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African Religion
Ethopian Cross
As you might have guessed from the architecture, the self-similarity of African art affects the lifestyle and thus the religious views of many African peoples. This changes the way the religion functions, and is shown clearly in many religious symbols like the Ethiopian cross below.
Ethiopian cross 1
Ethiopian cross 2
Roof of a church in Ethiopia showing 3 iterations of a cross
Many of the processional crosses of Ethiopia can be simulated with a three-fold iteration. While they are now used by Christian church proceedings and have symbolism involving the Trinity, related designs can be found on ornaments excavated from the city of Axum in Northern Ethiopia in the second half of the first millennium B.C.E.—more than 300 years before Ethiopia converted to Christianity. What happens when you redraw the shapes using some passive lines?
Ethiopian Cross 1
Ethiopian cross 1
Ethiopian Cross 2
Ethiopian cross 2
Three Crosses
Roof of a church in Ethiopia showing 3 iterations of a cross
Ghanian bull sculpture
Ghanian gold weight
Symbol associated with spiritual force of the river Tano
Previously, we saw that computer scientists often model both living structures and fluid turbulence using logarithmic spirals. The same applies to the traditional artists of Ghana. The spiritual force of life and the spiritual force associated with turbulent water (in the river Tano) are both symbolized by log spirals.
Bull Horn
Ghanian bull sculpture
Complexity and Self-Organization
Low complexity
High complexity
Low complexity
You might think that the more random something is, the more complex it is. But computer scientists measure complexity by how hard it is to model something. Completely ordered things like crystals have low complexity, but so do completely disordered things, because you can easily model them with randomness. Fractals however are half-way between completely ordered and completely disordered. Self-organizing systems like living things and turbulence give rise to the most complex patterns and behaviors. Fractals are a "signature" of self-organization.
Just as computer scientists view fractals as the most complex because they require the greatest computing power, African religions generally use fractal imagery for the gods with the most spiritual power. Gods representing orderly, cyclic patterns (such as Nummo in Mali and Dan in Benin, shown above) tend to have low power. Trickster gods representing disorder, more common in narrative form, tend to have low power. Fractals and related scaling shapes tend to be associated with the power of life (Nyame in Ghana, Mawu in Benin), and hence higher power.
Negative and Positive Feedback
In nature as well as culture, fractals tend to arise when there is a balance of negative and positive feedback loops. Negative feedback keeps things stable, like a thermostat. Positive feedback make things unstable-- a "vicious cycle"-- like economic inflation. In this last exercise, you have a sample shape which represents negative feedback. Because the line segments are small, the general shape is maintained (you can write your name in fractals!). Note the low dimension. You can change this to represent positive feedback by moving the lines to achieve a high dimension. Then, see if you can create a third that balances negative and positive feedback and gives us a "more fractal" looking fractal, with a dimension in-between.