Articles, Blog

Ron Eglash: The fractals at the heart of African designs

November 21, 2019

I want to start my story in Germany, in 1877, with a mathematician named Georg Cantor. And Cantor decided he was going to take a line and erase the middle third of the line, and then 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 two, and then four, 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. (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. He was 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 I’ll stick this somewhere — down there, OK — 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. (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’ll 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 second iteration, and the third, fourth 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. (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 — but 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 400 meters 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 then the chief’s immediate family in that ring. So here’s a little 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 because 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 Mandara 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, first iteration, second, third, fourth. 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 fertility were just like the recursive cycles in the geometric algorithm that builds this. And the recursion in some of 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 — you go inside and here’s pots in the fireplace, stacked recursively. Here’s calabashes that Issa 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 group 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 that 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 because it looks pretty, stupid.” (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, 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, this guy in Mali just outside of Bamako, and I asked him, “How come you’re making fractal fences? Because 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 because 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 wind speed 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. This is a religious matter.” And finally, out of desperation, I said, “Well, let me explain Georg Cantor in 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, “Come here. 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 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 four-bit symbol, you then put it together with another one sideways. So even plus odd gives you odd. Odd plus even gives you odd. Even plus even gives you even. Odd plus 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 of Santalla 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 two.” 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, but you know, I don’t think there’s enough African history in Brian Eno. (Laughter) (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 U.S. 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 that 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 would 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 you 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’s 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.


  • Reply AMN TV December 8, 2007 at 4:51 am

    This is one of the best videos

  • Reply Changeling9au December 8, 2007 at 9:22 am

    Further evidence that "primitive cultures" are anything but primitive. Fascinating!

  • Reply zanussi303 December 9, 2007 at 12:02 pm

    one for the people who think africans are simple and primitive now you jerks can eat your words

  • Reply Alastair Carnegie December 12, 2007 at 7:40 am

    A well deserved 'Standing Ovation'. Next time YouTubers upgrade your notebook computer, please consider making a gift of the old one to an African College. If as Ron Eglash says, 'Binary Notation' started there, those bright kids deserve our generosity.

  • Reply outthetube December 14, 2007 at 7:28 am

    Yeah….he's basically encouraging more stealing from Africa.

  • Reply Joula December 21, 2007 at 3:32 am

    Alot ppl who actually have access to the internet and PC's r idiots.

  • Reply sigma December 23, 2007 at 4:24 am

    Great video. Does anyone have the adress of the site he was talking about? The one with the applets..

  • Reply thedillestpickle December 23, 2007 at 7:29 pm

    can someone help explain where the second column of 4 symbols comes from in his diagram of the pseudorandom generator

    there are 4 rows each ending with a symbol either a 1 or a 1 1 next to this column is another column of symbols but where do these come from initially?

  • Reply xjaskix December 23, 2007 at 8:55 pm

    awesome stuff! *instant subscribe*

  • Reply mutatron December 27, 2007 at 6:52 am

    Google on "african fractals".

  • Reply Adrian Cline-Bailey January 3, 2008 at 10:35 pm

    That was inspirational, i'm from West Africa but been living in London all my life and its fantastic to see that and know that fractals contributed to the world in such a fundamental way, if not pracitically then philosophically. I am amazed, these video's need better marketing.

  • Reply EnigmaticBiker January 8, 2008 at 10:50 pm

    Fascinating blend of cultures, art, craft and mathematics, Great video.

  • Reply Gregory Festo January 15, 2008 at 7:30 pm

    he says you can go to their website… but never mentions the website. anyone know what it is?

  • Reply Sean Aucremanne January 25, 2008 at 12:54 pm

    google ron eglash and go to african fractals under research

  • Reply lionzion22 June 16, 2008 at 11:45 pm

    What you say about New Orleans shows your narrow mind and incompetence when it comnes to what I intially said. Don't you know Amsterdam also had a catastrophic flood? Not only did they rebuild, but they also improved their levee system. Not being above sea level was NOT the cause of the N.O. catastrophe.

    As for blaming those within a society and telling them to "help yourself"…I wonder if you also have these words for 1940s Germany and modern Israel.

  • Reply lionzion22 June 16, 2008 at 11:52 pm

    no home is safe from extreme weather or crime. It's also not safe from whatever government you pay taxes to.

    There is always a larger force than yourself, whether it be elemental or human, and you just may have to put your life on the line. Plain and simple.

