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"fractal geometry can take us into
the far reaches of high tech science, its patterns are surprisingly common in traditional African designs, and
some of its basic concepts are fundamental to African knowledge systems." 
...although fractal designs do occur outside of Africa (Celtic knots, Ukrainian eggs,
and Maori raftors have some excellent examples), they are not everywhere. Their strong prevalence in Africa (and in Africaninfluenced
southern India) is quite specific.  Page 7 of African Fractals Modern Computing and Indigenous Design
(1999) by Ron Eglash. African
impact on India is found in artefacts, ancient texts, genetic footprints, physical resemblance amongst populations,
cultural and linguistic similarities, gastronomic affinities, and a common world view. It is generally
agreed today by scientists and historians that an early migration of African population first settled the coastal areas of south India, then spread gradually
inland ...
 OAHSPE GOD'S BOOK OF BEN CHAPTER VII: 3. I am the living mathematics;  Rensselaer Professor Ron Eglash. Eglash, a professor in our Department of Science and Technology Studies, has made fractals a keystone in his efforts to show minority students the cultural relevance of the STEM
(science, technology, engineering and mathematics) fields. "African fractals are not just the result
of spontaneous intuition; in some cases they are created under rulebound techiniques equivalent to western mathematics."  pages 6869 of African
Fractals by Ron Eglash.  Mandelbrot coined the
term "fractals" for this new geometry, and it is now used in every scientific discipline from astrophysics to zoology.  Page 15 of African Fractals
by Ron Eglash.  Fractals are characterized
by the repetition of similar patterns at everdiminishing scales. Fractal geometry has emerged as one of the most exciting
frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced
by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists
have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and
America, we often see cities laid out in a grid pattern of straight streets and rightangle corners. In contrast, traditional
African settlements tend to use fractal structurescircles of circles of circular dwellings, rectangular walls enclosing eversmaller
rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous
fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge
systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African
architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft,
quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of
African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology,
and computer simulations.  From the book African Fractals by Ron Eglash.  The
fractal settlement patterns of Africa stand in sharp contrast
to the Cartesian grids of EuroAmerican settlements.  Page 39 of African Fractals.  Comparing the
Mayan snake pattern with an African weaving based on the cobra skin pattern (fig. 3.3b), we see how geometric modeling
of similar natural phenomena in these two cultures results in very different representations. The Native American example emphasizes the Euclidean symmetry within one size frame
('size frame" because the term "scale" is confusing in the context of snake skin). This Mayan pattern is composed of four shapes of the same size, a four fold symmetry.
But the African example emphasizes fractal symmetry,
which is not about right/left or up/down, but rather similarity between size frames. The African snake pattern shows
diamonds within diamonds within diamonds.  Page
43 of African Fractals.  ...but with the impressive exception of the Pacific Northwest carvings, fractals are almost entirely absent from Native American designs.  Page
45 of African Fractals. Moses was involved in the freedom of his people. In Kosmon
all people need freedom: "Free Your Mind and Your
Ass Will Follow"  1970 by George Clinton. What does "free your mind and your ass will follow"
mean? "It means change your state of thought and
your actions will change as well"  Mar 22, 2017 by GrailGuardian Space Age Hustle. 


He was a brilliant scholar, a man of profound wisdom, an adept at occultism, and a bound devotee of the false Osiris...he must build
a temple to Osiris, ...But first Thothma was required
to drive the
Faithists out of the land, and to make slaves of those who remained. Their numbers now amounted to three millions in the land of Egypt.
Thothma therefore levied a powerful army, driving out the Listians or Shepherd Kings with great slaughter, and enslaving the children of Abraham, the Israelites... Above: faces of original Hebrew Israelites tribe Above: Ancient Hebrew Israelites in Egyptian Captivity (slavery). they were oppressed by cruel laws and penalties,
and were forced to reveal the mathematical science
which had been preserved with them from their distant ancestors the I'hins, to whom it was committed by the angels in the first ages of mankind. Humanity was now ripe for this development, but the surrender of their secrets was a further blow to the Israelites. Both the knowledge and the slave labour of the Israelites
were now thus impressed into the construction of the temple of Osiris, the Great Pyramid. And the etherean dawn
in which Moses
would bring them deliverance was still five hundred years away. [2053  500
= 1553 B.C.E.].  Pages 189190 of Darkness, Dawn And Destiny (Drawn from Oahspe)
1965 by Augustine Cahill.  Oahspe Book of Wars Against Jehovih Chapter XLIX: 2.
...Thothma, made the following laws, to wit: 4. ...And of thy arts, of measuring and working numbers, thou shalt not keep them secret longer, or thy blood be upon thee. "measuring and working numbers" = mathematics. Definition of mathematics for Students. : the science that studies and explains numbers, quantities, measurements ... Algebra, arithmetic, calculus,
geometry, and trigonometry are branches of mathematics. https://www.merriamwebster.com/dictionary/mathematics  Mathematics and art are related in a variety of ways.
