Dreamestorical
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This is in relation to the thread just recently made about Solar winds found to be fractal. Wanted to share this information with coli brethren.
Sophisticated Mathematics Behind African Village Designs / Fractal patterns use repetition on large, small scale - SFGate
Here are some important quotes I highlighted from the piece
Sophisticated Mathematics Behind African Village Designs / Fractal patterns use repetition on large, small scale - SFGate
Here are some important quotes I highlighted from the piece
In 1988, Ron Eglash was studying aerial photographs of a traditional Tanzanian village when a strangely familiar pattern caught his eye.
The thatched-roof huts were organized in a geometric pattern of circular clusters within circular clusters, an arrangement Eglash recognized from his former days as a Silicon Valley computer engineer. Stunned, Eglash digitized the images and fed the information into a computer. The computer's calculations agreed with his intuition: He was seeing fractals.
After detecting the surprising fractal patterns, Eglash began going to museums and libraries to study aerial photographs from other cultures around the world.
"My assumption was that all indigenous architecture would be more fractal," he said. "My reasoning was that all indigenous architecture tends to be organized from the bottom up." This bottom-up, or self- organized, plan contrasts with a top- down, or hierarchical, plan in which only a few people decide where all the houses will go.
"As it turns out, though, my reasoning was wrong," he said. "For example, if you look at Native American architecture, you do not see fractals. In fact, they're quite rare." Instead, Native American architecture is based on a combination of circular and square symmetry, he said.
Pueblo Bonito, an ancient ruin in northwestern New Mexico built by the Anasazi people, consists of a big circular shape made of connected squares. This architectural design theme is repeated in American Indian pottery, weaving and even folklore, said Eglash.
When Eglash looked elsewhere in the world, he saw different geometric design themes being used by native cultures. But he found widespread use of fractal geometry only in Africa and southern India, leading him to conclude that fractals weren't a universal design theme.
Focusing on Africa, he sought to answer what property of fractals made them so widespread in the culture.
"If they used circular houses, they would use circles within circles," he said. "If they used rectangles you would see rectangles within rectangles. I would see these huge plazas. Those would narrow down to broad avenues, those would narrow down to smaller streets, and those would keep branching down to tiny footpaths. From a European point of view, that may look like chaos, but from a mathematical view it's the chaos of chaos theory -- it's fractal geometry."
Eglash said the fractal design themes reveal that traditional African mathematics may be much more complicated than previously thought. Now an assistant professor of science and technology studies at Rensselaer Polytechnic Institute in Troy, N.Y., Eglash has written about the revelation in the book "African Fractals: Modern Computing and Indigenous Design."
"We used to think of mathematics as a kind of ladder that you climb," Eglash said. "And we would think of counting systems -- one plus one equals two -- as the first step and simple shapes as the second step."
Recent mathematical developments like fractal geometry represented the top of the ladder in most Western thinking, he said. "But it's much more useful to think about the development of mathematics as a kind of branching structure and that what blossomed very late on European branches might have bloomed much earlier on the limbs of others.
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."
To remedy that oversight, Eglash said he's been working with African American math teachers in the United States on ways to get minorities more interested in the subject.