|Home, Cycles, Astrophysics, Human developmentMore science, Astronomy, PhysicsMore science 2 Chemistry, Physics, AstronomyHigher Advanced Knowledge of OahspeOptical Network Communications - Facial recognitionWeather, Climate, Dark Matter, Airborne PathogensExtrasolar planets, CEVORKUM, Light speedGeology - Pole-shift - Radiometric dating-A'jiSolar-Stellar Life Cycle - End of Earth - DeathBiology, Primary Vortex, Life, Computing, QuantumPhysics - Light - SoundPhysics - Magnetism - GravityThe Creator - The Father- and ManHuman origins - Pygmies - I'hinsHominidae - animal-manEarly Man - Races of Man - AnthropologyDinosaurs, Man, fossils, early EarthReligious History, Chinvat Bridge, Archeology, RaceConfucius, Po, China, Jaffeth & Caucasian originThe Great Pyramid of Ancient EgyptMathematical knowledge of Israelites and sub-Saharan AfricansHell, Knots, Flash devices, Riot controlBiblical flood and the sinking of PanLooeamong, Constantine, and The Roman EmpireThe Bible, Jesus, Joshu and the EssenesColumbus, Catholics, Conquistadors, Protestants, CrusadesQuakers and inner lightThomas PaineUS HistoryKosmon cycle, people, ancestry & SHALAMSubatomic particles - String Theory - Quantum - GUTMatter - Anti-Matter, Galaxies and CosmologyWalter Russell Cosmogony and EinsteinAerospace engineering, space-ships, space travelSpace clouds, Earth travel, ORACHNEBUAHGALAHTables of prophecy and historyThe BeastORACHNEBUAHGALAH CHARTS & Day Night CyclesAngels, universe, genetics, Loo'isNordic Aliens-Angels, Greys, Neoteny and ManPower of Attraction - Visualization - Spiritual giftsSpiritual message - UFOs - EthereansCosmic Consciousness, cycles, human behaviorCycles, Predictions, Earth events, A'jiNebula, Earth's atmosphere, heat & cold, eclipse, prophecyTrue PropheciesPredictionsDirect Inspiration, Walter RussellMisc. vortex, matter, periodic table, solar system, fractals, pi and cMisc. 2, E=mc2, geometry, pi and alphabet codes, chemical elementsMisc. 3, Sacred mathematics, geometry, music, harmonics, cosmology, cyclesMisc. 4 life and planets, E-O-IH and geometry, DNA, facial recognitionMisc. 5 human DNA, neuroscience, 9-8-5, 33, creativity, solar powerProphecy, Pan, Harvest & DNAMagnetospheres - Solar planetary vortex - 3D HologramsEther Vortex PhysicsLanguage - Symbols - Pictographs - Creator's nameTornados, name vs concept, flat earth theory, UV-light, sympathetic resonance, drujasTae and facial recognition, Ham, Shem, Guatama, I'huan, Ghan racesMathematics, Reality, primary 3, E-O-IH, Cevorkum, EthereansOriginal Israelites and JewsIsraelites I'huans Ghans OahspeETHICAL TEACHINGS OF OAHSPEAngelic star travelers, Human origins, racesAstrophysics, OpticsVisitors and CommentsDonation
"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,
raftors have some excellent examples), they are not everywhere. Their strong prevalence in Africa
(and in African-influenced
southern India) is quite specific. - Page 7 of African Fractals Modern
Computing and Indigenous Design
(1999) by Ron Eglash.-
impact on India is found in artefacts, ancient texts, genetic foot-prints, 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
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 rule-bound techiniques equivalent to western mathematics." - pages 68-69 of
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
Fractals are characterized
by the repetition of similar patterns at ever-diminishing 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.
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 right-angle corners. In contrast, traditional
African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller
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
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.
fractal settlement patterns of Africa stand in sharp contrast
to the Cartesian grids of Euro-American settlements. - Page 39 of African Fractals.
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
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.
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"
"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
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
would bring them deliverance was still five hundred years away.
[2053 - 500
= 1553 B.C.E.]. - Pages 189-190 of Darkness, Dawn And Destiny
(Drawn from Oahspe)
1965 by Augustine Cahill.
