If you look closely at the Lideta Mercato — a shopping mall in Addis Ababa, Ethiopia, designed by TED Fellow Xavier Vilalta — you will notice a unique pattern on its skin, inspired by the beautiful, bold patterns found on Ethiopian women’s dresses. But if you look closer, you will also notice something else: that the design is based on fractal geometry.

Xavier Vilalta: Architecture at home in its community In today’s talk, Vilalta shares that when he first was approached about designing this mall, his instinct was “to run away.” He hated the idea of building a big, Western-inspired mall that was generally empty because no one could afford the shops, that needed tons of energy to cool because its glass façade trapped the heat, and that took no inspiration whatsoever from Ethiopian traditions around it. In this talk, Vilalta shares how he approached this design, which is currently in the process of being built, by making the mall more like an Ethiopian open-air market with small shops. Rather than glass walls, he used concrete blocks with square cutouts to create a textile-like façade that would allow cross-ventilation.

But there is one story he didn’t tell in the talk: how he recognized that the pattern of the façade needed to follow fractal geometry. For that story, we’ll need to back up several years, to 2009.

At that time, Vilalta — who lives and works in Barcelona, Spain — had a Catalan client who wanted to build a vocational school in Ethiopia, the Melaku Center. Vilalta tells the TED Blog that, because his architecture is all about connecting buildings to the nature and culture around them, thinking about this project was a challenge. “It was the first time I was operating in an environment that was not like mine,” he said. “Trying to relate the project to the site, I had to really understand a whole new culture.”

Ron Eglash: The fractals at the heart of African designs
He began doing tons of research on design, architecture and culture in Ethiopia and nearby African countries. And he happened upon a book: Ron Eglash’s *African Fractals*. Entranced, he watched Eglash’s TED Talk, “The fractals at the heart of African design,” and kept on reading about how fractals — mathematical, recursive patterns that explain the geometry of nature, with smaller parts mirroring larger parts — also form the basis for the layout of African villages and the patterns that appear in African art.

Vilalta was fascinated.

“I found it extremely interesting, this scientific way of looking at African art and architecture. That was a whole new discovery for me,” says Vilalta. “This opened new possibilities in terms of architectural design. Thinking with fractals and geometry in designs was like a complete new world.”

Vilalta designed the Melaku Center campus — which is as big as three square blocks in Barcelona — on a fractal-based hexagonal grid, creating smaller communities within the school. Classrooms, workshops, administration buildings, a library, living spaces, dining spaces, a health care center, a supermarket and more were laid out in a scalar, circular mesh. Once the design was completed, Vilalta reached out to Eglash with an email. It struck up a working friendship that exists to this day.

Eglash tells the TED Blog, “I get a lot of inquiries, some of them pretty off the wall – hate mail from neo-Nazis, or strange declarations from mystics. Xavier’s email, on the other hand, was the kind you actually want to get.”

After a few correspondences, Eglash mentioned the TED Fellows program to Vilalta, as he had met several TED Fellows while giving his talk at TEDGlobal 2007. Eglash says, “[The Fellows] had a terrific combination of creative energy and practical skills. I knew [Xavier] would fit right in.”

At Eglash’s prompting, Vilalta decided to apply. He joined the TED Fellows class of 2011.

But Eglash’s influence didn’t stop there. Later, when Vilalta was commissioned to design a master plan for a university in Angola, he used fractal geometry again to place each building. And in the Lideta Mercato in Ethiopia, he used fractal design as a means of enclosure.

“The fractal geometry is a part of the design of the façade, it’s done with the same patterns as Ethiopian women’s dresses,” explains Vilalta. “These fractal geometries are used as something that people can relate to, as something of their own culture. But at the same time as something that has function. It’s for ventilating and lighting the building too.”

Eglash gives this new work the thumbs up.

“The Lideta Mercato design is beautiful, of course, but for me it is especially satisfying to see how [Xavier] has managed to nurture the fractal tradition from Africa into this new form, and help the next generation carry that into the future,” says Eglash. “It’s more than just aesthetics: the scaling structure provides a practical means of providing airflow and improving the building’s ecological fit.”

Sure, people walking past the building are unlikely to say, “Oh look, the façade uses fractal geometry.” But the design does strike an unconscious chord. Vilalta tells a story that illustrates this.

“This building is now getting finished, and I saw someone standing in front of the billboard there in the construction site with his wife and pointing to the billboard, and pointing to his wife, and saying, ‘Look, this is like your dress,’” he says. “For me it’s like, ‘Okay, they understood.’ The architecture needs to belong to people, you know? … When people make it theirs, that’s when it feels good.”