Mathematics has itself been described as an art
motivated by beauty. Mathematics can be discerned in arts such
as music, dance, painting, architecture, sculpture,
and textiles. https://en.wikipedia.org/wiki/Mathematics_and_art  Thothma did not
have the mathematical knowledge of the Israelites until he forced the Israelites
to REVEAL it to him. This mathematical knowledge was lost
to the Egyptian slave masters after the death of Thothma. The true
Israelites kept this sacred mathematical knowledge up to modern times. Above: OriginalIsraelitesAbraham75% and 75% facial matchAbove:
OriginalIsraelitesMoses92% and 81% facial match  Concerning the Great Pyramid
of Khufu, the theory proposed in my essay turns out to make 22/28 a very logical choice as the inverseslope for the slantangle of the faces. Now I will discuss the
pyramid exercises from the Rhind Papyrus. This papyrus as well as the other extant mathematical papyri were written
hundreds of years after the 4th dynasty. One can ask how accurately they represent the mathematical knowledge of the architect who built the Great Pyramid.
It is obvious that the architects undertaking the building of a pyramid would need a good mathematical knowledge of
the geometry associated with such a structure, and one can indeed find this in these later papyri.
Two of the five pyramid exercises from the Rhind papyrus
can be found here. As these exercises
show, the seked is represented as a certain number of palms and fingers. This is really the horizontal change in the distance for each change of one cubit in the vertical distance. The exercises make it clear that
one cubit is equal to 7 palms and
that one palm is equal to 4 fingers. Therefore, one cubit is equal to 28 fingers. (Not so different from the English measurement system in which one yard is 3 feet and one foot is 12 inches.) Thus, for example,
a seked of five palms, two fingers
would correspond to an inverseslope of (22 fingers)/(28 fingers), or 22/28. As I mentioned above, the Great Pyramid indeed has this seked, and with a high degree of accuracy.
...the famous relationship between &pi and the Great Pyramid of Khufu ...has its roots in two facts  one purely mathematical and the other historical, but
both involving the
number 7: 1. The rational number 22/7 happens to be an excellent approximation to the number
pi. 2. The
Egyptian measurement system involves dividing one unit of measurement(the cubit) into 7 equal units (palms)
Concerning the first fact, it is actually somewhat remarkable that an irrational number such as &pi can be approximated so well by a rational number with a small denominator. (The denominator
is 7 in this case.). There is also a frequently mentioned relationship
between the Great Pyramid and the number φ, ..The legend that the architect who designed the Great Pyramid of Khufu intentionally incorporated the Golden Mean (which is this number φ) into the proportions of that structure
...https://sites.math.washington.edu/~greenber/PiPyr.html  ...there is a specific proportional ratio that is found throughout nature. This ratio is called Phi .... This ratio is nature's most ubiquitous fractal scaling ratio and is easy to see present in plants, animals, seashells, vortices of water
and air, and many other phenomena of Earth. It is also present at both the atomic and galactic scales. http://cosmometry.net/phifractalscaling  Cantor set and fractals
 I
have read that the Cantor set is considered a fractal. I am referring to the Cantor set in which the middle third of
a real line is removed recursively...think of a fractal as some geometrical object with scale invariance such that if
you "zoom in" on the object it will look the same/similar...a classic fractal such as the Koch Snowflake or
the Sierpinski triangle. I do see that Cantor's set would look the same if you kept "zooming in". If you restrict your sight to [0,13] then the picture
of Cantor's set is exatly the same as it is in the whole [0,1]. Again, restrict to [0,1/9] and you get the same picture.
I think this is the main property of a fractal: a picture which repeats itself.
Remove
the (open) middle third of it, i.e. get (1/3, 2/3).
Now remove the middle thirds of each of the remaining intervals,i.e. get (1/9, 2/9) and (7/9, 8/9). Continue this process ad infinitum. The points left over form a fractal
called the standard Cantor Set. Check out C'vorkum lightyears numbers divided into 1/3 and 1/9 (Cantor Set fractal numbers) symmetrical number parts.  Logarithmic spiral  Wikipedia Logarithmic Spirals Several Ghanian
iconic figures, ...link a spiritual force with the structure
of living systems through logarithmic spirals.  page 78 of African Fractals by Ron Eglash.Above images show fractal design in Oahspe
and fractal spirals in computer graphics.Above: Spider web geometric fractal designs.
Below: fractal architecture in Oahspe:
OAHSPE: Book of Fragapatti CHAPTER IX: 3. Go build me an avalanza capable of carrying
three thousand million angels, with as many rooms, capable of descent and ascent, and east and west and north and south
motion, and prepare it with a magnet, that it may face to the north, whilst traveling. 4. The builders saluted,
and then withdrew, and went and built the vessel.
And it was two hundred thousand paces east and west, and the same north and south; its height was one thousand lengths, and the vesture around it was a thousand paces thick; ...The
floor was woven in copy of a spider's net, extending from the centre outward, and with circular bars at crosses;
...  Relative to science, fractals are essentially
geometric shapes or forms that are represented in natural objects, from a fern leaf or tree, to a spider web ... http://fractalarts.com/SFDA/whatarefractals.html African Fractals:
Modern Computing and Indigenous Design. Fractals are characterized by the repetition of similar patterns
at everdiminishing scales. Fractal geometry has emerged
as one of the most exciting frontiers on the border between mathematics and information technology and can be seen
in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology,
and other natural sciences. Anthropologists have observed that the patterns produced in different
cultures can be characterized by specific design themes. In
Europe and America, we often see cities laid out in a grid pattern of straight streets and rightangle corners. In
contrast, traditional African settlements tend to use fractal structurescircles of circles of circular
dwellings, rectangular walls enclosing eversmaller rectangles, and streets in which broad avenues branch down to tiny
footpaths with striking geometric repetition. These indigenous
fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs
and knowledge systems. Drawing on interviews
with African designers, artists, and scientists, Ron Eglash
investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving,
metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines
the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer
simulations.  I buy it because I like math and geometry. I'm really fascinating by fractals applied
at design and architecture.  Daniele De Rosa  I have used this book several semesters for teaching philosophy
of science, social science methods, and Southern African political economy. It quickly demonstrates that the colonizers understood little or nothing about 'messy, irregular'
African villages; it was Euclidean geometry which kept them from seeing. African engineering using fractals, such
as the fractalmeasured fence weave to match the wind, is amazing. We still have very much to learn from African
peoples and this book gets Americans started on a journey long past due. Read this book if you want
a different way of viewing the world, from hairstyles to sculpture to urban planning.  Carol Thompson  The
book makes no assumptions in knowledge and will cleanly bring in the topic of fractals in african culture. The concept is quite intriguing and shatters many of the held perceptions
of "the hierarchy of mathematics." Ron Eglash is a great man and I know he loves talking with
people that share similar interests in mathematics or cybernetics.  Lorne E. Nix https://www.amazon.com/AfricanFractalsModernComputingIndigenous/dp/0813526140 http://homepages.rpi.edu/~eglash/eglash.dir/afractal/afractal.htm   Fractals are used to model soil erosion and to analyze seismic patterns as well. Seeing
that so many facets of mother nature
exhibit fractal properties, maybe the whole world around us is a fractal
after all! Actually, the most useful use
of fractals in computer science is the fractal image compression.
Why is fractal geometry important?
Fractals help us study and understand important scientific
concepts, such as the way bacteria grow, patterns in freezing
water (snowflakes) and brain waves, for example. Their formulas
have made possible many scientific breakthroughs. ... Anything with a rhythm or pattern has a chance of being
very fractallike.Oct 13, 2011 Fractal patterns can also be found in commercially available antennas, produced for applications
such as cellphones and wifi systems by companies such as Fractenna in the US and Fractus in Europe.
The selfsimilar structure of fractal antennas gives them the ability to receive and transmit over
a range of frequencies, allowing powerful antennas to be made more compact. Above: Fulani wedding blanket (textile) showing fractal design. IN 1988, RON EGLASH was
studying aerial photographs of a traditional
Tanzanian village when a strangely familiar pattern caught his eye. The thatchedroof
huts were organized in a geometric pattern of circular clusters within circular clusters, an arrangement Eglash recognized from his former days as a Silicon Valley computer engineer. Stunned, Eglash digitized the images and fed the information
into a computer. The computer's calculations agreed with his intuition: He was seeing fractals. Since then, Eglash has documented the use of fractal geometrythe geometry of similar shapes repeated
on evershrinking scalesin everything from hairstyles and architecture to artwork and religious practices in
African culture. The complicated designs and surprisingly complex mathematical processes involved in their creation may force researchers and historians to rethink their assumptions
about traditional African mathematics. The discovery may also provide a new tool for teaching AfricanAmericans about their mathematical heritage. http://www.math.buffalo.edu/mad/special/eglash.african.fractals.html In contrast to the relatively ordered world of Euclidean geometry taught in most classrooms, fractal geometry yields less obvious patterns. These patterns appear everywhere in nature, yet mathematicians began deciphering them
only about 30 years ago. The principles
of fractal geometry are offering scientists powerful new tools for biomedical, geological and graphic applications.
A few years ago, Hastings and a team of medical researchers found that the clustering of pancreatic cells in the
human body follows the same fractal rules that meteorologists have used to describe cloud formation and the shapes
of snowflakes. But Eglash envisioned a different potential for the beautiful fractal patterns he saw
in the photos from Tanzania: a window into the world of native cultures. http://www.math.buffalo.edu/mad/special/eglash.african.fractals.html Eglash had been leafing through an edited collection of research articles on women and Third World development
when he came across an article about a group of Tanzanian
women and their loss of autonomy in village organization. The author blamed the women's plight on a shift from
traditional architectural designs to a more rigid modernization program. In the past, the women had decided where their
houses would go. But the modernization plan ordered the village structures like a gridbased Roman army camp, similar
to tract housing. Eglash was just beginning a doctoral program in the history of consciousness at the University of California at Santa Cruz. Searching for a topic that would connect cultural issues
like race, class and gender with technology, Eglash was intrigued by what he read and asked the researcher to
send him pictures of the village. After
detecting the surprising fractal patterns, Eglash began going to museums and libraries to study aerial photographs
from other cultures around the world. "My assumption was that all indigenous
architecture would be more fractal," he said. "My reasoning was that all indigenous architecture tends
to be organized from the bottom up." This bottomup, or selforganized, plan contrasts with a topdown, or hierarchical,
plan in which only a few people decide where all the houses will go. "As it turns out, though, my reasoning was wrong," he said. "For example,
if you look at Native American architecture, you do not see fractals. In fact, they're quite rare." Instead, Native
American architecture is based on a combination of circular and square symmetry, he said.