    As for Zimbabwe, the model for corruption over democracy was established decades ago and long before Mugabe. Until that root cause is addressed thoroughly, what you see now will always be the outcome.

  • Reply rmeddy1 August 9, 2008 at 5:57 am

    What is the name of that program?

  • Reply Abelard September 2, 2008 at 12:06 am

    What are you talking about? Are you saying fractals are imagined?

  • Reply IAMME000 February 20, 2009 at 10:32 pm

    i think georg cantor had the right idea about seeing god as a fractal. the universe (god) is possibly a self-perpetuated, endlessly expanding fractal, rather than a counscious deity separate from us. just a thought….

  • Reply TerriblePeril April 25, 2009 at 1:38 am

    the ideas were taken and implemented for different things because different social groups have different wants and needs specific to their circumstances and systems.

    simple ideas, with differing outside influences, creates beautiful variety. don't think of it as theft of an idea, or else the humans originating in africa, stole from nature by being born.

  • Reply TerriblePeril April 25, 2009 at 1:42 am

    use the internet, search for 'fractal design' and/or 'fractal architecture' and you should come up with many results. i built a simple cube with drawers based on a much more intricate fractal design. and i'm looking into doing more and more complex physical, and hopefully useful, fractals.

  • Reply Jerome Lam May 12, 2009 at 5:29 pm

    Does anyone knows what software did he use to generate fractals

  • Reply grahamjarman May 14, 2009 at 2:05 am

    i find it interesting people racking their brain to define and find god yet neglecting the improvement we as humans need to do here and now on earth

  • Reply planexzeropoint May 20, 2009 at 12:00 am

    by that reckoning a single celled organism is responsible for everything.

  • Reply TerriblePeril June 5, 2009 at 11:26 am

    theft is stealing of property. we're talking about aesthetics and ideas that adapted over time. i agree that africa has been oppressed and resources stolen, that continues to this day. but you're not even making a coherent statement.

  • Reply clearmenser June 29, 2009 at 10:49 pm

    There's a very good chance he wrote it by hand, purpose built. Recursive functions are conceptually tricky, but every Turing Complete programming language can do it. If you want some good fractal program check out "fractint", it rules!

  • Reply tonyrosam June 30, 2009 at 8:55 am

    Africa Is our forgotton mother. We need to praise her and make sure she is healthy. This feeling for africa is also fractal to your biological mother. i dont mean this in a scientific sense, but emotional. WE NEED TO HEAL AFRICA!!

  • Reply Mike B July 1, 2009 at 2:04 am

    no one gave him one =(

  • Reply KomonHouseholdObjex July 27, 2009 at 11:04 pm

    Good for him.

  • Reply KomonHouseholdObjex July 27, 2009 at 11:07 pm

    It happens because of dry mouth, which happens from being nervous, which happens from public speaking, which happens…. ITS A FRACTAL, MAN.

  • Reply KomonHouseholdObjex July 28, 2009 at 12:40 am

    I think you are an pretty cool guy. You always take things literally and doesn't afraid of anything.

  • Reply tussell r July 30, 2009 at 8:58 am

    allfract-The truth is what it is. You have to really try hard to get something negative from this video. The man found this in Africa and his conclusion is based on that and other findings. He looked at other locations and he even said some Africans did not have a clue about fractals. What location do you want him to be schmoozy over?What do you have to contradict his findings? Get a life. Greed = destruction of someone, that is capitalism at its best

  • Reply Arsalan Ibrahim August 24, 2009 at 11:01 pm

    Interesting how the weak mind responds to what it can't refute by attacking something completely irrelevant to the point.

  • Reply Arsalan Ibrahim August 25, 2009 at 4:18 am

    Have you ever been to Africa? I'm initiated in a few of the traditions he's mentioned. The divination process of the Ifa priests and the Marabu is a binary system of determinative chaos. It consists of 16 symbols logically compared to make 256 sacred verses.

    Every fence in Mali is built the same way, a fractal progression that matches wind speed as it rises from the ground. He showed photos of this and conscious fractal arrangements in city planning.

    What greater evidence do you need?

  • Reply Arsalan Ibrahim August 25, 2009 at 4:29 am

    So let me get this straight. To know anything about myself as an African is to be "bias[ed] for a particular race" but would I be biased if all I had were European interpretations on my profile page?

    What's tragic about this is that you're allowing your own bias to blind you from deeper truths. These African systems present fractals and mathematics at the very core of their cosmology and religion.