Watch Vilalta’s talk for more on the Lideta Mercato and on the biggest project he has ever taken on, an apartment complex called “Le Grand Tapis” in Tunis, Tunisia, which has a truly amazing park on the roof. Watch Eglash’s talk to understand much more about what fractals are and how they underpin African art, design and architecture. And in the TEDxMadrid talk below, hear more about how fractals have infused Vilalta’s work. (English speakers, just turn the closed captioning subtitles on.)

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+ Share Ron Eglash‘s **cool math tools**, for studying math via breakdancing, Latin beats and cornrow braids

+ Dive into Richard Baraniuk‘s **Connexions**, a massive repository of open-source class materials

+ Visit Phil Borges‘ **Bridges to Understanding** site, which rounds up student films from all over the world

+ Browse Erin McKean‘s booklist **“So You Want to Be a Lexicographer?“**

+ Check out the beta of **Gapminder World**, powered by Hans Rosling‘s Trendalyzer software

+ Watch video and take action at **The Hub**, a platform for human rights media and action — presented by Peter Gabriel‘s WITNESS

+ Discuss sustainable design and materials on the **Cradle to Cradle** forums, inspired by the work of William McDonough

+ Learn more about Nicholas Negroponte‘s **One Laptop per Child**

+ Catch up with Majora Carter‘s **Sustainable South Bronx** — or make a specific gift to SSBx via Changing the Present

+ **Calculate your personal CO2 production** — and start helping the planet — at the website for Al Gore‘s *An Inconvenient Truth*, produced by Jeff Skoll

TEDTalks is full of ideas for making change for oneself and for others — many more than we can list here. Please share your suggestions for other TEDTalks-inspired change!

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**Watch Ron Eglash’s talk on TED.com**, where you can **download it**, rate it, comment on it and find other talks and performances.

**Read more about Ron Eglash** on TED.com.

I want to start my story in Germany, in 1877, with a mathematician named Georg Cantor. And Cantor decided he was gonna take a line and erase the middle third of the line, and take those two resulting lines and bring them back into the same process, a recursive process. So he starts out with one line, and then 2 and then 4 and then 16 and so on.

And if he does this an infinite number of times, which you can do in mathematics, he ends up with an infinite number of lines, each of which has an infinite number of points in it. So he realized he had a set whose number of elements was larger than infinity. And this blew his mind. Literally. He checked into a sanitarium. *muted audience laughter* And when he came out of the sanitarium, he was convinced that he had been put on Earth to found transfinite set theory, because the largest set of infinity would be God himself. He was a very religious man. A mathematician on a mission.

And other mathematicians did the same sort of thing. A Swedish mathematician von Koch decided that instead of subtracting lines, he would add them. And so he came up with this beautiful curve. And there’s no particular reason why we have to start with this seed shape; we can use any seed shape we like. And I’ll rearrange this and stick this somewhere … down there, okay … and now upon iteration, that seed shape sort of unfolds into a very different looking structure. So these all have the property of self-similarity, the part looks like the whole. It’s the same pattern at many different scales.

Now, mathematicians thought this was very strange, because as you shrink a ruler down, you measure a longer and longer length. And since they went through the iterations an infinite number of times, as the ruler shrinks down to infinity, the length goes to infinity. This made no sense at all, so they consigned these curves to the back of the math books. They said these are “pathological curves,” and we don’t have to discuss them. *muted audience laughter* And that worked for a hundred years.

And then in 1977, Benoit Mandelbrot, a French mathematician, realized that if you do computer graphics and used these shapes he called “fractals,” you get the shapes of nature. You get the human lungs, you get acacia trees, you get ferns, you get these beautiful natural forms. If you take your thumb and your index finger and look right where they meet — go ahead and do that now — and relax your hand, you see a crinkle, and then a wrinkle within the crinkle and a crinkle within the wrinkle, Right? Your body is covered with fractals. The mathematicians who were saying these were pathologically useless shapes? They were breathing those words with fractal lungs. It’s very ironic. And I’ll show you a little natural recursion here. Again, we just take these lines, and recursively replace them with the whole shape. So here’s the 2nd iteration, and the 3rd, 4th … and so on.