Pueblo Bonito, an ancient ruin in northwestern New Mexico built by the Anasazi people, consists of a big circular shape
made of connected squares. This architectural design theme is repeated in Native American pottery, weaving and
even folklore, said Eglash. When Eglash looked elsewhere in the world, he saw different geometric
design themes being used by native cultures. But he found widespread use of fractal geometry only in Africa and southern India, leading him to conclude that fractals
weren't a universal design theme. Focusing on Africa, he sought to answer what property of fractals made them so widespread in the culture. http://www.math.buffalo.edu/mad/special/eglash.african.fractals.html "use of fractal geometry only in Africa and southern
India". Southern India is where the concept of zero (used in numerical computing) came from along with "arabic
numerals' and the decimal system.  Eglash expanded on his work in Africa after he won a Fulbright Grant in 1993. He toured
central and western Africa, going as far north as the Sahel, the area just south of the Sahara Desert, and as far south
as the equator. He visited seven countries in all. "Basically I just toured
around looking for fractals, and when I found
something that had a scaling geometry, I would ask the folks what was going onwhy they had made it that way,"
he said. In many cases, however, Eglash found that stepbystep
mathematical procedures were producing these designs, many of them surprisingly sophisticated. Eglash
realized that many of the fractal designs he was seeing
were consciously created. "I began to understand that this is a knowledge system, perhaps not as
formal as western fractal geometry but just as much a conscious use of those same geometric concepts," he
said. "As we say in California, it blew my mind."
In Senegal, Eglash learned about a fortunetelling system that relies on a mathematical operation reminiscent of error
checks on contemporary computer systems. In
traditional Bamana fortunetelling ...The mathematical operation is called addition modulo 2, which
simply gives the remainder after division by two. But in this case, the two "words" produced by the priest,
each consisting of four odd or even strokes, become the input for a new round of addition modulo 2. In other words,
it's a pseudo randomnumber generator, the same thing computers do when they produce random numbers. It's also a numerical feedback loop, just as fractals are generated by a geometric
feedback loop. "Here is this absolutely astonishing
numerical feedback loop, which is indigenous," said Eglash. "So you can see the concepts of fractal geometry
resonate throughout many facets of African culture." Lawrence Shirley, chairman of the mathematics
department at Towson (Md.) University, lived in Nigeria for 15 years and taught at Ahmadu Bello University in Zaria,
Nigeria. He said he's impressed with Eglash's observations
of fractal geometry in Africa. "It's amazing how he was able to pull things out of the culture and
fit them into mathematics developed in the West," Shirley said. "He really did see a lot of interesting new
mathematics that others had missed." Eglash said the fractal design themes reveal that traditional African mathematics may be much more complicated than previously thought. Now an assistant professor of science and technology
studies at Rensselaer Polytechnic Institute in Troy, Eglash has written about the revelation in a new book, "African
Fractals: Modern Computing and Indigenous Design."  Recent mathematical developments like fractal geometry represented the top of the ladder in most western thinking,
he said. "But it's much more useful to think about the development of mathematics as a kind of branching structure
and that what blossomed very late on European branches might have bloomed much earlier on the limbs of others. "When Europeans first came to Africa, they considered the architecture very disorganized
and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics
that they hadn't even discovered yet." Eglash said educators also need to rethink the way in which
disciplines like African studies have tended to skip over mathematics and related areas.
To remedy that oversight,
Eglash said he's been working with AfricanAmerican math teachers in the United
States on ways to get minorities more interested in the subject. Dr. Ron Eglash: Assistant Professor .
Department of Science
and Technology Studies Rensselaer Polytechnic Institute (RPI) Troy, NY 121803590 http://www.math.buffalo.edu/mad/special/eglash.african.fractals.html  43210 (Walter Russell and Michael James 98765) wave pattern number system found in African mathematics: numeric systems in Africa: Players in Ghana use the term "marching group" for a selfreplicating
pattern, such as the example below. Here the number of counters in a series of cups each
decrease by one (e.g. 4321). As simple as it seems, this concept of a self replicating pattern is at the heart
of some sophisticated mathematical concepts. http://homepages.rpi.edu/~eglash/eglash.dir/afractal/Eglash_Odumosu.pdf  The valid question arises, in what ways can
an understanding of African mathematical representations, fractals, complexity and chaos in indigenous
cultural practices assist us in theorizing about the future?  In our opinion, probably,the greatest point that can be taken away from our recent
research Eglash (1999) into African mathematics is an appreciation of African indigenous
creativity and quantitative ability. As Hull (1976) noted, large urban centers were
disregarded by the colonialists because they did not utilize Cartesian
typology. The complex fractal nature of these settlements went unappreciated. This point
is crucial in any discussion of possible applications of current research.
