The Fractal Geometry of "The Matrix"

"Fractal geometry will make you see everything differently. There is danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies,leaves, feathers, rocks, mountains, torrents of water, carpets, bricks, and much else besides. Never again will your interpertation of these things be quite the same."
Michael F. Barnsley

Barnsley's quote, prefacing one of his own pioneering works, applies to the following as well and even more so than he points out. In the matrix as represented by the Ifa system, human behavior itself in all its ramifications is included in addition to the manifold physical manifestations we can witness in nature.

Nothing, absolutely nothing can come to existence in this Universe without embedded in the Matrix and thus following the rules as they are visible in Fractal Geometry.

To start with, the ancient wisdom 'as above, so below' reflects the phenomenon of 'self-similarity': inner structures are similar to the structure they are contained in. In recent decades an entire branch of mathematics appeared that is dealing with this and related topics under the heading of 'Chaos Theory'. In simple cases, self-similar structures are quite obvious. See the Sierpinsky gasket as an example,

in which a triangle is mirrored repeatedly into itself.Such "copy-itself" approaches are based on rigid algorithms and are needed for a variety of explorations of 'The Matrix'.

Surprisingly, the same pattern can be achieved by an another approach of creating structures which is called Iterated Function Systems (IFS). The structures created with IFS are much, much closer to manifestations occuring in nature and therefore closer to the manifestations of the 'Matrix' as such.

To get an impression how an Iterated Function System works, imagine tiny magnetized particles being thrown into a space that contains an electromagnetic field. The random particles will align with the electro-magnetic field structure and the structure of the
field itself will thus become visible.

(Note, that while an electromagnetic field is invisible, it is still measurable with instruments and therefore very much part of the Universe and not transcending it. This experiment is just for creating the picture being used below.)

An Iterated Function System is modeling above random throws of particles into space by creating numbers through a random number generator and then feeding these numbers into a set of mathematical functions. The result is the spatial position at which the new particle will be located.

With every new particle thrown into this virtual space, the picture will become more distinct. Various basic structures can be generated in this way, solely depending upon the initial coefficients of the function systems. The most famous of these is the 'Barnsley fern' but many other basic structures that can be found in nature
can be generated this way.



The initial configuration that describes the 3-dimensional structure actually created, is
called an 'Attractor' and often a 'Strange Attractor'. In Ifa, the system we will be using to describe the workings of the 'Matrix', the (strange) attractor is just the result of the configuration of the initial coefficients and, as the 'thing as such', doesn't even carry a specific name. However, the *initial coefficient array* that prescribes the resulting manifestation has a name and this makes much more sense. The (Yoruba) name of this pattern is 'odu'.

What is significant in both mathematical approach and in the Ifa view is that the way the spatial location is being determined is inherently 'outside the system', hence *transcending* the system as a whole.This observation parallels the view of the Ifa system as the 'odu' principally transcending the entire Universe. If one is combining now the (strange) attractor with the general self-similar propagation functions of fractals, we can find a way of explaining countless properties within the 'Matrix' that are otherwise difficult to explain. In Ifa, the initial coefficients of the (odu) of the
principal 'attractors' in the Universe fractalize from 4 into 16 and then into 256 new odu, each of them capable to spawn new subhierarchies. While self-similar propagations and 'detailing' alike in general do not generate NEW formations but
a combination of basic strange attractors or 'odu' certainly will.

The properties of the newly created manifestations are not predictable and were in Ifa determined through diligent observation and verification over large spans of time. In short, what the pioneers of Fractal Geometry achieved was finding IFS coefficients that are creating interesting objects.

Ifa is determining the prime coefficients for *everything* that exists or that could possibly exist, effectively reverse-engineering the Creation as such, and abstracting the myriad of forms in the manifestations in the Universe to its basic minimum, the prime patterns, or primordial odu.