    Besides, what evidence do you have to the contrary or to back your indictment of the speaker?

  • Reply Adriano Panes Rinesi November 22, 2009 at 5:55 pm

    haha…. awkward silence at 14:55

  • Reply MrBlaqgold January 31, 2010 at 7:04 pm

    A great video.
    Shame some posters are unable to see beyond their prejudices and celebrate the diversity of human philosophy.

  • Reply oridniv March 5, 2010 at 6:18 pm

    This is the foundation of all infinite possibilities affecting each other. Proves further that nothing is unaccounted for in this universe and it all affects everything else therefore be careful about supporting your own opinions, you could be defending your own ignorance and not see the infinity in everything of everything within everything of everything 🙂

  • Reply Jared Katz May 2, 2010 at 3:19 pm

    @JeromeMatthewLam im wondering the same thing

  • Reply Dancehall Politics June 30, 2010 at 12:15 pm

    @iArsalan I was learning this in African Religions class its too complicated but I had to learn it.

  • Reply hannityforpres July 26, 2010 at 6:46 pm

    @ddsharper Are you kidding?? You can't even teach black kids fractions. They don't get it.

  • Reply cosmopolite1 October 20, 2010 at 9:21 am

    @godofthisshit – Satan is alive and well on planet earth. Read it.

  • Reply cosmopolite1 November 12, 2010 at 2:00 pm

    @godofthisshit Tell that to the new world order and all of its tentacles, to the illuminati who worships him, to the UN and their lucis trust organization, whose new world order is based upon a satanic order.

  • Reply usikuwrites December 8, 2010 at 8:30 pm

    The obvious about true history speaks for itself. The less obvious that was briefly stated is that human life is best when it incorporates nature on larger and larger levels and smaller and smaller levels.

  • Reply Tough Nuggets January 30, 2011 at 7:25 pm

    I was with him all the way up until he started giving us the anticapitalism schtick. Sigh. Funny how "egalitarianism" usually ends up making society more unequal than a straw man capitalist's wettest dream.

  • Reply goyavesETmangues June 13, 2011 at 9:46 pm

    White RACISTS are crying their eyes out while watching this video
    Keep trolling, it makes you look even more pathetic and desperate ^__^
    Typical symptoms of someone who cannot exist or have a strong sense of self without putting others down and feel threatening every time this false sense of superiority is crushed by hard evidences like the facts exposed in this video ^__^

  • Reply goyavesETmangues June 13, 2011 at 9:52 pm

    i meant threatened

  • Reply truselfcrew August 22, 2011 at 10:38 pm

    white people have problem with this video because they have been lied to about africans and european history… Black are the parent race of people…. there is no birth record!

  • Reply Larry Finney October 15, 2011 at 8:44 pm


  • Reply thinkpad20 April 3, 2012 at 8:00 am

    Fascinating. I suppose the history of mathematics might have been very different if some of these African cultures had had a system of organized study and scholarship like Europe did.

  • Reply Archangel Raphael April 11, 2012 at 7:37 pm

    u r an idiot and that is no joke dude.

    the common denominator to African fractals, southwest rock art and even names of YHVH are phosphenes.

    phosphenes explains why cross culture mixing is not necessary to share in the same symbols based on similar geometry as witnessed via the phosphene experience.

    NASA has studied them. There are essentially 15 groups.

    you want to try again?
    how about getting a library card dude?

  • Reply Archangel Raphael April 11, 2012 at 7:59 pm

    Ron FAILS around 7:03 he states "only the African ones were fractal."
    It appears Ron E. and ME are using a different definition for fractal. I thought Fibonacci ratios = phi were related to fractals?

    IF phi is related to fractals then his next statement @7:23 certainly suggests he does not have a clue about how the indigenous Anasazi would have recorded their fractal awareness >>> phi geometry at the small scale is rectangular and then as it expands as a spiral it becomes more circular.

  • Reply Archangel Raphael April 11, 2012 at 8:03 pm

    Here is another FAIL by the PhDuh Ron E.

    He is correct about the Native Americans using circular and four-fold symmetry, but he FAILS to mention the asymmetry of the swastika and the asymmetry of the spiral are more congruent with phi spiral motifs.

    And the distinction must be made between the perfect symmetry displayed by the circle and the imperfect circles most medicine wheels actually are along with many of the 'henges' like Stonehenge which was asymmetric.