So nature has this self-similar structure. Nature uses self-organizing systems. Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, “This is FABULOUS! I wonder why?” And of course I had to go to Africa and ask folks why. So I got a Fulbright scholarship to just travel around Africa for a year asking people why they were building fractals. Which is a great job if you can get it. *muted audience laughter*

And so I finally got to this city, and I’d done a little fractal model for the city just to see how it would sort of unfold … and when I got there, I got to the palace of the chief, and my French is not very good; I said something like, “I am a mathematician and I would like to stand on your roof.” But he was really cool about it, and he took me up there, and we talked about fractals. And he said, “Oh yeah yeah! We knew about a rectangle within a rectangle, we know all about that.” And it turns out the royal insignia has a rectangle within a rectangle within a rectangle, and the path through that palace is actually this spiral here. And as you go through the path, you have to get more and more polite. So they’re mapping the social scaling onto the geometric scaling; it’s a conscious pattern. It is not unconscious like a termite mound fractal.

This is a village in southern Zambia; the Ba-ila built this village about 400m in diameter. You have a huge ring, the rings that represent the family enclosures get larger and larger as you go towards the back, and then you have the Chief’s ring here towards the back and the Chief’s immediate family in that ring. So here’s the fractal model for it. Here’s one house with the sacred altar, here’s the house of houses, the family enclosure, with the humans here where the sacred altar would be, and then here’s the village as a whole – a ring of ring of rings with the Chief’s extended family here, the Chief’s immediate family here, and here there’s a tiny village only this big. Now you might wonder how can people fit in a tiny village only this big. That’s `cause they’re spirit people. It’s the ancestors. And of course the spirit people have a little miniature village in their village, right? So it’s just like Georg Cantor said, the recursion continues forever.

This is in the Mondara mountains, near the Nigerian border in Cameroon, Mokoulek. I saw this diagram drawn by a French architect, and I thought, “Wow! What a beautiful fractal!” So I tried to come up with a seed shape which, upon iteration, would unfold into this thing. I came up with this structure here. Let’s see, 1st iteration, 2nd, 3rd, 4th. Now, after I did the simulation, I realized the whole village kind of spirals around, just like this, and here’s that replicating line, a self-replicating line that unfolds into the fractal. Well, I noticed that line is about where the only square building in the village is at. So, when I got to the village, I said, “Can you take me to the square building? I think something’s going on there.” And they said, “Well, we can take you there, but you can’t go inside. Because that’s the sacred altar, where we do sacrifices every year to keep up those annual cycles of fertility for the fields.” And I started to realize that the cycles of were just like the recursive cycles in the geometric algorithm that builds this. And the recursion in these villages continues down into very tiny scales.

So here’s a Nankani village in Mali. And you can see, you go inside the family enclosure and here’s pots in the fireplace, stacked recursively. Here’s calabashes that Issa Diabate was just showing us, and they’re stacked recursively. Now, the tiniest calabash in here keeps the woman’s soul. And when she dies, they have a ceremony where they break this stack called the zalanga and her soul goes off to eternity. Once again, infinity is important.

Now, you might ask yourself three questions at this point: Aren’t these scaling patterns just universal to all indigenous architecture? And that was actually my original hypothesis. When I first saw those African fractals, I thought, “Wow, so any indigenous that doesn’t have a state society, that sort of hierarchy, must have a kind of bottom-up architecture.” But that turns out not to be true.

I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes they use. So Native Americans use a combination of circular symmetry and fourfold symmetry. You can see on the pottery and the baskets … Here’s an aerial photograph of one of the Anasazi ruins; you can see it’s circular at the largest scale, but it’s rectangular at the smaller scale, right? It is not the same pattern at two different scales.

Second, you might ask, “Well, Dr. Eglash, aren’t you ignoring the diversity of African cultures?” And three times, the answer is no. First of all, I agree with Mudimbe’s wonderful book

, The Invention of Africa, that Africa is an artificial invention of first colonialism and then oppositional movements. No, because a widely shared design practice doesn’t necessarily give you a unity of culture — and it definitely is not “in the DNA.” And finally, the fractals have self-similarity — so they’re similar to themselves, but they’re not necessarily similar to each other; you see very different uses for fractals. It’s a shared technology in Africa.

And finally, “Well, isn’t this just intuition? It’s not really mathematical knowledge. Africans can’t possibly really be using fractal geometry, right? It wasn’t invented until the 1970s.” Well, it’s true that some African fractals are as far as I’m concerned just pure intuition. So some of these things, I’d wander around the streets of Dakar asking people “What’s the algorithm? What’s the rule for making this?” and they’d say, “Well, we just make it that way `cause it looks pretty, stupid.” *muted audience laughter* But sometimes, that’s not the case. In some cases, there would actually be algorithms, and very sophisticated algorithms. So in Manghetu sculpture, you’d see this recursive geometry. In Ethiopian crosses, you see this wonderful unfolding of the shape.