More complex structures are the result of 'mixing' odus, resulting in new attractors. Our current mathematical tool of algebra is not suited to deal with the mutations of strange attractors.Algebra uses the concept of zero (0), a concept that cannot manifest in the Universe. Zero implies infinity and both exceed the Universe. (Note: we will make use of this 'feature' in the next chapters to engineer an entire serie of valuable processes.)

In contrast, the *geometrical* manipulation of Ifa coefficients allow several basic but important predictions. At first glance, Ifa uses only two states to describe one coefficient. These states are often described as 0 and 1. With the above in mind, it is better to write these two states as 1 and 2 and this is the way it is traditionally written or marked (one or two lines) both in Ifa (vertically piled) and in the I-Ching (horizontolly stacked).

On the surface, 256 prime patterns don't seem enough to describe a primal pattern. However, these 256 are better called 'classes' of pattern rather than patterns. A closer examination reveals that every odu has two vectors and therefore a total of more than 16 Million possibilites. If one attaches yet another odu to the vector(s), one can 'zoom in' to any depth one likes. The fractal structure as such explains why ANY process
that addresses one tiny part of the Universe can THEORETICALLY be used to transcend the Universe altogether.

However, as pointed out in the 'Purple Notebook On How To Escape From This Universe' repeatedly, other effects WILL kick in when such a lop-sided attempt is being made. The Matrix as a whole must be addressed and that is what we are after in the following chapters.We will look at the basic elements of the 256 prime patterns (Odu Ifa) that are spawned by a 16x16 matrix. After inspecting and understanding the phenomenon of 'Polarity' in the next chapter, we will then be able to collapse the 16 prime-prime patterns into 8 pairs.

After careful investigation one can speculate that these 8 pairs have a historical precedent, namely the 'Noble Eightfold Path' of Gotamo Siddharto, now called the 'Buddha'.Special care will be given to detect the initial 4-fold matrix, since they are the key to successfully blow holes into the matrix as a holistic entity.

In these chapters, the comparison of the Ifa system with some aspects of modern mathematics is meant only and only as a means to provide some definitions that are more easily understandable and to outline some properties of the matrix which would otherwise be difficult to accept.

The main downfall of attempts to use Ifa as a way to describe 'The Matrix' has been to assign labels to its elements without keeping in mind that the 'odu' itself is a primal pattern that is *transcending* the Universe. An 'odu' doesn't manifest in one single, simple way. It serves as a 'template' for creation and it can spawn manifestations that may appear unrelated or even contradictory.

All of above is also true for the interrelations in between the primordial odu, relations that are expressed through 'triads'. It is likewise true for the set of primordial 'identities' and their primordial 'scripts', all concepts that will be discussed in the next chapter(s).'Traditional Ifa', in itself and as the underlying pinnacle of a multitude of religions and cults, is basically inaccessible to the uninitiated.

Consequentially, the vast majority of information on Ifa on the Internet is either
plain wrong or so much out of its original context that any attempt to understand its deeper meaning is utterly futile.

The paradigm of Ifa is still extremely useful, even in a distilled, crude, and abbreviated form, and we will use it here for this and no other reason.

Again, the sole goal of this presentation is to bring about an understanding of a systematic systemic approach to a comprehensive liberation of the Being itself. Most 'roads to freedom' advertised around the world, past and present, end up with a rude awakening. Many people fool themselves by entering 'exalted' states of the mind, thinking: "I'm one with everything", "I'm the only one", "I'm one with the nothingness.", "I'm eternal bliss", and the like.

From a larger perspective, these states are but states of the matrix in which one can get lost in no time. Upon 'return', the rest of the matrix is still there, untouched or even more solidly in place than ever before.

To point to a road out of this dilemma is the purpose of these notes.

Copyleft © 2002  by Maximilian J. Sandor, Ph.D.

A few links to Fractal Geometry and Self-Organizing Systems:


Dynamics of Attractors:

Self-Organizing Systems (SOS)

Mathematics of Ifa: