Introduction of the Rainbow Equation

The Rainbow Equation is a description of how the base universal building blocks of linear/circular, zero/1st/2nd/3rd/4th dimensions and time/space flow together as one. Contained within its descriptions are mathematical equations that show through our multi-expressive universe all is connected. To a casual observer it might appear a sphere, tetrahedron and cube are different. Essentially, these forms are different yet there are underlying connections that allow them all to flow from the same source and intertwine with each other. On an atomic level it is clear form arises out of similar conditions at the smallest levels. As the creative process continues to manifest from this smallest level it is interacted upon by the universal matrix. The universal matrix is a blending of base geometrical shapes and energies. The Rainbow Equation uses the visible light spectrum to guide to the observer through a process where the apparent differences of a circle, triangle and square can flow in consciousness as a single unbroken expression.
In the Rainbow Equation there is a flow of the base building blocks of the universe. The building blocks of linear, circular and dimensional expansion are shown to work together as one through utilizing the rainbow – the visible color spectrum. Upon the shell of what is called in the Rainbow Equation the “4th Frequency Clear Cube” are these base relationships. There are three axes of base relationships that are used to illustrate this interconnectedness. They are: plane axis, 3D/plane axis, 3d axis. The Rainbow Equation is unique among equations as it blends Sacred Geometry, as expressed in planes and 3D, and allows the visible color spectrum to be “painted” upon its sectors. In the Rainbow Equation the congruency of the color spectrum is maintained all the time when base principles are adhered to – flow, dimensionality and time/space. The net result of this is an equation that flows from the simple counting of the sectors produced from the division of white light as it flows across the varied planes and 3D models of the Rainbow Equation. This allows the observer to see connections and interlinking ratios that mathematically flow throughout the entire set. In this chapter we will discuss the abbreviations that are used the express in a logical way the process of synergy throughout the Rainbow Equation.

 In the Rainbow Equation the congruency of the color spectrum is maintained all the time when base principles are adhered to – flow, dimensionality and time/space.

The Rainbow Equation is aligned with the six directions of space in a particular manner. Precisely in the center of the 4F Clear Cube is the 3F Rainbow Cube. It is the alignment of left/right, front/back and top/bottom to this which determines the three axial arrangements of the planes and 3D models. Along the orange left/right axis (a.=plane axis) is the left/west facing Space Symmetry Six and facing right/east is the Logos Circle Seven. Along the indigo front/back axis (b.=plane/3D axis) is the front/south facing Time Symmetry Co-incidence and facing back/north is the Third Eye Open. The third axis in the polarity arrangement of the 3F Rainbow Cube is the green top/bottom axis (c.=3D axis) of the top/heaven facing 3F Rainbow Sphere and the down/earth facing 3F Rainbow Tetrahedron.

Aspects of the Rainbow Equation

a.=plane axis=(space symmetry six)+(logos circle seven)
b.=3d, plane axis=(3rd eye open)+(time symmetry co-incident)
c.=3d axis=(3f. rainbow sphere )+(3f. rainbow tetrahedron)
r.a.=rainbow aspects=(r.l.+r.s.), (r.a.,a. + r.a.,b.)=(r.a.,c.)

The counting and thereby the mathematics of the Rainbow Equation is done by accounting for all the rainbow, white and clear sectors and lines. Each and every part inside, out and in between and even the sectors that face the inside of hallows connect to give complete mathematical statements. The polarities of the three rainbow structural arrangements are utilized – secondary, primary and neutral. This allows for the total continuity of the rainbow throughout the Rainbow Equation. When the observer views along the plane axis (a.) it is a total of all the aspects including sectors, lines, polarities, etc. that are accounted for in the equational statement: a.=plane axis=(space symmetry six)+(logos circle seven). The same is true for the totals for axial arrangements of b. and c. The total of these using the variations as listed is called “Rainbow Aspects”, abbreviated “r.a.” Looking at the total rainbow aspects of the three axial arrangements of the Rainbow Equation the observer arrives at this mathematical statement: r.a.=rainbow aspects=(r.l.+r.s.), (r.a.,a. + r.a.,b.)=(r.a.,c.). This is to say that the total rainbow lines (r.l.) plus total rainbow sectors (r.s) of the axes of a. plus b. equals the same exact number of rainbow lines and rainbow sectors of c. axis. In other words, mathematically the total rainbow lines and sectors of Space Symmetry Six + Logos Circle Seven + Third Eye Open + Time Symmetry Co-incidence = the total rainbow sectors of 3F Rainbow Sphere + 3F Rainbow Tetrahedron. This is but one of many examples of a perfect flow and interconnection between what might appear to be opposites. Over the next several paragraphs we will look at these components in more detail. Through following the path of the rainbow the many are merging into the one.

s.=secondary polarity rainbow
p.=primary polarity rainbow
n.=neutral polarity rainbow

 Showing the axial relationship to the colors next to neighboring colors connects the polarity of each color and how the colors “merge” together geometrically and equationally.