In Angola, the Chokwe people draw lines in the sand, and it’s what the German mathematician Euler called a graph; we now call it an Eulerian path — you can never lift your stylus from the surface, and you can never go over the same line twice. But they do it recursively, and they do it with an age-grade system, so the little kids learn this one, and then the older kids learn this one, and then the next age-grade initiation, you learn this one, and with each iteration of that algorithm, you learn the iterations of the myth. You learn the next level of knowledge.

And finally, all over Africa, you see this board game. It’s called Owari in Ghana, where I studied it, it’s called Mancala here on the east coast, Bao in Kenya, Sogo elsewhere. Well, you see self-organizing patterns that spontaneously occur in this board game. And the folks in Ghana knew about these self-organizing patterns and would use them strategically. So this is very conscious knowledge.

Here’s a wonderful fractal. Anywhere you go in the Sahel, you’ll see this windscreen. And of course fences around the world are all Cartesian, all strictly linear. But here in Africa, you’ve got these nonlinear scaling fences. So I tracked down one of the folks who makes these things, a guy in Mali just outside of Bamoko, and I asked him, “How come you’re making fractal fences, `cause nobody else is?” And his answer was very interesting. He said, “Well, if I lived in the jungle, I would only use the long rows of straw. Because they’re very quick, and they’re very cheap. It doesn’t take much time, doesn’t take much straw.” He said, “But wind and dust goes through pretty easily.” Now, the tight rows up at the very top, they really hold out the wind and dust. But it takes a lot of time, and it takes a lot of straw, `cause they’re really tight. Now, he said, “We know from experience that the farther up from the ground you go, the stronger the wind blows.” Right? It’s just like a cost-benefit analysis. And I measured out the lengths of straw, put it on a log-log plot, got the scaling exponent, and it almost exactly matches the scaling exponent for the relationship between windspeed and height in the wind engineering handbook. So these guys are right on target for a practical use of scaling technology.

The most complex example of an algorithmic approach to fractals that I found was actually not in geometry, it was in a symbolic code, and this was Bamana sand divination. And the same divination system is found all over Africa. You can find it on the east coast as well as the west coast, and often the symbols are very well preserved, so each of these symbols has four bits — it’s a four-bit binary word — you draw these lines in the sand randomly, and then you count off, and if it’s an odd number, you put down one stroke, and if it’s an even number, you put down two strokes. And they did this very rapidly, and I couldn’t understand where they were getting — they only did the randomness four times, I couldn’t understand where they were getting the other 12 symbols. And they wouldn’t tell me. They said, “No, no, I can’t tell you about this.” And I said, “Well look, I’ll pay you, you can be my teacher, and I’ll come each day and pay you.” They said, “It’s not a matter of money.” It was a religious matter.

And finally, out of desperation, I said, “Well, let me explain Georg Cantor and 1877.” And I started explaining why I was there in Africa, and they got very excited when they saw the Cantor set. And one of them said, “C’mere, I think I can help you out here.” And so he took me through the initiation ritual for a Bamana priest. And of course, I was only interested in the math, so the whole time, he kept shaking his head going, “You know, I didn’t learn it this way.” But I had to sleep with a kola nut next to my bed, buried in sand, and give seven coins to the seven lepers, and so on. And finally, he revealed the truth of the matter. And it turns out it’s a pseudo-random number generator using deterministic chaos. When you have a 4-bit symbol, you then put it together with another one sideways. So even + odd gives you odd. Odd + even gives you odd. Even + even gives you even. Odd + odd gives you even. It’s addition modulo 2, just like in the parity bit check on your computer. And then you take this symbol, and you put it back in so it’s a self-generating diversity of symbols, they’re truly using a kind of deterministic chaos in doing this. Now, because it’s a binary code, you can actually implement this in hardware — what a fantastic teaching tool that should be in African engineering schools.