The sheer redemptive power of knowledge is at play here. Even today, people living on the African
continent may still think of their indigenous past as primitive and nonrational. An understanding
of the fractal characteristics of indigenous culture enables an appreciation of the
complexity of the ‘mundane’ indigenous artifacts. This singular understanding can act
as a powerful motivator for rethinking modernity.  "Bottomup"
social political structure of Africans vs the topdown colonial structure: It is widely accepted in the
STS [science and technology studies] community
that indigenous communities often posses tacit knowledge that may be invaluable
in problem solving (Wynne 1996, Epstein 1996) but is usually deprivileged within the dominant discourse. We have shown, for example, that many traditional African villages were structured in a “bottomup”
process, using selforganization rather than imposed order. Could
the topdown hierarchal approaches that linger on in so many postcolonial African countries – often due to the legacies of colonialism – also give way to more bottomup selforganizing social processes?
There is an obvious need for a change in the methodologies of modernity on the African continent; perhaps hybridizing
indigenous mathematical representations can provide fresh thinking to a persistent problem. http://homepages.rpi.edu/~eglash/eglash.dir/afractal/Eglash_Odumosu.pdf  A discussion of the relationship between pi and the Great Pyramid of Khufu. ... we know about ancient Egyptian mathematics (based primarily on the Rhind Papyrus), .... the mathematical knowledge of the architect who built the Great Pyramid. It’s
possible that pi , phi or both, as we understand them today, could have been the factors in the design of the pyramid. A detail of the geometries and calculations is below: 
relationship
of fractals to pi: Pi and fractal sets The Mandelbrot set  Dave Boll  Gerald Edgar In 1991
David Bolle tried to verify if the narrowing we can see at (0.75,0) was actually infinitely thin. That is to say that that however wide a nonzero width vertical line would be passing through that
point it would meet the fractal set before the xaxis. And
D Bolle then had the idea of using the point c=(0.75,X) for the quadratic iteration and to make X tend to 0. And there, what was his surprise when he counted the number of iterations before which
the series diverged and by discovering the following table .: Xiterations 1.0 3 0.1 33 0.01 315 0.001 3143 0.0001 31417 0.00001 314160 0.000001 3141593 0.0000001 31415928 Yes,
it was Pi that was appearing magnificientely ! As he could not manage to prove this he posted it in 1992 on the sci.maths newsgroup. Gerald Edgar from a university of Ohio answered it
on 27 march 1992 by bringing an intuitive explanation of this result.
This has been put lower down in the "Trial" section. http://www.pi314.net/eng/mandelbrot.phpThe relationship of the Allperson to individual man or woman is a fractal. Jehovih saith "I
AM within man and man is within me" = a fractal relationship "I AM within all things centering them, and I
AM without all things controlling them"  Walter Russell.<Fractal geometry, <"The Ocean Lives Within
The Drop" Fractal geometry (mathematics) = sacred mathematics (geometry) of the I'hins and the Israelites: Not only does fractal geometry and fractal mathematics describe
much of the natural universe, but fractals also describe
the relationship of the Creator and spiritual man, such as: Selfsimilarity (exactly or approximately similar,
sameness) Scaling (tiny section looks similar to whole and Vice versa) Infinity (unlimited extent, boundless) Recursion (repetitive process) Fractional Dimension (such as 1.26 dimensions,
infinite length in finite boundary) Above are the five
essential components of fractal geometry  pages 17 18 of African Fractals by Ron Eglash. Oahspe Book of Inspiration Chapter I: 1. ...I am Light; I
am Central, but Boundless, saith Jehovih. The central
part is a fractal of the whole part (both containing boundless infinity, selfsimilarity). Oahspe Book
of Cosmogony and Prophecy ch 2: 26. one light, with a central focus. [The FatherCreator is One Boundless Light with
a central focus, his central focus is man. Man is the focal point of the Father God] Man is the fractal of the CreatorGod. Oahspe Book of Inspiration Chapter I: 12. As out of
corpor I made thy corporeal body, so, out of My Light, which
is My Very Self, I built thee up in spirit, with consciousness that thou art. "out of My Light, which
is My Very Self" = selfsimilarity = fractal. Definition of very in US English: adjective 1 Actual;
precise (used to emphasize the exact identity
of a particular person or thing). 'those were his very words' "exact identity of a particular person"
= SELFSIMILARITY (fractal).◄ John 14:11 ► of the Bible: "I am in the Father and the Father is in me"
= fractal relationship. The fractal (mathematical) universe: Oahspe Book of Sue, Son of Jehovih: Chapter V 16.