The Rainbow Equation looks at the expansion of base geometry and moves it to higher levels of connectivity to allow for an explanation of universal process. The universal creative process is not a static condition and neither is light's spectrum upon Sacred Geometry. Certain conditions must be met in order for a clearer understanding to be realized, for instance, colors flow in a certain frequency and order to each other – flowing red through violet in the visible spectrum. In the Rainbow Equation certain criteria is established to “view” the translucent rainbow we see in the sky as an operational principle that can be drawn or painted upon paper and in equational format. In a translucent rainbow the colors flow into each other. In an equational rainbow the flow of the colors must be accounted for by showing the polarities from which they flow. A translucent or “Natural” rainbow flows red-orange-yellow-green-blue-indigo-violet. The equational rainbow accounts for more sectors of colors to show the polarities. In what is termed: “Secondary Polarity Rainbow” the 9 color sectors are red-orange-yellow-yellow-green-blue-blue-indigo-violet. In the Secondary Polarity Rainbow the color polarities are illustrated or “painted” down to account for an extra yellow moving into orange and green on either side of it and an extra blue sector moving into green and indigo simultaneously. To show additional polarities in the equational rainbow there is also what is termed: “Primary Polarity Rainbow.” This nine sector polarity arrangement allows for the orange, green and indigo to serve double duty as they flow into the colors on either side of them: ½ red-orange-orange-yellow-green-green-blue-indigo-indigo-½ violet. The red and violet colors represent a ½ sector for a total of one sector when combined. In the “Neutral Polarity Rainbow” all the colors of the visible spectrum are doubled except for the end colors of red and violet which occupy one sector each. In the neutral polarity arrangement of the equational rainbow all the polarities of the combined colors are accounted, making for a total of 12 sectors: red-orange-orange-yellow-yellow-green-green-blue-blue-indigo-indigo-violet.

Allowing for the three polarities of the equational rainbow to express themselves in the manner of doubling color sectors moves the translucent rainbow to a rainbow that can be expressed mathematically. Showing the axial relationship to the colors next to neighboring colors connects the polarity of each color and how the colors “merge” together geometrically and equationally.

Using the abbreviations for the total of the secondary and primary rainbow polarities of the Rainbow Equation looks like this:

(1s.=9)+(1p.=9)=18. The total of sectors for the Neutral Polarity Rainbow is (1n.=12).

r.s.=rainbow sectors
ws.=white sectors
c.s.=clear sectors
h.s.=hollow sectors
i.s.=in-between sectors
i.s.i=in-between in sectors

 It is the 7 colors and their polarity combinations flowing in harmony with nature's translucent rainbow that has brought about the name “Rainbow” Equation.

In the Rainbow Equation there are two-dimensional diagrams and three-dimensional models. The 3 two-dimensional diagrams are the ones that appear on and as a plane surface. They are Logos-Circle-7, Space Symmetry Six and Time Symmetry Co-Incident. The 6 three-dimensional models are: 3F Rainbow Sphere, 3F Rainbow Tetrahedron, 3F Rainbow Cube, 4F 3D Rainbow Triangle, White Symmetry Vector Equilibrium, 4F Clear Cube. The 2D diagrams and 3D models contain various combinations of rainbow, white, clear, hallow sectors and in-between sectors. In order to describe the layout of the various components of the Rainbow Equation it is necessary to distinguish these various sectors as they appear on each subset.

Rainbow sectors are characterized by sectors of the Rainbow Equation that are in the visible color spectrum – red-orange-yellow-green-blue-indigo-violet. Generally speaking, it is these 7 colors and their polarity combinations flowing in harmony with nature's translucent rainbow that has brought about the name “Rainbow” Equation. These seven colors flow throughout the set remaining congruent with the flow of neighboring colors as a complete seven color series and/or as a subset, such as orange-green-indigo. Each individual color sector accounts for one unit or rainbow sector (r.s).

 White sectors show vortices or direction of axial rotation.

White sectors are sectors that appear white in colorization. White is a combination of all the colors in the primary visible spectrum. White represents the white light before it has been refracted into a spectrum of color. White sectors show vortices or direction of axial rotation on the 3F Rainbow Sphere and 3F Rainbow Tetrahedron. Both of these models contain two neutral rainbows on their shell for a total of 24 rainbow color sectors each. The white sectors on the top and bottom of the sphere and the four vertices or tips of the tetrahedron allow for the total expression of third frequency, that is third stacking, and alignment with the total of the rainbow structure. In the White Symmetry Vector Equilibrium, which is entirely white inside and out, the white sectors represent white light and energy before it is refracted into the rainbow spectrum. In the Rainbow Equation each single white sector =w.s.=1.