And the most interesting thing I found out about it was historical. In the 12th century, Hugo Santalia brought it from Islamic mystics into Spain. And there it entered into the alchemy community as geomancy, divination through the Earth. This is a geomantic chart drawn for King Richard II in 1390. Leibniz, the German mathematician, talked about geomancy in his dissertation called De Combinatoria. And he said, “Well, instead of using one stroke and two strokes, let’s use a one and a zero, and we can count by powers of 2.” Right? Ones and zeros, the binary code. George Boole took Leibniz’s binary code and created Boolean algebra, and John von Neumann took Boolean algebra and created the digital computer. So all these little PDAs and laptops — every digital circuit in the world — started in Africa, and I know Brian Eno says there’s not enough Africa in computers; you know, I don’t think there’s enough African history in Brian Eno. *applause*

So let me end with just a few words about applications that we’ve found for this. And you can go to our website, the applets are all free, they just run in the browser, anybody in the world can use them. The National Science Foundation’s “Broadening Participation in Computing” program recently awarded us a grant to make a programmable version of these design tools, so hopefully in three years, anybody’ll be able to go on the web and create their own simulations and their own artifacts. We’ve focused in the US on African-American students as well as Native American and Latino. We’ve found statistically significant improvement with children using this software in a mathematics class in comparison with a control group that did not have the software. So it’s really very successful teaching children they have a heritage that’s about mathematics, that it’s not just about singing and dancing. We’ve started a pilot program in Ghana, we got a small seed grant, just to see if folks’d be willing to work with us on this; we’re very excited about the future possibilities for that.

We’ve also been working in design; I didn’t put his name up here, my colleague [Kerry] in Kenya has come up with this great idea for using fractal structure for postal address in villages that have fractal structure, because if y

ou try to impose a grid structure postal system on a fractal village, it doesn’t quite fit. Bernard Tschumi at Columbia University has finished using this in a design for a museum of African art. David Hughes at Ohio State University has written a primer on Afrocentric architecture in which he’s used some of these fractal structures.

And finally, I just wanted to point out that this idea of self-organization, as we heard earlier, it’s in the brain. It’s in the … it’s in Google search engine. Actually, the reason that Google was such a success is because they were the first ones to take advantage of the self-organizing properties of the web. It’s in ecological sustainability, it’s in the developmental power of entrepreneurship, the ethical power of democracy. It’s also in some bad things. Self-organization is why the AIDS virus is spreading so fast, and if you don’t think that capitalism, which is self-organizing, can have destructive effects, you haven’t opened your eyes enough. So we need to think about, as was spoken earlier, the traditional African methods for doing self-organization. These are robust algorithms. These are ways of doing self-organization, of doing entrepreneurship, that are gentle, that are egalitarian. So if we want to find a better way of doing that kind of work, we need look only no farther than Africa to find these robust self-organizing algorithms. Thank you.

Transcription by Janis Cortese

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**Erik Hertsman at White African reports: Google has hired its first sub-Saharan Africa employee!**

Joseph Mucheru has been named the new site lead for Google Kenya. This was whispered to be happening, but at today’s Google lunch at TEDGlobal the position was made official by Francoise Brougher, Director of Google Business Opportunities.

**Mentalacrobatics posted a fascinating blow-by-blow of his Day Two, ending with this wonderful image:**

Back at the hotel is when TED came home. I sat down to write my thoughts on the day when Harinjaka shared with us the crazy deforestation that is taking place in his country of Madagascar. That was the beginning of all night thinking, sharing, debating session. Two Kenyans, one Madagascan, one Nigerian, one Italian, one American. We had never met before TED, all but one of us are at our first TED conference and we had our own TED session then and there. We talked about HIV/AIDS, about social disempowerment, about colonial legacy, about Nollywood, Bollywood and the Chinese film industry, about music, about deforestation in Madagascar …

**Afromusing was captivated by Ron Eglash’s work on African fractals, including a web tool that integrates fractal design and hair braiding:**

!! Indeed !!

Design cornrows using transformational geometry. Click here.

Ron Eglash spoke on looking at fractals in African architecture and design. For non comp sci people, fractals make for some of the most beautiful designs. For African geeks, egm and mathematicians, get the book.

**David McQueen blogged his highlights from the second day:**

Idris Mohammed – The suggestion of a “Fund of Funds” from G8 as a means of smarter aid. Encourage Africans or Europeans who can invest in Private Equite Fundraising. Remove the focus from “Poverty Reduction” and place more emphasis on “Wealth Creation”.

**Don at fifthculture shared a ride with investor and TED Day 2 speaker Idris Mohammed:**

Idris Mohammed, a private equity pioneer, said that energy is the next big job in Africa. … I had the opportunity to ride to the hotel from the airport with Idris. I asked him what form of power (fossil fuels, wind, hydro), he said that most likely it would be fossil fuels. It seems we can’t avoid creating problems even when we are solving them. Both options are grave.

