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case study on the innovation of


a shared technology




The layout of this book is loosely based on this fractal from the place of the chief in Longone-Birni, Cameroon. The fractal spirals in with rectangles within rectangles. The closer you get to the center, the more respectful you have to be.


Kidest Mulugeta Sande History of Interpretation and Innovation Prof Christine Miller Ph.D, Winter 2011

CONTENT african fractals




ron eglash


definition of innovation


attributes of innovation


heterogeneous engineering adoption of innovation

19 20



fractals antecedents


technical drivers


swarm creativity







AFRICAN FRACTALS Fractals have been a shared technology in Africa for centuries. Some cultures use them out of pure intuition by observing their environment, while other groups use them through complex algorithms.


The purpose of this study is to explore the process of innovation by looking at the development and diffusion of African fractals.


FRACTALS 1st iteration

2nd iteration

A fractal is a pattern that repeats itself on different scales. It uses self-similarity which means that the part looks like the whole. It is the same pattern at many different scales.

3rd iteration

4th iteration



“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.”

RON EGLASH Ron Eglash is the author of African Fractals. He is an ethno-mathematician; he studies the relationship between mathematics and cultures.


DEFINITION OF INNOVATION An innovation is a new idea that can be diffused and utilized by a group of people, influencing their lifestyles and occasionally their belief systems.


ATTRIBUTES OF INNOVATION There are five attributes of innovation by which an innovation can be described.


The Baila settlement in Zambia is structured with a fractal of rings. This village is organized in a specific manner, where one ring is a cluster of many rings thus grouping families together. The buildings get bigger towards the back showing more status and more livestock.

observability The degree to which the results of an innovation are visible to others. Fractals are not accidental, they are used in a specific manner. Everyone in the community is aware of them. 13

trialability The degree to which an innovation may be experimented with on a limited basis. Much like the Baila architecture in Zambia, there are cultures where a whole community is involved in the application of fractals.

The process of making Fullani wedding blankets is believed to be charged with spiritual energy increasing at each iteration of the pattern. Releasing this energy is dangerous and even deadly in some cases; the weaver cannot interrupt the process.


However, some cultures only allow trained individuals to be involved in the application of fractals, a good example is the making of the Fullani wedding blanket.



compatibility The degree to which an innovation is perceived as consistent with the existing values, past experiences, and needs of potential adopters. Fractals are embedded in individuals’ belief systems and everyday life. The Kirdi live in the Mandara Mountains of Cameroon. Their village is structured in self-replicating spiral; the center of which is the village alter of spiritual and political authority.

relative advantage The degree to which an innovation is perceived as better than the idea it supersedes. Holistic design of the village facilitates communal lifestyle. Fractal villages are often structured by social status and familial relationships. 17

complexity There are more than a hundred types of processional crosses in Ethiopia. Most of them are the result of an algorithmic fractal. They can be simulated with three-fold iterations.

The degree to which an innovation is perceived as relativey difficult to understand and to use. In the case of African fractals, complexity varies with each culture. Ethiopian crosses are a good example to illustrate these subtle variations. Their use as jewelry or decoration is straight forward and simple. However, in the context of the church, the use of these crosses is very complex and exclusive. Only a select groups of people within the church are allowed to touch them.


HETEROGENOUS ENGINEERING African fractals are used for multiple reasons. This list shows some of the domains that inform African fractals.

Nature individuals inspired to mimic the fractals they see in nature; motivations in these cases are mainly aesthetic Architecture social status, familial relationships Religion crosses, divination Art Social groups hierarchy, social decorum Culture Fullani blanket, spiritual beliefs



It is difficult to trace the rate of adoption for fractals in Africa. Fractals are deeply rooted in the cultures that use them; they have reached their tipping point and are part of the norm. Chronologically, European mathematicians are what we would call laggards in the adoption of this innovation. They put fractals into use centuries after the African cultures.


There are many examples of recontextualization when looking at the different projects generated by Ron Eglash and his colleagues. A good example is his collaboration with a colleague in Kenya to use fractals for postal address in villages that have fractal structures. A grid system for postal service cannot function on a fractal village.

RECONTEXTUALIZATION African fractals are also being recontextualized by each culture in architecture and art. Modern Architects are using indigenous and modern principles in their designs. Fractals can also be found in tourist art.



FRACTALS ANTECEDENT Nature has a way of using self-similarity and self-organization to create harmony, rewarding us with awe aspiring patterns. In 1977, the French mathematician, Benoit Mandelbrot, identified the self-organizing systems in nature as fractals. 23

TECHNICAL DRIVERS “All the these PDAs and laptops, every digital circuit in the world started in Africa� Dr Ron Eglash, Ted Talk


Bamana Sand Divination The Bamana sand divination in West Africa follows the steps in the image above. It is an exclusive practices learned through initiation only by a few members of community. Bamana priests use deterministic chaos, it is a pseudorandom number generation.

In the 12th century, Santalla brought the Bamana sand divination from Islamic mystics into Spain. It entered the alchemy community as geomancy (divination through the earth)

Hugo Santalla

Took Leibniz’s binary code and created Boolean algebra


George Bool

He talks about Geomancy in his dissertation Decomunitaria “instead of using one stroke and two strokes, let’s use a 1 and a 0; and we can count by powers of two. Ones and zeroes, the binary code.”

John von Neumann Took Boolean algebra and created the digital computer.



Ron Eglash’s African fractal studies and the software he has developed have let to these multi-disciplinary projects.


Teaching mathematics in school Redesign of the postal system in a village in Kenya Design of modern art museum in NYC Modern African Architecture

Through his studies on African fractals, Ron Eglash and his team have created a software that generates fractals based on African fractals. The software is free and available online for anyone to use. African American, Native American, and Latino students can use the software in their mathematics class. This program has enabled better performance from the students. They also have a pilot program in Ghana.

“It is really successful in teaching students that they have a heritage that’s about mathematics, that it’s not just about singing and dancing.” 27

CONCLUSION An innovation is a new idea that can be diffused and utilized by a group of people, influencing their lifestyles and belief systems. Fractals in Africa have gone beyond being a shared technology. They are in most cases the skeleton that holds social structure and a core for belief systems. 28

REFERENCES The Sapling Foundation. 1996. Ron Eglash on African fractals | Video on Ron Eglash. n.d. African Fractals. Eglash, Ron. 1999. African Fractals. Rutgers University Press McGuire, Michael. 1991. An Eye for Fractals. Addison-Wesley Publishing Company Glore, Peter. 2006. Swarm Creativity. Oxford University Press Rogers, Everett M. 2003. Diffusion of Innovations. New York: Free Press





Kidest Mulugeta Sande History of Interpretation and Innovation Prof Christine Miller Ph.D, Winter 2011


A case study on the innovation of African Fractals


A case study on the innovation of African Fractals