Steven Wells
Self-Organization in Science and Society, Prof. Ron Eglash
3/26/2014
Reflection Paper #2
The first part of this course helped gain a knowledge for and an understanding for
complexity theory and fractal design. This second part of this course has given us valuable
insight to the world of African Fractals in the book, “African Fractals: Modern Computing And
Indigenous Design” by Ron Eglash. I have found this book very interesting and very well written
because I continue to learn more every day that I had never known before. In this book we go
in depth into the world of African fractal design in architecture and African cultural settlements.
The book touches upon the different types of recursion that are involved with fractals and how
infinity and self-similarity are prevalent in fractal design and African architecture; but not just in
the non-western world alone. First I will talk about the first three chapters in our first reading
assignment.
In the first three chapters of this book I found a lot of commonalities with Mitchell. In
chapter one, we touched upon the five essential components for fractal geometry. They are:
Recursion, Scaling, Self-Similarity, Infinity, and Fractal Dimension. We also read about the
History of Fractal Geometry and such examples as the Cantor Set and the Koch Curve examples.
In chapter two, we focused on African fractals in the African culture styled architecture,
especially circular architecture as well. An example was the Ba-ila settlement. “The settlement
as a whole has the same shape: it is a ring of rings. The settlement, like the livestock pen, has
a front/back social distinction: the entrance is low status, and the back end is high status. At
the settlement entrance there are no family enclosures at all for the first 20 yards or so, but
the farther back we go, the larger the family enclosures become.”(Eglash p. 26). Eglash goes
on to say that this circular shape can be easy to create with fractals. The image in the book
helps to show the re-occurring round-circular pattern as you go from the outer public
settlement ring to the interior chief ring. Eglash also discusses a Branching type of architecture
in fractals that is used in the Senegalese Settlement. Chapter three talks about how fractal
architecture doesn’t just apply to non-Western cultures. Native Americans used the fractal
designs in their cultural settlement setup and had a more Euclidean geometric style of
architecture. There are also linear concentric forms of Native American architecture. Overall I
thought that the first three chapters of this book really helped me understand various sections
and parts of the rest of the book; in other words, the information laid the paths to getting a
better understanding for fractals in African culture. These ideas were continued into the next
reading assignment.
I thought these chapters, (four, five, and six), were very interesting and I found various
commonalities with the readings in Mitchell on topics in the reading in your book. I found that
adaptive scaling with triangles in African Culture is very interesting and you can see the
recursive shape in pretty much everything they wear in a fashion sense. I am also a little
confused about the 45 degree angle feature used in the fashion and art in the African culture.
Many cultures also used fractal designs in their carvings and art displays. An example is the
ivory carvings in the book on pages 66-67 where the geometric algorithms are shown to figure
out the math to place the reoccurring head of the ivory sculpture in the right spot. If you use
your imagination you can imagine the design just continuing off into infinity, one of the topics
discussed in the previous reading of chapters 1-3. Other ideas that were mentioned in this
reading were: the nonlinear additive series in Africa, doubling in the shango religion and
geomancy, as well as others. In the next reading we talked about the different types of
recursions and examples of a simple situation of recursion.
I was intrigued by the three types of recursion part in chapter 8 as you talked about the
Fibonacci Series and the process of recursion from when someone cuts there christmas tree
because it is too big and keeps getting passed down to smaller organisms. The three types of
recursion also caught my attention: 1) Cascade Recursion, where there is a predetermined
sequence of similar processes, 2) Nesting recursion, where loops are made within loops (almost
seeming like they are never ending I thought), and 3) Self-Reliance recursion, a symbol referring
to itself. I also found the section on recursion in construction techniques to be fascinating as
well. “A wig made from metal wires (fig. 8.2a) shows a similar iterative construction using
coils made of coils.” (Eglash p.112). A common sight for African fractals, you can find such selfsimilarity in the fashion and hair styles of many African cultures. “In chapter 6 we saw some
examples of African hair styles in which either adaptation to contours or abstract spatial
transformation resulted in the scaling pattern.” (Eglash p.112). Eglash goes on to say that the
picture of the braids in one of the examples in chapter 6 have no direct connection to the shape
of the head, rather they are the “result of successive iterations that combine strands of hairs
into braids”,(Eglash p.112), and then even more braids and on and on. I can now look at people
that are walking down the street (not in a stalker-ish way) that have braids in their hair and
immediately think about the unique shape that they are wearing.
Chapter nine talked about Infinity and how it came about to be used as a symbol for
eternity and many things including fractals. Chapter 10 revisited complexity and Analog
Computation. The example of placing a refinery in the right place in a sectioned off area to
maximize its profit by placing three holes on the map and, by using a brass ring and string, tying
three weights to the ends of each of the three strings to see where the ring would fall. In the
last reading we are basically tying everything together.
I thought that the section in the reading of chapters eleven through 14 about Fractals in
African Contemporary Art and the section about Fractals in Contemporary Architecture were
pretty cool. It is clear that many people have embraced the use of African fractals in modern
structures today; an example is The library of the University of Dakar. “This scaling design, in
which the alteration of painted rectangles at the small scale matches the alteration of the
building walls at the large scale, is reminiscent of certain African Fractals.” (Eglash p.217). The
design of the building shows a self-similarity look to it and a sense of non-linear scaling as you
move toward the center building. Even looking into the indigenous parts of Africa you can see
how everything the people use and/or build has some type of fractal-like look to it. “For
example, the Sierpinski-like iterative triangles from Mauritania were used in an institutional
building in Senegal, and the circles of circles in the architecture of West African villages
became the basis of a design for a building complex in downtown Bamako, the capital of Mali
(fig. 14.3).” (Eglash p.218). African Fractals have had a huge impact on modern architecture
around the world. There is something about the type of fractals that are used in African cultural
art that is pleasing to the eye. From the way the design their clothes to the way they design
their villages is all very fascinating and their fractal based mathematics helped them complete
their task, whatever it might be.
As we can see, African Fractals have a very huge impact of society in the arts and fashion
sense as well as the education and political side of society. I think Professor Ron Eglash wrote a
very good and informative book about African Fractals and I enjoyed reading it. Like I said
earlier in the paper, as we move through the course more and more, it’s hard not learn
something new from this material.
Nicely done! One error – above you say the book describes fractals in native American culture
– that chapter was actually showing the comparative lack of fractals in native American design.
Otherwise a very accurate account of the book. It was helpful for me to hear which things stuck with
you after reading – now I know what to emphasize in the next book!
Grade = A.
Works Cited
1) Eglash, Ron. African Fractals: Modern Computing and Indigenous Design. New
Brunswick, NJ: Rutgers UP, 1999. Print.