 A clear sector represents space having no color or manifestation.

Clear sectors of the Rainbow Equation appear in areas of the 2D diagrams Time Symmetry Co-incidence and Space Symmetry Six. A clear sector is found in these because of the lines within their structure. Lines act as indicators of direction of intentionality and/or connection with center to outer expressions. Geometrically, lines have only one dimension and the space they do not occupy is clear. A clear sector represents space having no color or manifestation. Clear sectors are enclosed by other rainbow sectors or the parameter of the diagram in which they appear. In the 4F Clear Cube all the sectors are clear representing space's matrix before it manifests as white light or the visible color spectrum. In the Rainbow Equation each single clear sector =c.s.=1.

Hollow sectors of the Rainbow Equation are found in all the 3D models: sphere, tetrahedron, cube, vector equilibrium and 3D triangle. Hollow sectors are those sectors that face toward the inside of hollow space. In the construction of various components of Sacred Geometry there are hollow spaces created. In the inside of a single hollow cube, for instance, there is a hollow space. A hollow cube consist of six planes arranged left/right, front/back and top/bottom to totally enclose space from six directions. The inside facing portion of these six planes are rainbow colored hollow sectors. White sectors on the other side of other white plane sectors are white. In the physical arrangement of third or fourth frequency stacking of 3D models there are many hollows which stack together to make a single model, for instance, the 3F Rainbow Cube is a closest stacking of 27 smaller hollow cubes. Both sides, inside and out, of each smaller cube are accounted for in the formulation of rainbow equations. A single smaller cube has six outside sectors and six inside sectors. The sectors on the outside or shell of any of the 3D models are “painted” with the color arrangement found in the secondary polarity rainbow. The sectors on the inside facing the hollow space are in the arrangement of the primary polarity rainbow. In other words, colors on a single sector reflect or form complementary to the color on its opposing plane side. A secondary outward facing sector is complemented by a primary inward facing color. In the Rainbow Equation each single hollow sector =h.s.=1.
 Secondary Polarity Rainbow Primary Polarity Rainbow (Complementaries to Secondary) RED GREEN ORANGE YELLOW YELLOW ORANGE GREEN RED-VIOLET BLUE INDIGO INDIGO BLUE VIOLET GREEN

(table 8.1) Secondary/Primary Polarity Rainbow Complementaries

This table represents complementaries between inside and outside facing color sectors. In-between sectors are sectors that are physically touching another sector. These sectors are found in the 3D models of the Rainbow Equation. Since the 3D models are examples of rainbow flows and polarities they are more than cubes, spheres, etc. They are representative of 3rd and 4th frequencies. Each larger 3D model contains many smaller pieces within its overall composition. Each sector upon each single smaller piece is a rainbow or white color. Many of the pieces have their sectors on the inside of the larger form when they are stacked against another piece. The places where they touch is not visible without separating the smaller pieces. These sectors are called: in-between sectors (i.s.) Sectors that are in-between sectors and are in the inside of hollows facing space of the subset of the model they are in are called: in-betweens facing in (i.s.i.).

sh.=shell=(sh.i.+sh.o.)
sh.i.=those shell sectors facing in
sh.o.=those shell sectors facing out

 Inward facing sectors are facing space or hollows and therefore are painted with the complementary primary polarity rainbow color based upon the secondary colors reflecting them.

Sectors on the outside plane or shell (sh.) of 3D models have a specific designation as well. The shell outside (sh.o.) is the very outside sectors of the 3D models. The shell inside (sh.i.) is the sector immediately on the opposing plane side of the shell outside and faces hollow space. The shell of a 3D geometric model is considered the part that is on the outside of a 3D object and is visible. In the Rainbow Equation all the 3D models have shells yet, unlike a standard cube, sphere, tetrahedron, etc., the models show polarity arrangements to frequencies. The shells are therefore divided into frequencies, which is a number of sections, to show the flow the visible color spectrum upon them. All of the shells contain sectors that are visible on the outside and are “painted” with secondary polarity rainbow colors. On the immediate other side of these outside plane sectors are shell sectors facing inwardly. These inward facing sectors are facing space or hollows and therefore are painted with the complementary primary polarity rainbow color based upon the secondary colors reflecting them. Shell sectors, either color or white, are considered a combination of both sides of the sector they are painting upon, inside and out. A white shell sector will always be white on both sides of the plane it appears on. A clear shell, such as with the 4F Clear Cube, is also entirely clear. The plane diagrams; Logos Circle Seven, Space Symmetry Six, Time Symmetry Co-incidence, also follow the rules for alignment with secondary and primary polarity arrangement. The three diagrams appear on the outside walls of the 4F Clear Cube. The plane of the diagrams that face outwardly, away from the 3F Rainbow Cube in the center, are painted with the polarity colors of the secondary rainbow. The side of the three diagrams that face inwardly toward the 3F Rainbow Cube are painted sector per sector with the complementary colors of the primary polarity rainbow.

