis, and as such, is a working model that requires continued testing and reformulating based on current evidence. In effect, I am proposing the "Imaginary Space" cosmology as a refinement of the layer cake models one sees in some of the systems of belief. Terms such as "plane" and "vibration" remain useful metaphors, but they are too often taken literally--as I am sure some people take Imaginary Space literally despite my cautions to the contrary. I am not sufficiently insightful to know what descriptive terms might come from this cosmology. I like "loci of reality" rather than "plane," "aspect" and "Self" rather than "Soul" and "energetic agreement" rather than "same vibration."

It will be interesting if you contemplate this cosmology for a time and see how it fits your understanding of things etheric. Perhaps after you have tried it on for a while, you can offer an alternative or modifications to this one. One litmus test to any theory that is intended to describe the relationship of Self to reality is the distinction between physical body and Self. There is way more evidence that Self is an etheric being that is in a symbiotic relationship with the physical body. There is no real proof that Self does has a biological origin, and any theory that proposes otherwise has probably ignored the evidence

In this section, I briefly address the math of set theory. It is only necessary to spend time in this section if you whish to understand the details of fractal and set theory.

Figure 2: Imaginary Space

Calculating the Mandelbrot Set

The Mandelbrot Set is represented by the nonlinear mathematical formula: Z_n+1 = Z_n² + C where both Z  and C are complex numbers (x + yi).  The complex plane is represented as aplane bounded by X and Y as shown in Figure 2. The formula is calculated by selecting a value from the complex plane for C so that C = x+yi, to be used as a constant, and letting Z be a variable.  After each iteration (calculation of the equation), the resulting complex number is substituted for Z and the calculation is repeated with C held constant. The usual way that the results are illustrated are shown in Figure 1, in which the changes in color are indicative of the number of times the calculation can be iterated before the resulting answer exceeds a predetermined limit--usually approaching infinity.  Thus:  Z begins at zero and C is the complex number (x+yi) being tested.  So to begin an iterative process for this formula, substitute 0 for Z to get 0² + C = C.  Take the result, C, and add it to the original value of Z to get (O + C)² + C = C₂ + C, then repeat by substituting C₂ + C for Z and on until your threshold is reached or until enough iterations have been made to determine that the selected number for C is not likely to go to infinity.  Then, the next number for C is selected and the process is repeated to produce the next point in the plot.  This sequence is repeated until all of the numbers, x + yi, in the target area of the complex plane have been tested.

In Figure 2, -2.0 X is at the left, +1.0 X is at the right, -1.5Y at the top and +1.5 Y at the bottom. The two arrows in the middle point to 0 + 0i. For our purposes, the point of the Apple Man fractal is that calculations using numbers from the black area can be iterated an infinite number of times and the result will never go to a "large" number. However, beyond the rather definite boundary of the fractal, the numbers will take the calculation to infinity with decreasingly fewer and fewer iterations.  Thus the fractal (the Apple Man) is an attractor toward which points become more stable.

An excellent, simple explanation of how the set is calculated is Introduction to the Mandelbrot Set, A guide for people with little math experience. by David Dewey. See also, (almost) the Mother of All Fractals: The Mandelbrot Set for a fascinating exploration of its features.

A plot is a picture made by repeatedly testing points in the complex number plane to see how quickly the result will go to infinity (or become very large). The plots in the examples shown here are formed by assigning a color value to the point being tested, depending on how stable it is in the calculation. A degree of order tends to emerge as the range of possible numbers, X and Y are tested and plotted.  The most popular example of this is the plot derived from what is commonly called, the Mandelbrot Set, named after the mathematician, Benoît Mandelbrot.  The Mandelbrot Set itself, is only one of a group of numbers known as the Julia Set, which was documented by Gaston Julia.  Figure 1 is a plot of the Mandelbrot Set made with the Black Saturn Mandelbrot Set Explorer.

The objective here is to introduce the concept of boundaries, fractals, and the use of simple instructions to convey complex systems of information.  All of these features are present in nonlinear equations, but mathematicians are finding that simple linear processes can also produce fractals and very complicated systems of information, as is illustrated in the Sierpinski Triangles.

The Mandelbrot Set also contains fractals, but on a much more complicated scale.  Figure 4 illustrates how the virtual world of the Mandelbrot Set can be viewed, as if with a microscope. It is possible to select a specific area of the complex plane and expand the image to see more detail.  What you see is part of the “V” shaped curving section at the top of the large cardioid shape in Figure 1.  The large black area is the stable region of numbers that can be used in the formula, Z_n+1 = Z_n² + C and that will not take the result out of range even after a very large number of calculations (200 for each point in this case).  The bands of color represents groups of complex numbers that take the calculation to infinity, faster and faster, as you move away from the black area.  In a bigger computer, this would be shown as a gradual shading, from left to right, and not as abrupt divisions as is shown here.  The fringe between the large black area and the color pattern is a range of complex numbers that approach infinity very slowly and represent the boundary between stability and chaos (infinity).  It is in this thin boundary that the wonders of the Mandelbrot Set unfolds.

Figure 4
Magnification of the area located above and between the main cardioid and the larger circle in Figure 1

Figure 5
"Magnification" of the bottom of the large circle in Figure 1

Figure 6
Far right of the cardioid in Figure 1 at even greater magnification.

As a reference, for the point where the spine intersects the left side of the picture,

X = 0.4242606570763012 and Y = 0.3412283517941925
That is a very extreme amount of magnification.

If these plots are considered contour maps with the vertical axis representing number of iterations of the equation for each point, then the large black area of stability might represent a very high plateau, and pattern of colors might represent some distance down a very long slope.  As the boundary is approached, the lines would begin to get closer and closer together.  The numbers represented here would eventually take the calculation to infinity, but only after more and more iterations.  As is illustrated in Figure 6, the contour lines continue to get closer to the black in a fashion known as "asymptotic," meaning that the distance between them approaches zero, but that it will not become zero before they reach infinity--they never actually reach zero.  Here and there in this well of infinity are other islands of stable numbers that might look like sharp, flat-topped spires reaching up from the sides of the descending curves.  They are flat toped only because of our method of representing them. In reality, they will apparently continue to infinity.