    TBC > asymmetric DNA *wink*

  • Reply Archangel Raphael April 11, 2012 at 8:27 pm

    @ 13:25 Ron E. makes another questionable statement and claims it as FACT.

    History shows Leibniz gave credit to the I Ching as a binary system that predated his, and the development of the I Ching comes well before the 12th century alchemy and geomancy.

    Thus every digital circuit of the world may have started in China not the continent of Africa.
    But if you see DNA as a potential algorithm then the start may have been in Africa but later developed in China on a larger self similar scale.

  • Reply ghelyar April 27, 2012 at 1:35 pm

    He went through the initiation ritual for priests just to work out that they used a cyclic xor? This guy has never met cryptography, has he?

  • Reply kojo Ndur May 27, 2012 at 1:38 pm

    I think you are useless than any body on this earth. Have you hear programing before or because it is about Africa? but not pigs

  • Reply Awbrfg55 June 18, 2012 at 8:59 pm


  • Reply Leonard Shelby September 12, 2012 at 7:14 pm

    This shit is amazing! Outstanding!

  • Reply jubileemama2000 October 22, 2012 at 2:37 am

    wow,wow, wow, and double wow!! my people never cease to amaze me!!

  • Reply Archangel Raphael March 11, 2013 at 6:11 pm

    ignorance is bliss, this is your reply?
    why do ignorant twats try to bring the world down to their level called stupid?
    have ewe learned anything these past 9 months?

    Troyintom did ya know that Troy went through 9 levels of evolution….Rome only 7….I find that very interesting.

  • Reply Archangel Raphael March 11, 2013 at 6:14 pm



  • Reply Archangel Raphael March 11, 2013 at 6:18 pm

    p.s. kinshasa orchestra is two thumbs up

  • Reply Ally Bing March 12, 2013 at 4:42 pm

    This is really interesting, but a bit upsetting in the way Mr. Eglash handled the telling of the Bamana sand divination. They were wary about sharing a secret spiritually sacred to them, and yet trusted this man anyways and took the time to get him through the ritual required to be able to learn about it. Then he unashamedly goes and shares it with the entire world. I liked the talk but I'm apologetic towards any Bamana people for the way he disregarded the sacrosanct of their culture.

  • Reply Ryan Reno April 25, 2013 at 4:57 am

    He described the mathematics behind their method, I don't think he divulged any spiritual or cultural secrets. As far as I could tell, it seemed he was respectful toward that culture.

  • Reply mike west July 17, 2013 at 7:53 am

    so do electron clouds and atoms form self-forming patterns? 😉

  • Reply fuck off google July 17, 2013 at 8:59 pm


  • Reply fuck off google July 17, 2013 at 9:01 pm

    Well I think the point is that they let him in on what was going on because he already had an understanding of fractal patterns, and since that is common knowledge in our society already I don't think it's a big deal. Also, what he shared was only a small part of the ceremony, as he described it. I certainly couldn't sit down and recreate this entire ceremony if I tried.

  • Reply MartinDxt September 3, 2013 at 9:39 pm

    in some sense yes since electron clouds are standing waves in 3D (like a standing wave in 1D or 2D which are really cool)
    and repeat for each resonance frequency as you get nearer to the nucleus.
    The term electron cloud is somehow misleading think of it as a 3D standing wave and you'll get a much better idea of it 😀

  • Reply MaNaturalWhispers September 15, 2013 at 5:24 am

    There is no such thing as a concept such as "zero" being "unknown" and ONE person "coming up" with the concept. Mathematics is a reflection of NATURE. It is based off of universal, natural law and therefore, it is inevitable that different people, in different parts of the world…and at different times would "discover" the concept and apply it. Also the "Arabics" that brought us certain mathematical concepts were not really "Arabic", they were Moors (Berber tribe of North Africa)

  • Reply MaNaturalWhispers September 15, 2013 at 5:36 am

    (..says the person who belongs to a culture that has nothing original and thus, steals from evryone else's.) lol! While Africans were building empires in Egypt (Kemet), Ethiopia (Axum), India (Indus Kush Civilization), Greece (yes I said GREECE), Meso-America (Olmecs), North America (Washitaw/Moundbuilders), Spain (Moors), Italy (Moors), West Africa (SoSo/Mende), Jeruselem (Hebrews), and China (Xi)..Caucasoids were still in the mountainous caves eating each other's babies. There is evidence 🙂

  • Reply Nitul shah April 14, 2014 at 7:49 am

    can someone paste the link to the software for producing such algorithms. I would be happy to use it 🙂 Thanks

  • Reply Dale Allender May 4, 2014 at 9:32 pm


  • Reply Phaeces Mars June 21, 2014 at 6:21 pm

    dry mouth

  • Reply gement August 13, 2014 at 10:35 pm

    I was really impressed with his cultural respect until the bit where he says "they inducted me into their religion to trust me with this knowledge so here it is in a powerpoint." 🙁 Other than that, this is really awesome.