God: I see nothing in all the universe but Thee! All selfs are but fractions of Thyself, O Eoih! 1/1000 = fraction = 1/1000 of Infinity = Infinity = a selfsimilarity fractal. Google
frac·tal: MATHEMATICS 1. a curve or geometric figure, each part of which has the same statistical character as the whole. Word Origin & History: fractal,
1975, from Fr., from L. fractus "broken," pp. of frangere "to break" (see fraction). Coined by Fr. mathematician
Benoit Mandelbrot in "Les Objets Fractals." Relationship of fractals to phi (golden ratio): 2: The Golden Ratio as a Continued Fraction A
unique feature of the Golden Ratio is that it can be written as an Equation which calls itself:
Equation 1:
Phi = 1 + 1 / Phi This Process is called Iteration. Mathematical Iteration can also be used to generate a Fractal. at every scale. It is
also known as an expanding symmetry or evolving symmetry. C'vorkum lightyears numbers (when rounded to nearest whole number) show a fractal pattern of expanding symmetry. Example 2727 (one whole C'vorkum) is a symmetrical expansion
of 909 (1/3 C'vorkum) 9 x 3 (expanded) = 27. Both 2727 and 909 are symmetrical numbers (same numbers to
the left and right of center, 99 or 2727).  In
this illustration below, every spiral is the same phi spiral
repeated:  The binary number system is an alternative to the decimal (10base) number system that we
use every day. Binary numbers are important because using
them instead of the decimal system simplifies the design of computers and related technologies. 
Below: Binary code. Above: Binary punched card. 
"In Africa, on the other hand base2 calculation
was ubiquitous, even multiplication and division. ...The implications of this trajectoryfrom subSaharan Africa to North Africa to Europe are quite significant for the
history of mathematics.  Page 99 of African Fractals.
 Zaslavsky
(1973) shows archaeological evidence suggesting that ancient
Egypt's use of base2 calculations derived from the use of base2 in SubSaharan Africa.  Page 89 of African
Fractals.  ...the binary code appears to have a distinct
African origin (Eglash 1997a) The modern
binary code, essential to every digital circuit from alarm clocks to supercomputers, was first introduced
by Leibnitz around 1670. Leibniz had been inspired by the binarybased "logic machine" of Raymond Lull,
which was in turn inspired by the alchemists’ divination practice of geomancy (Skinner 1980). But geomancy is
clearly not of European origin. It was first introduced
there by Hugo of Santalla in twelfth century Spain, and Islamic scholars had been using it in North Africa since at
least the 9th century, where it was first documented in written records by the Jewish writer Aran ben Joseph. The
nearly identical system of divination in West Africa
associated with Fa and Ifa was first noted by Trautmann (1939), but he assumed that geomancy originated in Arabic
society, where it is known as ilm alraml ("the science of sand"). The mathematical basis of geomancy is, however, strikingly out of place in nonAfrican systems. Unlike Europe,
India, and Arabic cultures, base 2 calculation is ubiquitous in Africa, even for multiplication and
division. Doubling is a frequent theme in many other African knowledge systems, particularly divination. The African origin of geomancy  and thus, via Lull and Leibnitz, the binary code
 is well supported. http://homepages.rpi.edu/~eglash/eglash.dir/ethnic.dir/r4cyb.dir/r4cybh.htm  Oahspe The Lord's Fifth Book: Chapter VI: 29....and the seer sat therein, with a table before him, on which table sand was sprinkled. And the Lord wrote in the sand, with his finger, the laws of heaven and earth. 
Below: first three steps in Bamana sand divination. Below: 4th and 5th steps in Bamana sand divination. "I
did receive permission from my teacher to make the Bamana algorithm public. The TED format only gives
you 17 minutes, and in that time I had to explain what fractal geometry is, how to simulate fractals in African material
design, and what the connection is between the fractal design and the indigenous knowledge. So I had to cut a lot of
details. I should also mention that the divination priests told me that I was just reading a sentence or two from
whole libraries of knowledge; the algorithm itself is
just one drop in their recursively infinite bucket."  Ron Eglash, November, 2017 https://www.youtube.com/watch?v=7n36qV4Lk94

Oahspe Book of Apollo, Son of Jehovih: Chapter XI: 2. Cim'iad was a small woman, dark, and of deep love,
most jovial of Goddesses; and had long looked
forward with joy to her pleasure of bringing so large a ship
to deliver two thousand million of Jehovih's Brides and Bridegrooms into etherean worlds. 
Practical
fractals: recursion in construction techniques...Williams goes on to note that much African metal work, unlike European investment casting, uses a "spiral technique" to build
up structures...resulting in ..."helical coils formed from smaller helical coils."  Page 112
of African Fractals by Ron Eglash. Figure 8.2h A single iteration of a threedimensional version of the recursive triangle construction, created by Akan artists in Ghana. [Ghana Akan worshipped
the Great Spirit like the Israelites]. Above: Kitwe community clinic fractal design in Zambia, Africa by David
Huges and Alex Nyangula. Above: Jola fractal settlement of Mlomp, Senegal  Page
163 of African Fractals by Ron Eglash. Above: Geometric analysis of
Mangbetu iterative squares structure of ivory sulpture Pages 6668 of African Fractals figure 5.5 ...the
construction algorithm can be continued ...applied to a wide variety of math teaching applications from simple
procedural construction to trigonometry (Eglash 1998a). 
it·er·a·tion noun: iteration. the repetition of a process or utterance. repetition of a mathematical or computational
procedure applied to the result of a previous application, typically as a means of obtaining successively closer approximations
to the solution of a problem. a new version of a piece of computer hardware or software.

Fractal geometry is a field
of maths born in the 1970’s and mainly developed by Benoit Mandelbrot.
The process by which
shapes are made in fractal geometry is amazingly simple yet completely different to classical geometry. While classical
geometry uses formulas to define a shape, fractal geometry
uses iteration. It therefore breaks away from giants such as Pythagoras, Plato and Euclid and heads in
another direction. Classical geometry has enjoyed over 2000 years of scrutinisation, Fractal geometry has enjoyed only
40. How to make a fractal shape
The rules are as follows:
1. Split every straight line into 3 equal segments.
2. Replace the middle segment with an equilateral triangle,
and remove the side of the triangle corresponding to the initial straight line.
 After this has iterated an infinite amount of times the fractal shape is defined. This may sound
bewildering but it is still possible to analyse it mathematically and visually you can see what the shape starts
to look like. The gif below (from Wikipedia) is a good illustration of what the curve looks like by zooming in on it: The von Koch curve [above looks exactly like a snowflake]
is a great example of a fractal: the rule
you apply is simple, yet it results in such a complex shape.
This kind of shape is impossible to define using conventional maths, yet so easy to define
using fractal geometry. Fractal trees: On the tree above, if you snapped a branch off it and stood it up, it would look like the original
tree. If you took a twig from the branch and stood it up, it
would still look like the original tree [selfsimilar]. Again, this is a property that occurs in nature,
but until fractal geometry there was not a good way to put it into maths.  Not
only do these shapes look like natural objects, but the process
of iteration sounds intuitive when thinking about nature. When a tree
is growing, its trunk will create branches, these branches create further branches, these branches create twigs. It’s
as if the function is a genetic code telling the branch how to grow and repeat itself, eventually creating
shapes that are ‘natural’.  Fractal
fibonacci numbers (sequence) and iterations:  A realistic map of the branching of a tree (or a variety of other plants too) is shown in the figure below. In this case, the tree grows from the bottom
up, and the rule here is that a branch grows one unit long in each iteration. When a branch is two units
long, it is strong enough to support a node, which is where a new branch splits off. The branches alternate on the left and the right, and very quicky a recognizable plant pattern emerges.  The rules that generate this fractal are really identical to the rules for the rabbit family tree
above, since it takes two iterations for a branch in the rabbit family tree to bifurcate, and it also takes a tree branch two iterations before it is strong enough to bifurcate.
The same kind of selfsimilar pattern emerges,
because at any step you can look at a new rabbit pair, or branch, as being the beginning of an entirely new sequence.
A little branch on a tree can be cut off and planted and
will form a whole new tree. A grandchild rabbit can turn into the grandparent of many rabbits. Any
unit, at any iteration, is just a scaled version of any other unit in the system. How many branches are there at the 6th generation? [ ]  In theory, one can argue that everything
existent on this world is a fractal: the branching of tracheal tubes, the leaves in trees, the
veins in a hand, water swirling and twisting out of a tap, a puffy cumulus cloud, tiny oxygene molecule, or
the DNA molecule, the stock market Fractals will maybe revolutionize the way that the universe is seen. A
dissident group of scientists claims that the
structure of the universe is fractal at all scales.
If this new theory is proved to be correct, even the big bang models should be adapted. The real world is well
described by fractal geometry. fractals can occur over
time as well as space—one example is how hearts beat across time. Robust hearts have fractal heartbeats, according to Ary Goldberger, a professor at Harvard Medical School. Using graphs of heart rate time series (like the 30minute time series show below),
he quantified the "fractalness" of heartbeats using a method called detrended fluctuation analysis, which identifies similarities in curves across different scales. 
It may seem like sudden spikes and falls
in the stock market are anomalous flukes, but they happen all too often to just be random, according to Benoit Mandelbrot, a mathematician who is often called "the father of fractals." Based on his belief that market fluctuations follow
fractal geometry, he has created fractalbased financial models that better account for extreme events than traditional
portfolio theory, which is based on a normal bell curve. Furthermore, these models can be applied to any timescale, from
years to hours. 