Oahspe Book of Wars Against Jehovih Chapter XLIX:
...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.
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,
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.
Israelites kept this sacred mathematical knowledge up to modern times.
Above: Original-Israelites-Abraham-75% and 75% 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 inverse-slope for the slant-angle
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 4-th dynasty. One can ask how accurately they
represent the mathematical knowledge of the architect who built the Great
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
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,
of five palms, two fingers
would correspond to an inverse-slope 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
1. The rational number 22/7 happens to be an excellent approximation to the number
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
...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/phi-fractal-scaling
Cantor set and fractals
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
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.
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 light-years numbers divided into 1/3 and 1/9 (Cantor Set fractal numbers) symmetrical number parts.
Logarithmic spiral - Wikipedia
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 ...
Modern Computing and Indigenous Design.
Fractals are characterized by the repetition of similar patterns
at ever-diminishing 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,
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 right-angle corners. In
contrast, traditional African
settlements tend to use fractal structures-circles of circles of circular
walls enclosing ever-smaller 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
Drawing on interviews
with African designers, artists, and scientists, Ron Eglash
fractals in African architecture, traditional hairstyling, textiles, sculpture, painting,
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
I buy it because I like math and geometry. I'm really fascinating by fractals applied
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
fractal-measured fence weave to match the wind, is amazing. We still have very much to learn
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
book makes no assumptions in knowledge and will cleanly bring in the topic of fractals in
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
Fractals are used to model soil erosion and to analyze seismic patterns as well. Seeing
that so many facets of
exhibit fractal properties, maybe the whole world around us is a fractal
after all! Actually, the most
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
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 fractal-like.Oct 13, 2011
Fractal patterns can also be found in commercially available antennas, produced for applications
cellphones and wifi systems by companies such as Fractenna in the US and Fractus in Europe.
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.
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
computer. The computer's calculations agreed with his intuition: He was
Since then, Eglash has documented the use of fractal geometry-the
geometry of similar shapes repeated
on ever-shrinking scales-in
everything from hairstyles and architecture to artwork and religious
African culture. The complicated designs and surprisingly
complex mathematical processes involved in their creation may force
researchers and historians to rethink their assumptions
traditional African mathematics. The discovery may also provide a new
tool for teaching African-Americans about their mathematical heritage.
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.
of fractal geometry are offering scientists powerful
new tools for biomedical, geological and graphic applications.
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
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.
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
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
grid-based 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.
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
to be organized from the bottom up." This bottom-up, or
self-organized, plan contrasts with a top-down, or hierarchical,
which only a few people decide where all the houses will go.
"As it turns out, though, my reasoning was wrong," he said. "For
if you look at Native American architecture, you do not see
fractals. In fact, they're quite rare." Instead, Native
architecture is based on a combination of circular and square symmetry,
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
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.
"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
numerals' and the decimal system.
Eglash expanded on his work in
Africa after he won a Fulbright Grant in 1993.
central and western Africa, going as far north as the
Sahel, the area just south of the Sahara Desert, and as far south
equator. He visited seven countries in all.
"Basically I just toured
around looking for fractals, and when I
something that had a scaling geometry, I would ask the folks what
was going on-why they had made it that way,"
In many cases, however, Eglash found that step-by-step
were producing these designs, many of them surprisingly sophisticated.
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
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
In Senegal, Eglash learned about a fortune-telling system that
relies on a mathematical operation reminiscent of error
contemporary computer systems.
traditional Bamana fortune-telling ...The mathematical operation is called addition modulo 2,
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
it's a pseudo random-number 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
"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
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
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
thus primitive. It never occurred to them that the Africans might have been using a form of
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
To remedy that oversight,
Eglash said he's been working with African-American math teachers in the
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 12180-3590
4-3-2-1-0 (Walter Russell and Michael James 9-8-7-6-5) wave pattern number system found in African mathematics:
numeric systems in Africa:
Players in Ghana use the term "marching group" for a self-replicating
such as the example below. Here the number of counters in a series of cups each
decrease by one (e.g. 4-3-2-1).
As simple as it seems, this concept of a self replicating pattern is at the heart
sophisticated mathematical concepts.
The valid question arises, in what ways can
an understanding of African
mathematical representations, fractals, complexity and chaos in indigenous
practices assist us in theorizing about the future?