**Mweshi‘s roundup captured the buzz around entrepreneur Ted Kidane:**

… a wonderful talk by Ted Kidane of Feedelix which is a mobile phone piece of software that enable text messaging in non-Latin scripts. But the thing that stood out the most about Ted’s talk was his challenge to everyone in the room to change the manner in which they look at the word POVERTY; which in his words defined as Prosperity, Opportunity, Validation, Enthusiasm, Resilience, Trust and Yes!

**Big, brave ideas are flying around. Ellen Horne reports on a lunchtime conversation:**

Today, I sat down at lunch with three African men. One was a grad student from Cape Town, S.A., and the other two were ex-pats from Ghana – living abroad but very much engaged in a conversation about the reasons that Africans leave. The conversation turned to the topic of corruption. How to address the massive short-term incentives for supporting the ‘big man’ power system fueled by corruption. One quickly brainstormed talked about a public humiliation website where people could anonymously post photos of bribes being given. I asked innocently ‘Why would someone exchange bribery cash in public?” He agreed — sure you aren’t going to get many — but maybe the few would set a powerful example — and hopefully not a unique one.

And as always, for minute-to-minute coverage of the conference sessions, turn to **Ethan Zuckerman** at My Heart’s in Accra.

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“What we call governments are vampire states, which suck the economic vitality out of the people.” *— Economist George Ayittey*

“I want to make Africans rich. If you make Africans rich, they’ll be less poor. That’s my development strategy.” *— Private equity pioneer Idris Mohammed*

“What we’re trying to do is create a family tree for everyone alive today.” *— Anthropologist and geneticist Spencer Wells, who’s leading the Genographic Project, a landmark study tracing human origins to their roots in Africa*

“There is no region of the world and no period in history that farmers have had to bear the burden of risk that African farmers bear today. But I’m not here to lament or wring my hands. I’m here to tell you that change is in the air.” *— Economist Eleni Gabre-Madhin, who is founding the first commodities market for farmers in Ethiopia*

“World progress needs a good dose of spontaneous human intelligence to realize that the answers to many of the questions we ask ourselves are just around the corner.”* — Architect Issa Diabete, who draws inspiration from innovative, makeshift urban solutions found in Africa’s sprawling squatter cities*

“I’m hopeful because nature is amazing resilient. Seemingly dead tree stumps — if you stop hacking them for firewood, in 10 years you can have a 30 ft tree.” *— Primatologist and conservationist Jane Goodall*

“I am a mathematician and I would like to stand on your roof.” *— Mathematician Ron Eglash’s standard greeting to African families, when he was researching the intriguing fractal patterns observed in many villages across the continent*

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And now we step sideways to exercise other parts of the brain: Stanford-based bioengineer Kwabena Boahen gave a brain-twisting overview of his research, which aims to first understand how brains work, and then build a computer that works more like the brain. His beautiful simulation of neurons at work, and cogent explanation of the brain’s networked approach to data transmission had all synapses firing.

From neural networks to urban grids… Architect Issa Diabaté took us next on a tour of African cityscapes that inspire his work. Clean lines and well-executed plans hold less interest for him than the messy, makeshift solutions so common in growing cities. “World progress needs a good dose of spontaneous human intelligence to realize that the answer to many of the questions we ask ourselves are just around the corner”

And from urban grids to fractal-shaped villages… “Ethno-mathematician” Ron Eglash set my mind on fire with his talk, explaining the research that led to his book, *African Fractals*. By looking at aerial-view photos — and then following up with detailed research on the ground — Eglash discovered that many African villages are purposely laid out to form perfect fractals, with self-similar shapes repeated in the rooms of the house, and the house itself, and the clusters of houses in the village. The shapes and algorithms vary from village to village (and not all villages are laid out this way), but always correspond perfectly to mathematically predictable patterns — the same sort of patterns we see in nature (in Acacia trees and fern leaves and snowflakes). Isn’t that fascinating? And bizarre? And: What does it mean? I don’t know, actually. But I can feel some theories coming on …

**For more extensive descriptions of each talk**, see **Ethan Zuckerman**‘s real-time posts on Kwabena Boahen, Issa Diabaté, Ron Eglash and Russell Southwood.

*Watch for these talks on TED.com beginning midsummer 2007.*

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