Following specific Rainbow Equation abbreviations, sector colors flowing in the direction of the central smaller cube to the shell of the 3F Rainbow Cube flow along this pattern: i.s.i.>i.s.>i.s.>i.s.i.>i.s.i.>i.s.>i.s.>i.s.i.>sh.i.>sh.o.

Looking at this same polarity relationship moving from the same small inner central cube to the shell of the orange axis of the 3F Rainbow Cube the flow would look like this:

(table 8.2) 3rd Frequency Rainbow Cube Color Flow

Primary polarity rainbow colors are in the hollow sectors of the smaller cubes showing a complementary reflection to the in-between sectors just on the other side of their square planes. The orange axis of the outer shell of the large cube is a secondary polarity color of orange and is complemented by the primary polarity color of yellow just on the other side of the outer shell's square plane.

f.=frequency,
n.f.c.=not facing 3f cube,
f.c.=facing 3f. cube
Frequency as it is used in the Rainbow Equation primarily deals with the “stacking” together of similar shaped pieces. In the 3F Rainbow Cube it means 27 smaller cubes have been stacked together in the closest packing of cubes three cubes high, wide and deep, which is 3 to the 3rd power of cubes. The usage of 3f or 4f in the equations of the rainbow refers to the frequency to the third or fourth level for that particular 3D model.

 Frequency as it is used in the Rainbow Equation primarily deals with the “stacking” together of similar shaped pieces.

When calculating the number of lines or sectors of the three plane diagrams of the Rainbow Equation the mathematics consider both sides of the plane, both the side facing the 3F Rainbow Cube and the side facing outwardly. The abbreviation for not facing the 3F Rainbow Cube is n.f.c. This is the side that is visible from the outside of the shell of the 4F Clear Cube without looking through the glass to the opposing side of the planes. The sides of 3D models or planes that face inwardly is abbreviated: f.c., meaning they face inside toward 3D Rainbow Cube.

tri.s.c.=orange, green, indigo of secondary combination
quad.s.c.=red, yellow, blue, violet of secondary combination
tri.p.c.=orange, green, indigo of primary combination
quad.p.c.=red, yellow, blue, violet of primary combination
r.l.=rainbow lines
s.l.=straight lines
c.l.=curved lines
In the Rainbow Equation there are a few different ways to view the polarities of the rainbow upon the diagrams and 3D models. A visible color spectrum consist of seven colors. These seven colors can be viewed as tri- colors; orange-green-indigo, and merge with the quad-colors; red-yellow-blue-violet. There are many examples throughout the equational set the tri-colors flow within sectors or lines of a diagram or 3D model and merge correlating with the quad-colors. Allowing for specific tri and quad-color equations gives more data to show the natural flow of rainbow polarity combinations. When the colors are on the outside of a shell, in-between sectors or on a plane surface facing away from the 3F Rainbow Cube they are considered tri. or quad. secondary polarity rainbow colors (tri.s.c.) or (quad.s.c.). The color sectors or lines that appear on plane diagrams facing the 3F Rainbow Cube and the ones that face the space side of hollow subsections of larger 3D models are complementaries of the secondary polarity rainbow colors and are considered of the tri. or quad. primary polarity rainbow combination (tri.p.c.) or (quad.p.c.).

 Lines are a first dimensional representation that connect showing flow or movement from a zero point and its first presence or manifestation within the field of space.

In a few instances lines are used in place of sectors when it is necessary to show the flow of intent along a color axis. Rainbow lines (r.l.) are lines of visible spectrum color within the Rainbow Equation to show connection and movement through space. Lines are a first dimensional representation that connect showing flow or movement from a zero point and its first presence or manifestation within the field of space. Tri-color lines from the secondary combination, (tri.s.c. lines) of the Space Symmetry Six and Time Symmetry Co-incidence illustrate this movement from zero point, through clear space as first dimensional projections merging into second dimensional planes of the quad. secondary combination. Painted upon the outermost circle of the Time Symmetry Co-incidence within the six clear sectors are six slightly curved tri-color lines (c.l.) These curved lines show a connection between the lines in the center, within the clear space field, and lines in the outer circle clear space field. Between the two sets of lines the planes of manifestation occur represented on the quad.s.c. sectors. The primary combination is on the reverse side of all three Rainbow Equation diagrams facing the 3F Rainbow Cube. The secondary and primary polarities are exact complementaries of the color sectors and lines showing movement of energy along the color spectrum from space to the manifest world.