[MUSIC] Okay, so what Alan Touring did when he studied this, he certainly proved, conclusively, that was the case. In one single entity, you cannot get anything but symmetry in the end. The things flattens out. So very boring. But he said, you could have interesting pattern, that destroying symmetry by having something little different. You should have at least two Interacting bio-chemicals. We can call them different things, but let's for the moment, just for the sake of discussion call them bio-chemicals. The word morphogen has been used. In any case, some of these morphogens, some of these bio-chemicals, are activators. They sort of stimulate things. That the other kind is an inhibitor, a sort of preventing things from happening. So to have anything interesting, you should have at least one activator and one inhibitor in your mix, in that organism. And you allow them also to diffuse. You have to allow them to diffuse as you do with heat. So diffusion is taken for granted with an activator and an inhibitor interacting. And you allow them to diffuse at different rates. Then you have some interesting thing happening. Here's a slide to summarize what the requirements are. So Turing then predicted, with this combination, few things. Allowed any organism not to have just a boring developement. In fact, if you have, again, the decomposition of a pattern, initial pattern, into different things, different components from the basic set, then it is not the case that the slowest oscillatory component stays around. In fact, what stays around is somewhat, is predictable but it has to be done in calculating, worked out depending on the parameter value in the system, that is, the characteristics of the system. How, whether your stimulation is short-range or long-range. Their inhibition is long-range or short-range. If you have directional diffusivity, and whether you have size, a size of a certain kind and aspect ratio of certain level. So all these dictate what kind of a pattern you will get and not just always getting to the boring symmetric, even things out situation. And so this is summarized in a sense that formerly defined what Turing, so-called Turing Instability is. It destabilized symmetry to form interesting patterns. And a Dominant Pattern that survives may not be the one with least oscillation. For example, here's the same long one dimensional organism, except now because you have more than one bio chemical interacting within the organism, you can have pattern. Because of the size and the aspect ratio, the patterns are not as interesting, but still more interesting then the completely symmetric zero flat pattern. This is what is predicted by Turing's theory. Nowadays, with the computing power we have, we can generate them easily. You can go look at the real life animals you see around us. And you see exactly what is seen in nature is pretty much, predicted by Turing's theory. And there's some more. The one on the left is new. The patterns are different from this rings. The one on the left, the black and white on the left is what the computer generated for a certain combination of system characteristics. On the right is what you see in a leopard. So, similarly with the other one. And then some more complicated ones, the hind of the zebra. And the left is what's predicted by the Turing's theory and with the help of the computer, perhaps modified a little bit by some modern formulation. And the right is what you see in a zebra, the hind. So in general, you would say that that's all ready allowed us to have kind of an interesting combination of things. But things get a little more interesting because in two dimensions, for example, you have much more possibility. What do I mean by that? Look at the one dimensional case. Cosine 7x certainly oscillate more and faster, often, than cosine x, which is just much slower. Only one oscillation would hit the certain interval. On the other hand, in two dimension, cosine x and cosine 8y, does it oscillate more than cosine 7x and cosine 4y? The answer is, they are the same, in a certain sense, cuz one squared plus A squared is the same as four squared plus seven squared. They're all 65. Come out to be 65. In that sense, the two combinations of patterns are not different, in terms of oscillations. So, with these many different aspects contributing to interesting patterns, you now can see the leopard can have much more interesting pattern than something else that we seen in a single entities like, okay, zebras. Then in general, Turing also said size is important. In certain sense, when you're too small you can not have much pattern. And you're too big, you don't have much pattern either. That's what's predicted by the theory. And on the computer simulation, you can use this theory to generate things of different size using the same, for the same constitution of the organism. And you see when it's very small, it's completely black. When it's slightly bigger, you've gotten to half and half, and so on. And when it gets big enough, it becomes more complex. And then the next one is even more complex as it grows. But when it grows beyond a certain level, it begins to blacken out the more uniform again, and in the end you get all black. And for that reason you see elephant because of the aspect ratio and the size which falls in the category predicted by Turing to have no interesting patterns. And when the elephant is small, well, large and small is the same in this case. Similarly, lions, compared to the leopard, even though it's roughly the same size but because of the constitution, it's constitution, it doesn't, by that I mean the inhibitors and long range or short range, the stimulators and so on. They don't have much interesting pattern. Okay, many biological organism grows with age. So, when you're young, you're small, the size is small. And when it gets older, it becomes bigger. But by Turing's theory, the small size should not have interesting pattern. But when it gets big enough, some new pattern would emerge. And this is precisely what happened to the penguin, right? On the left, when it was still young, just hatched, it was kind of interesting. But when it grew up to full size, is much more complex. And leopard is similar. The zebra, he is only changing color, but not as drastic. And so, in the end, Turing's remarkable theory have very few ingredients. The biology is minimum. Just a few inhibitors and inactivators. It requires a size deterred showing an aspect ratio determining what comes out. And then you have different diffusive rays in different directions, that's even better. So here's one that's predicted by his theory in terms of given constitution. You see the spots are different from the stripe of the zebra. This is precisely the pattern that you've seen in giraffe. Okay, let's come back to this changing with size business. At the left is, I say when it's very small for this particular combination of characteristics of the internal constitution, this artificial organism if generated by the computer has no pattern, all black. But slightly bigger, becomes black and white and then so on, we become more complex. We've seen this earlier. But the reason that I come back to this is that certainly, you could see that what is certain size, I don´t have a better example but, the panda, so has soul like what you see in one of the guys on the right. So it's not too far but I´m sure that you can find something similar by look hard enough. But what about the one on the second one? Okay, the second one seems kind of unreal, right? One all black in front and all white in the back, half and half? No such thing has been seen before, so this theory seems to be a little absurd. But if you go look at Jim Murray's article in American Scientist, many years ago, he reported that some people find exactly that animal of that combination of color, black and white, black in front, white in back, just half and half, a pig. He found it in Africa. So in this sense, while we don't know and we haven't seen everything on Earth, the theory of Turing and his generalization allow us not only to explain, confirm a lot of pattern that we see in the biological system. But it also allowed us to predict what could be, and what may be, and what might have been. Just that we haven't seen it. We just haven't gotten around to finding it. So in that sense, there's a possibility of emerging phenomena lying in wait for us in biological patterns. And for that, we remind you the leopard that has the spots, as Jim Murray article's name, that's where you can find more information about this whole theory. And then folks, you might not see what this says. But if you clean it up a little bit, with so called image enhancement, you see thank you, folks. Well why did I show you this slide? Because this whole idea of highly oscillated component dies out first. Well, the highly oscillated components are the noise. And in the one before, you have all this flickle flickle, they are noise, they are highly operating components. And if you run this through the Turing system, you will filter out all the noise and you get a better picture. Thank you. Bye.