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Mathematics African fractals in modern computing
By Dr. Ron Eglash
* Ron Eglash visited Central Africa and the west, going as far north as the sahel, the region to the south of the Sahara Desert, and as far south of the equator, where he visited seven countries in all , this is his conclusions:
" the widespread use of the fractal geometry is found only in Africa and in the south of India, which implies that the fractals are not a theme of universal design.
Focusing on Africa, the properties fractals are so prevalent in their culture that when they use circular houses, they also use circles within circles, when they use rectangles, you'll see rectangles on the inside of the rectangles .
In the huge plazas, the broad avenues to shrink in smaller streets as do the branches of a tree to finish in small trails and even if from a European point of view, this can only seem chaotic, a mathematical point of view , this translates into the "Chaos Theory" scientifically known as the fractal geometry
In Senegal, the priests of the people of bamana oracular in dakar, calculate the good or bad fortunes using a binary code generated recursively, where the seers using an arithmetic on the basis of two, just like we use the "one" and the "zeros" in the digital circuits which calculate every exit of the procedure arithmetic before the one of the following entry, producing a series of symbols that priests interpret as the fortune of the client.
This technique is similar to a sort of generation of random numbers in the calculation of which the technique of bamana can produce more than 65 000 numbers before the following sequence repeats.
Although of fractals are located in very ancient cultures on other continents like for example the celtic knots, it is a fact that the fractals are particularly prevalent in Africa, and which shows that the mathematics of Africa are much more complex than we Thought it would.
The knowledge of the fractal geometry today allows scientists to model complex processes in biology, chemistry and geography by computer, it also helps to generate realistic computer images of the natural elements such as uneven terrain or tree branches intertwined , however, most schools teach only the classic geometry, the study of simple shapes like circles or squares but never the fractal geometry.
By visiting the company mangbetu in Central Africa, I studied their tradition of using multiple angles at 45 degrees in their works of art in which the concept is similar to the geometric shapes of American Architectures But here, where our students produce them in Using only a compass and a straight edge, in society mangbetu, the uniform rules have enabled their artisans of competing with the best of our designs,
There is a more complex example of fractal geometry widely used in pare-winds of the sahel region, including the strong winds of the sahara frequently sweep the earth dry and dusty, where for better protection against the wind, these winds is bulletproof Make up approximately ten rows diagonals of stem of millet, where every row is shorter than the one below, but this screen geometric is quite extraordinary and I've never seen something like that, they had learnt from the experience that The wind is blowing stronger and more wide on the ground, so that they did what an engineer would call "the analysis of the costs and benefits
These artisans had measured the length of each row non-Linear, where they had drawn the data on a graph and I could understand that these lengths were based on the wind, and not only they had done this by using a formal geometric system in order to produce These forms of scale, but they had also been able to put them in practical value.
I realized that a lot of conceptions of fractal had been created mentally or consciously and I began to understand that it was a system of knowledge, which was perhaps not as formal as the western fractal geometry, but he was just as much Useful that the same concepts geometric aware
In Senegal, I also learned about a system of predictions that the design is based on a mathematical operation which recalls the error checking on the computer systems contemporaries.
In the traditional cartomancy bamana, the priests of divination begins with trace quickly four dotted lines in the sand that they connect by pair to other indents and other lines containing odd numbers then he repeats the together in a process of which the operation Mathematics is called " addition modulo 2 " who simply gives the rest after a division by two but where in this case, the two " words " produced by the priest, each consisting of four pairs or odd cycles, become the entrance of a New cycle "of addition modulo 2". In other words, it is the same pseudo-random generator that computers, when they produce random numbers, which is both a digital feedback loop, in the same way that the fractals are generated by a loop of Geometric feedback
When the Europeans came in Africa, not including architecture, they considered very disorganized and therefore as primitive but they weren't come to the idea, that Africans had been able to use a form of mathematics they did Not even discovered, this is the reason why educators must now rethink disciplines and African studies who tend to be ignore in mathematics and the areas connected.
Today, the fractal geometry appears as fundamental and it is located in the most exciting borders in the fusion between mathematics and computing, it's the reason why, fractals can now be seen in a large number of models swirling products By the computer graphics, which have become a new important tool for the modeling of biology, geology, and other natural sciences.
While the fractal geometry can take us in the far reaches of the science of high technology, its models are surprisingly common in African traditional designs, and some of its basic concepts are also fundamental to the advanced systems of African knowledge
African fractals that I present to readers, explored the fractal geometry and the manner in which it is expressed in the African cultures, from interviews with creators, artists and scientists africans during my investigations in the traditional architecture of African fractal But also in the hairstyles, textiles, Sculpture, painting, Sculpture, the ironwork, spirituality, the games, the quantitative techniques and symbolic systems, as well as its implications in the political and social life
The City of aztek tehotihuakan was pronounced and wrote himself a tutu-Hu-akan or tehuti-Hu-Akan, where we find the name of the keeper; "hu" who was at the same time another aspect of ptah, which personified, the power Inherent and authority who hides behind every word every word or sentence when they are associates, have the ability to be able to abstract ideas to a tangible reality
The akan people of Southern Ghana and côte d 'Ivoire " claim to be originating in or be exiles from the valley of hapi but also of the country of kana' Anu (Kanaan) and the anu naakhi of sumeri and that their name means "people first", even if, however, the akan also share many cultural elements, linguistic and a same script with their neighbours my-Ndé, (children of my / MU) which bear a resemblance with the same elements olmek
Akan would be a linguistic abbreviation of Ankh-Anu and a historical narrative reports that the name of one of the oldest founder of the meso-American civilization was tamu-ANK-Anu who is a variation of the word olmek; " tamo akan " or " Tamu-ANK-Anu ", which remain in agreement with the term anu meaning " first " which we now know, they are also part of one of the most ancient peoples on the earth, among them, some were already living in the country Of Kush In Country Khanitu (Nubia) and country SU-Meri (children of meri), where a colony cushite city, called the children of anu were known as the anu-naki
The Olmek-My-Nde (XI or zingh) like the anu were also a people afrikain very old and very LG, known addition Atlantic long before the time of the aztek does in the pages of history since they were the cells Black people of all the greatest and most ancient civilizations meso-American, where the so-called Mayan calendar including all the middle "new age" was talking about, had also been introduced by the olmek around-3100, which coincides to day Close, to the year of dynastic afurakan of Kampala (KMT), which at that time opened the era of great kings, including that of the king nara meri of the haute-Earth when he had conquered his rival, the scorpion king of the north already known As the great black