Climate cycles and the rules of prophecy
in Oahspe are fractal in nature. 3.7 year cycle is a
1/3 fractal of the 11.1 year cycle. The 11.1 cycle is a 1/3 fractal of the
33.3 year cycle. The 33.3 year cycle is a 1/3 fractal of the 99.9 year cycle. The 1000 year cycle is a 1/3 fractal of the
3000 year cycle. The 11.1 year cycle divided into three 3.7 years is
selfsimilar to the 33.3 year cycle divided into three 11.1 years, etc... See "Cycles, Predictions,
Earth events, A'ji" page of this website.  Using the golden ratio gets you the same proportion no matter what scale or how big or small you go…it
is infinite in keeping the same proportion throughout whatever scale. Think in terms of the geometry and the Golden Ratio Spiral. Each revolution retains the same proportion and is therefore self similar, i.e. fractal. Fibonacci's Fractals (they are actually African in artistic & mathematic origin). Indeed, these are not "Fibonacci's" fractals any
more than Georg Cantor's "Cantor set" was "Cantor's" i.e. European in origin. In
both cases the earliest documented human creative reproduction
of nature's fractals are found in Black Africa. https://www.youtube.com/watch?v=AhhODnji4hg  Badawy (1965) noted what appears to be use of the Fibonacci series in the layout of the temples of ancient Egypt. Using a slightly
different approach, I [professor Ron Eglash] found a visually
distinct example of this [Fibonacci] series in the successive chambers of the temple of Karnak, as shown in
the figure 7.22. Figure 7.2b shows how these numbers can be generated using a recursive loop. This formal scaling plan may have been derived from the nonnumeric versions of scaling architecture
we see throughout Africa.  Page 8789 of African Fractals.
Above: Golden ratio fibonacci spiral and Oahspe cyclic coil of the Great
Serpent of the solar system. Both showing decreasing in size twists. Above images show a pyramid
has spiral fractal design. a pyramid has spiral fractal design from base to top. A pyramid has a fractal
structure from bottom to top. The top of a pyramid is a fractal of the whole pyramid. A pyramid spirals ever smaller and smaller from the base to the tip.The Great Pyramid of Egypt is composed of smaller
fractal pyramids from tip to base. Image above shows each pyramid
is a fractal of the whole pyramid in a geometric fractal design. The
top two levels is a fractal of the whole pyramid. Above: Fractal selfsimilar
pyramids (parts of the whole pyramid) show the same
statistical properties (self similarity) at smaller scales. Above: Fractals of neurons in brain (see dark matter network below) and passages in lungs. Above: Etherean worlds and roadways have fractal architecture. Oahspe Plate 44 SNOW FLAKES [Snow flakes are symbols
of Etherean worlds] . Look at the snowflakes
as though they were microscopic patterns of the worlds in high
heaven . Above: many traditional
subSaharan African villages have fractal architecture.
1.1 Definition of Fractal The formal
mathematical definition of fractal is defined by Benoit Mandelbrot. ... Generally, we
can define a fractal as a rough or fragmented geometric shape that can be subdivided in
parts, each of which is (at least approximately) a reducedsize copy of the whole.  Below
logarithmic spirals and fractals: Smaller pyramid within smaller spiral in center
is a fractal of larger pyramid within larger spiral.
Below: Logarithmic scaling and Great Pyramid of Egypt:
Figure Three shows a graph of the mean orientation among structures on a log scale. This produces a linear
decline according to pyramid number. The measured values hold amazingly well to a mathematical equation expressing the
decay, with small variance from the regression line.
The mathematical expression for this line is: Y = A (intercept at 0 pyramid number)  B (slope) (pyramid number). or Y = A  B X P where P denotes the pyramid
number. Note that we are now dealing with logarithmic numbers
on the vertical scale, not linear numbers. The orientations are expressed in the natural logarithm of the original number, while the pyramid numbers are
expressed on an ordinary linear scale. For those who may not be acquainted with logarithms, two forms are commonly used
in mathematics and the physical sciences. The first is called "common logs" based on multiples
of 10. 100 = 1, 101 = 10, 102 = 100, and so on. The second is called "natural logs" based on an important
physical constant we symbolize by the letter e = 2.71828. e0 = 1, e1= 2.71828, e2 = 7.389, and so on. e most often
expresses the rate of natural decay processes. In following discussion I shall use the symbolism of log to denote common
logs, and ln to denote natural logs, following common practice in modern scientific and technical fields. We might
argue that the data from the pyramids are not natural; they do not come from natural processes. They were devised by
human intelligence and control. However, the data plots show that the designer prearranged his structures to express
a curve similar to natural decay. He probably did so because he knew that anyone competent enough to detect the form of the curves would be familiar with natural processes.
He also had to be familiar with natural decay processes, and how they are expressed mathematically, otherwise he could
not imitate them. After I calculated the intercept and the
slope of the orientations from the data on the basis of a natural decay curve I bumped into another amazing
value. The intercept was 10 Pi and the slope was very
nearly 1/Pi or possibly Pi/10. I show both the regression line calculated from the data (solid) and the
two theoretical lines (dashed) on Figure Three. We saw in the Great Pyramid Pi chamber that the designer used (Pi X ln
10) for one of his dimensions to show his knowledge of
higher mathematics. Here he displays it with the intercept values and the slope of the logarithmic decay.Above: logarithmic scaling in Ghanaian design  African Fractals by Ron Eglash page 79.  Recent mathematical developments like fractal geometry represented the top of the ladder
in most western thinking, he said. "But it's much more useful to think about the development
of mathematics as a kind of branching structure and that what blossomed very late on European branches
might have bloomed much earlier on the limbs of others.
 Any comments about Oahspe or this website? Email Me. I look forward to talking to you about Oahspe and this website.

