Living with Fractals

Fractal math is a longstanding tradition in African cultures.

see previous posts:

Ron Eglash explored the self-similar design of African art, architecture and living design. He travelled around Africa and discovered these fractal designs in a variety of cultures in a variety of countries. It is a widespread way of thinking on the mother continent, and is not widespread beyond it. We have much to learn from these. Fortunately, Eglash has provided an online tool to do so.

Above is the plan for a Ba-ila village in southern Zambia. the self-similar horseshoe shape not only recurs around and within the village, but it also reflects a certain social standing. The focal settlement is the chief, who is surrounded by immediate family, then extended family. Also of interest is a small scale-model village, which is the place where the spirits (ancestors) live. This small village also contains a tiny village, which is consistent across levels of scale. It’s an amazing design.

Labbazanga in Mali, displaying a recurring of circular design

Time and Place or Spacetime

I’ve already gone on at length about fractal time (see links at the top of the post), but here we have a nice new (to me anyway, that talk is already 4 or 5 years old) physical incarnation to add to the mix. I attest that time is fractal in nature, or at least self-similarly recurring, and thinking in terms of recurring archetypes is a healthier way to see the world than simply as the iteration of unique individuals (bit of both is the healthies approach – no one of anything, no two the same, right?) along a linear timeline.

So with this fractal, or self-similarity of design. It is not unique to African cultures, however, it has been fundamental to their art and visualizations for far longer. With the advent of computers, fractal art has been making progress.

What I’d like to see is something akin to the Inca civilization – their calendar was writ in the landscape of their empire, such that the landscape held monuments that represented the position of the sun throughout the year, dividing the land as we divide the heavens and time, with imaginary lines. If our concept of time is recurring self-similarity, and our urban design were to follow suit, the two could be brought into alignment to create a harmonized living environment.

I don’t know if the African examples that Eglash explored incorporate a fractal or self-similar idea of time to accompany the village organization, however, this would strike me as an ideal balance between time and space in a manner that is both aesthetically and mathematically sound. The specific African Calendars I’ve discovered are:

  • Akan calendar (Ghana & Ivory Coast): 42-days of interlocking market weeks (doesn’t seem fractal). Check out here for more.
  • Ethiopean (and Eritrean): 12 months of 30 days with 5 extra – based on Egyptian calendar – not fractal as it doesn’t take larger measures into account, although the recurrence of regular 30-day months could be the base for such a time-reckoning.
  • Igbo Calendar (southern Nigeria): 4-day week, 7-week month, 13 month year (ie 364 days +1). Although deeply ritualistic, with months tied to different dieties and activities, it’s difficult to say if this is fractal, although the potential exists.
  • Yoruba Calendar (Nigeria, Benin, Togo) – as the Igbo calendar, but with concessions made post-colonialization – ie. 52-week year
  • Namoratunga (NW Kenya) – astro-archeological site with 19 basalt pillars aligned to constellations
  • Rwanda, Tanzania, Cameroon, Togo,  [Democratic Repuglic of Congo], Ghana, Nigeria, and the Upper Volta all used different lengths of market weeks, which suggests that the peoples of these countries (and most certainly beyond) had their own methods of daykeeping, which may or may not have been self-similar, fractal, or had anything to do with their village & art design. This bears further research.


Using these examples of fractal design from Africa would certainly be a step in the right direction over the clusterfuck of urban design as in Ottawa, where the cycles of planning and development follow election cycles, and often cave to public interest groups. This city is build as if it was designed by a sandbox full of sugar-amped ADD children.

It’s entirely possible to do it. All we need is the collective will, and the means to do it. Strength + balance = beauty.

255 Days to Dec 21st 2012

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