  • Reply A. Randomjack October 5, 2014 at 10:27 pm

    Ever since I was introduced to Fractals by Arthur C Clarke, I see them everywhere, from the far reaches of space and time, to biology, weather and human behavior to name a few.
    Fractals is one of the most important concept to grasp on the knowledge trail.
    Although I know it's everywhere, I didn't know it could be found there, and much less it would of have been intentionally designed so long ago. Just shows what daydreamers can achieve if they have enough day dreaming time.
    Lucky Ron Eglash pointed out one more of my misconceptions. Thank you!

  • Reply Raynayk October 22, 2014 at 12:23 am

    So Black Africa use the same fractal system of city building, have the same divination system, play the same game, and have the same numbering scheme… but no, no, no, there is no such thing as a cultural unity of African. If you think so you are an Afrocentric loon who should be shunned by humanity. Good bye.

  • Reply xinavaneify October 31, 2014 at 7:56 am

    Very interesting. It confirms what many of our Africentric scholars have been revealing over the last few decades. The principles are underlying the Ausarian spiritual path of KMT (Ancient Egypt) as well as west African spiritual paths such as Yoruba scientific system. Too bad he still can't grasp that it is connected to DNA.

  • Reply yasina baka May 16, 2015 at 3:54 pm

    Infinite Afrikan genius!

  • Reply Diane Plymel December 3, 2015 at 6:20 pm

    That was awesome! And I've always found fractals to be very fascinating, Have you ever played with a fractal generator? Thanks for sharing this.

  • Reply msGvious January 19, 2017 at 7:55 pm

    OMG, this was just a fabulous presentation. Can't believe Dec 2007 … still rocking!! Brought here by the love of Benoit 🙂

  • Reply Alan S March 7, 2017 at 2:15 pm

    12(57), 46(10), 57(35), 9:11. [23(10)22(3-9)8].

  • Reply Ron Eglash November 9, 2017 at 1:24 am

    I did receive permission from my teacher to make the Bamana algorithm public. The TED format only gives you 17 minutes, and in that time I had to explain what fractal geometry is, how to simulate fractals in African material design, and what the connection is between the fractal design and the indigenous knowledge. So I had to cut a lot of details. I should also mention that the divination priests told me that I was just reading a sentence or two from whole libraries of knowledge; the algorithm itself is just one drop in their recursively infinite bucket.

  • Reply WeylandYutaniInc November 20, 2017 at 6:14 pm

    This is Africans should keep there mouth shut. Europeans will find a way to misuse this knowledge if they have not already.

  • Reply J Taylor March 23, 2018 at 9:14 pm

    Math was born in Africa.

  • Reply Bro. Tolliver July 13, 2018 at 1:44 pm

    This is PEAK TED Talk right here.

  • Reply Sarah Hunter-Munhuweyi August 15, 2018 at 7:31 pm

    This is one of the best videos I've seen.

  • Reply Alexis H-P September 4, 2018 at 12:56 am

    I was only interested in the maths. Its not just about singing and dancing. Interesting view into the way eurocentric perspectives value another culture's knowledge and how they achieved it.

  • Reply الهيبي ابراهيم February 27, 2019 at 4:54 pm


  • Reply EtianEvian May 13, 2019 at 2:51 pm

    *lip smacks*

  • Reply DZ Author July 25, 2019 at 9:43 pm

    For weather geeks, #9:41 begins a conversation of how fractal design is applied to wind engineering

  • Reply Fyjo Molly 非洲茉莉 July 31, 2019 at 8:26 am

    Dr. Eglash please look at ancient Chinese mathematics and The Book of Change. We also used binary calculations on geometry and astrologies. One and two(Yin and Yang) composed the infinity of the universe. Love your study, very informative

  • Reply andrew bryan August 7, 2019 at 3:44 pm

    This how we built our space ships – using fractal generating [maths] we built fracatal generating sytems that enabled us to traval across our galaxy many sols ago. It's how you will build yours, one day.

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