As discussed earlier, the above is equivalent to an atom fullfilling its shell 2s, equivalent to atom Be8, which is known to decay in exactly two alpha particles, each of which we explained, take the shape of a tetrahedron. We also know that the second tetrahedron is an exact mirror image of the first one about a central mirror core. Now these two shapes are similar but not the same entity and somehow need to be identified. It's like having to define an uphill from a downhill, so we will call the one with its pointed vertex upwards as the positive tetra and the other as negative tetra. Once the two counter rotating tetrahedrons are summed up in the same spherical space, one gets the geometric shape shown below.
These interactive 3D graphics were created with the help of some Mathematica code written by Robert M. Dickau available on his homepage.
The shape is called the Sierpinski tetrahedron and is the three-dimensional version of the famous Sierpinski gasket. You can rotate this graphic in 3D using your mouse. If you study the shape you will find the the inner shape enclosed between the positive and negative tetrahedrons is in fact a perfect octahedron. This hidden octahedron plays an important role in nature as we shall see later on. For the sake of clarity, the three vertices of the negative tetrahedron are not shown in the 3D diagrams. This fractal is of immense importance as it is probably the key not only to generation of particles but to nature's secret mechanism of growth itself. With the help of this graphic, one can easily understand how nature works out the way from a single entity, in this case the parent tetrahedron (positive), into an opposite parent tetrahedron (negative), and adding them onto the same space coordinates to get three similar structures, each of which have the same 'reproducing' mechanism of their parent structure. Remember that the tetrahedron represents the most basic spherical solution existing in 3D and is thus the best candidate for natures mechanism. Now the wavelength of the EM standing wave generating the structure is equal to twice the distance between vertices, oscillating at a frequency F. What would happen if the structure is twice as energetic? Each positive tetrahedron will replicate itself into its image negative tetrahedron, and four tetrahedrons each oscillating at 2F will take place each parent tetrahedron. Such a mechanism might easily explain the fact that there are peaks and dips of energy per nucleon repeating every fourth nucleon.
|Doubling the standing wave EM frequency 'mates' each tetrahedron to its opposite polarity tetrahedron and replaces the original with four similar tetrahedrons. The original structure of four tetras is now replaced with sixteen similar tetrahedrons. Doubling the frequency further, gives a structure of 64 positive tetrahedrons as shown on the right. The process of fractal generation does not go for infinity but is restricted by planck's length which defines the shortest wavelength for the distance between vertices of the smallest hidden octahedron. Nature does not in fact set a higher limit for wavelength and that's why we can generate dc (zero frequency currents) in the first place. It is now clear that any possible energy combination within this structure will be a multiple of planck's wavelength represented by the smallest tetrahedron in the fractal structure.|