Self-Organization in Science and Society
STSH 4580
Reflection Paper 2
3/27/2014
African Fractals
By
Botagoz Mirzagalikova
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The development of science and art, as well as biological evolution is an infinite process. However,
people did not always believe in existence of infinity, it took people thousands of years to actually come
to recognize the inevitability of its existence and to the realization of its use. And as it usually goes, a
human science now turns its face to a different source of knowledge, the intentional knowledge of
African fractals. African fractal art and lifestyle, which indigenous civilizations of the continent has have
developed and practiced throughout centuries and even millennia, people of the so called ‘civilized
world’ have only recently started discovering. [I don’t have time to make further corrections but you
need to turn in grammatically correct sentences—as before, if you want to resubmit after making
corrections you are welcome to do so]
Unlike ‘linear’ European and Asian civilizations, most of African civilizations practice fractal way of living.
Fractals appear very frequently in culture and everyday life. Fractals tell stories of nations, clans, families
and distinct people. One of the first examples represented in the book of African Fractals – the Fulani
wedding blanket shows the “report of the spiritual energy, being woven into the pattern” (African
Fractals, Chapter 8, pg.119). To a person more competent in the Fulani art and culture, the pattern will
certainly mean much more that to a person like me. May be it is even possible to ‘read’ this story of the
spiritual energy, the story of weaving, and the story which the “storyteller” (weaver) wanted to tell.
Another good example is kente cloth design (Fig.1). This traditional design regulates looks of other
people on the person wearing this kente cloth as a toga, by regulating the “heavy looks” and the “light
looks”, or saccadic eye movements. This regulation is created and maintained using different scaling
transformations. In other terms, what western people have studied for years and what they created as
mathematical science and art was used by African people in their everyday life.
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Figure 1. Different Kente Cloth Designs
Another example of fractals being used in African civilizations is the architecture of traditional villages
and settlements. All of the examples use self-replicating, scaling patterns. In most of the settlements,
such as Ba-ila settlement before 1944 (Fig.2), Mokoulek (Cameroon), Labbezanga (Mali) houses of
members of a community differ only in size (bigger for richer and more powerful people) and location
(social role and place of members of family in a community). This fact creates and shows closer
relationships between population of a village and its chiefs in these civilizations. In fact, this relationship
is coded in the Baule carving of two crocodiles, biting each other’s tales. This can serve as a use of
feedback loops in the everyday life. If one of the crocodiles represents the chief and the other
represents people, then the loop shows a balance and primary interaction between these two forces,
equal in power and influence.
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Figure 2. Ba-ila settlement before 1944 (photograph and simulation)
Another example of feedback loops in African cultures is the vodun god Dan, pictures as the snake biting
its own tale. Feedback loops are important for understanding the nonlinear systems, complexity and
most of the processes in nature. The feedback loops are applied in all modern computer technologies,
used to measure the analog complexity with digital representation. The importance of feedback loops is
clearly shown in the three types of machines in Chomsky hierarchy. It is also shown in recursion
characteristics and classification. So, the least powerful recursion is cascade recursion, at the same time
least powerful machine is the Finite State Automaton – both of them are very restricted in their use,
though very simple ones. The next type of recursion is iteration (“nesting” is an important variety of
iteration), and the Push-Down Automaton (capable of memory storage). The third type of recursion is
self-reference, and at the top of the Chomsky hierarchy is the Turing Machine(TM). Since in “the Turing
Machine memory interactions can occur over any past sequence of any length, and it does not lose
memory after it is read”(African Fractals, Chapter 10, pg.157), the TM is considered as the most
powerful in computing. It is also directly connected with the self-reference recursion – it is able to
analyze its own program. The main role of memory in all of the recursion types and machines is in the
interaction between past and present inputs, feedback and comparison of them and, hence, further
behavior of the system.
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Telling about computing techniques and modern computer technologies, it is impossible to skip the
doubling series in Africa as a huge cultural phenomenon. Used in everyday life (e.g. counting system),
art, religious services (e.g. doubling sequences of a Shango temple and religious ceremonies, binary
codes in divination) the doubling series address not only to African life, but also to modern computing
and mathematics. These series appear in the very old documents and artifacts, not only in present
culture. The doubling series were used in the Ishango bone (8000 years old), in ancient Egyptian
mathematics as powers of two, in Christian-animist syncretism (cyclic rebirth of pairs Adam-Eve, CainAbel, Christ-Virgin Mary). Doubling series are used nowadays as well.
A closer review shows the importance of scaling in African designs. Most of the relationships between
parts in African art, architecture, design and many other aspects of culture obey the power law. One of
the most impressing example for me is the wind screen design of Sahel, where rows of straw change
according to the power law. The reason for that is in better ability of shorter straws, located at the top
of windscreen, to keep wind and dust. So, where European, Asian or American artisan would probably
use rows of equal length, African artisan used the power law.
With the discovery and further explanation of fractal geometry and the power law was one of the most
important ones for modern science and art. However, the number of African civilization had used these
mathematical laws throughout centuries, and throughout centuries these people lived in the non-linear
world of fractals, doubling series and recursions, that people nowadays find so very important for the
development of computer technologies. And centuries before, these things were banned, changed to
the linear standards, the minds of the people using these ideas changed, but if humanity would only
think differently, behave more thoughtfully, tolerant, flexibly, look around and learn from different
peoples and cultures, the cost of new inventions might have been much lower, the invention process
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smoother, and the scientific progress faster. Well-reasoned and nicely organized. Grade = A-, but you
can raise it by submitted a corrected version.
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