In our opinion, probably,the greatest point that can be taken away from our
research Eglash (1999) into African mathematics is an appreciation of
creativity and quantitative ability. As Hull (1976) noted, large
urban centers were
disregarded by the colonialists because they did not utilize
typology. The complex fractal nature of these settlements went unappreciated.
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
continent may still think of their indigenous past as primitive and non-rational.
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.
social political structure of Africans vs the top-down colonial structure:
It is widely accepted in the
STS [science and technology studies] community
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
process, using self-organization rather than imposed order. Could
hierarchal approaches that linger on in so many post-colonial African countries – often due to
the legacies of colonialism – also give way to more bottom-up self-organizing social processes?
There is an obvious need for a change in the methodologies of modernity on the African continent;
indigenous mathematical representations can provide fresh thinking to a
of fractals to pi:
Pi and fractal sets
The Mandelbrot set - Dave Boll - Gerald Edgar
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 non-zero width vertical line would be passing through that
point it would meet the fractal
set before the x-axis.
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 .:
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 All-person 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
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:
Self-similarity (exactly or approximately similar,
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.
part is a fractal of the whole part (both containing boundless infinity, self-similarity).
of Cosmogony and Prophecy ch 2:
26. one light, with a central focus. [The Father-Creator 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 Creator-God.
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" = self-similarity = 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"
= SELF-SIMILARITY (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
God: I see nothing in all the universe but Thee! All selfs are but fractions of Thyself, O E-o-ih!
1/1000 = fraction = 1/1000 of Infinity = Infinity = a self-similarity fractal.
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
unique feature of the Golden Ratio is that it can be written as an Equation which calls itself:
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 light-years numbers (when rounded to nearest whole number) show a fractal pattern of
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, 9-9 or 27-27).
this illustration below, every spiral is the same phi spiral
The binary number system is an alternative to the decimal (10-base) number system that we
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 base-2 calculation
was ubiquitous, even multiplication and division.
...The implications of this trajectory--from sub-Saharan Africa to North Africa to Europe are
quite significant for the
history of mathematics. - Page 99 of African Fractals.
(1973) shows archaeological evidence suggesting that ancient
Egypt's use of base-2 calculations derived from the use of base-2 in Sub-Saharan Africa. - Page 89 of African
...the binary code appears to have a distinct
African origin (Eglash 1997a)
binary code, essential to every digital circuit from alarm clocks to super-computers,
was first introduced
by Leibnitz around 1670. Leibniz had been inspired by the binary-based
"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 al-raml ("the science of sand").
The mathematical basis of geomancy is, however, strikingly out of place in non-African systems.
India, and Arabic cultures, base 2 calculation is ubiquitous in Africa, even for
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
-- is well supported.
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
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
libraries of knowledge; the algorithm itself is
just one drop in their recursively infinite
bucket." - Ron Eglash, November, 2017
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.
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 8.2-h A single iteration of a three-dimensional version of the recursive triangle
construction, created by Akan artists in Ghana. [Ghana Akan worshipped
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 66-68 of African Fractals figure 5.5 ...the
construction algorithm can be continued
...applied to a wide variety of math teaching applications from simple
to trigonometry (Eglash 1998a).
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,
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
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.
On the tree above, if you snapped a branch off it and stood it up, it would look like the
tree. If you took a twig from the branch and stood it up, it
would still look like the
original tree [self-similar]. Again, this is a property that occurs in nature,
but until fractal
geometry there was not a good way to put it into maths.
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
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
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.
kind of self-similar 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,
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.
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 30-minute time series show below),
he quantified the "fractal-ness" 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 fractal-based 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
self-similar 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
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.
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 87-89 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.
top two levels is a fractal of the whole pyramid. Above: Fractal self-similar
pyramids (parts of the whole pyramid) show the same
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
Above: many traditional
sub-Saharan 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 reduced-size copy of the whole.
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).
Y = A - B X P where P denotes the pyramid
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
expressed on an ordinary linear scale.
For those who may not be acquainted with logarithms, two forms are commonly used
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.
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
western thinking, he said. "But it's much more useful to think about the development
mathematics as a kind of branching structure and that what blossomed very late on European
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.