The Fractal Planes

"When I look at thy heavens, the work of thy fingers, the moon and the stars which thou hast established; what is man that thou art mindful of him, mortal man that thou dost care for him? Yet thou hast made him little less than divine, and dost crown him with glory and majesty." Psalm 8:3-5

The image above illustrates the manner in which the edges of the infinitely reproduced "fractal tree" would be expressed if the 45 intersecting planes of the fractal were to be truncated at one dodecahedron face. As you can see from the complexity of this example of a single face that the complete illustration of all 45 planes involving all twelve dodecahedron faces and three dimensions would not provide a clearer avenue of understanding. By counting features of the diagram we can directly deduce the exact nature of the whole configuration of intersecting planes.

Receptive Planes

The violet segments in the above diagram are indicative of the edges of ten planes from the total of 15 planes that would be seen if the entire form of the dodecahedron were shown. These 15 planes are established by the 30 outer *pentagon* edges of the dodecahedron. Pairs of edges are established in polar opposite positions on the dodecahedron; each pair residing in and establishing a single plane.

Dodecahedron and also Icosahedron and octahedron edges lie completely within these 15 intersecting planes. This means that these planes contain the Sephirot symbols for: Keter, Chesed, Tipareth, Hod, Yesod, Malkut. Without detailed explanation we should simply think of these as the Receptive Planes. The intersections of these 15 planes with each other form 31 lines that all pass through the center of the fractal tree. These lines are themselves the symbol for Ein-Sof, the lines are purely symbolic and do not constitute an "image" of Ein-Sof; the infinite *no-thing*. With the six geometric *symbols* of Sephirot and the *symbol* of Ein-Sof, the Receptive Planes evoke *seven* divine attributes. There is with the geometry a bit of counting coincidence that is akin to *music*, if you will allow that understanding. The 31 Ein-Sof lines can be seen as two sets.

One of the lines is denoted by the central point of the diagram; where five violet edges intersect. This line is directed directly perpendicular to the page, so it is seen as only a single point and can be thought to symbolize the Hebrew letter Aleph which is sometimes a silent letter having a number value of one. The remaining 30 lines when seen in shadow form ten intersecting lines or twenty rays emanating from that center. To these 30 lines which are the basis of the shadow composed of rays emanating from the central line we assign the letter Lamed, and together with Aleph these letters express The Name which means Divine Being.

It is also of some interest to note the Hopi Indian prophesy that the world was originally formed from 15 hoops. If these fifteen planes were truncated by a spherical surface centered with the fractal, the edges of the planes would be 15 intersecting circles(hoops) expressing the pattern of the violet lines of the diagram repeated 12 times covering the sphere's surface.

Expressive Planes

The remaining 30 planes are formed by the infinite reproduction of Cubes and Tetrahedrons within the fractal tree, and edges of fifteen of those are illustrated by the blue lines of the diagram above. There are four Sephirot *symbols* reproduced within these planes: Hokmah, Binah, Geburah, Netzach. Also the symbol for the non-Sephirah Daat is also infinitely reproduced within the 30 Expressive Planes. In the modern sense these planes are what we limit our scientific studies to. Modern science is largely the application of our understanding to our strength. Strength produces motion and science most generally defines everything as originating in motion (Cause/Effect: F=MA etc..).

So the Expressive Planes are the planes of mind and muscle, even to 'speak' involves the use of muscle, in other words. When these 30 planes are considered within the fractal we see that the additional planar intersections that they introduce are 300, which correspond to 300 lines passing through the center of the fractal tree. Three-hundred is the number value of the Hebrew letter Shin which is held as a symbol of Fire. Fire then would be a signifier of energy or the agent of expression and the mother of the form of the muscles themselves.

A Few Summary Remarks

My hope for readers of this small article on the planes of the fractal tree, would be to get that precious glimpse of understanding that has the effect of transcending western duality. Kabbalah offers duality not as polar irreconcilable opposites, but instead as beautiful compliments of a unified whole. Kabbalah is primarily *reception* for the purpose of the wholesome *expression*.

September 3, 1998

Copyright (c) 1998 J. Vincent Beall