On Tigers, diffusion and chaos

Tiger

RT @sanchan89 Always good to know that my mojo is still intact after 4 years 🙂 Take a look http://bit.ly/bGv5su

So, after quite a while, I tried sketching again. And it came out pretty neat, I suppose. But then, I want this to be a tech blog, right?

We humans, have a somewhat dull skin[1]. It is completely bereft of any fur[2] and any pattern to be had on are to be painfully tattooed. Look, on the other hand , at the pervasive presence of spacial patterns on animal coats and flora. Most commonly seen in plants are the rosette patterns, and self replicating branching systems. Mammals and fishes are so much richer – their fur coats come with stripes, spots, rosettes, bands, blocks, combination of these  and in the case of some sea shells – Serpenski triangle! Even in animal behavior, there is so much elegance – if you have not seen the movements of large schools of fish or birds in flight, you have a serious problem and you should consult a psychotherapist. Even the inanimate desert sands are beautifully patterned with near parallel curves.

Spatial patterns collage

Spacial patterns collage

It makes us think, doesn’t it? How are these patterns formed?

If every skin cell were to take on either black or white color with a uniformly random probability, then a zebra would look like white noise. Try imagining one with a coat like that. No probabilistic distribution is ever going to generate patterns as fantastic as those on every tiger. Does every cell, then, have a global spacial view of itself? Is it possible that a single cell knows that it is a part of the stripe across the head of the tiger, and therefore, it should take on a black pigmentation? That seems like something phenomenally complex for a single living cell to know.

Related problems in developmental biology are cell differentiation, and Morphogenesis. Every cell in an embryo is the same. Embryos are homogenous; and yet without a single central controller, cells in different areas of the embryo develop into different parts of the body. Some develop into the the heart and lungs and others into brain and legs.

The first explanation for this phenomenon was provided by the British Mathematician, code breaker, logician, computer scientist ( and during the later days of his life, a chemist )  Alan Turing in his paper titled ‘The Chemical basis of Morphogenesis” in 1951.  ( This paper has its own wiki page ) The paper described mechanisms; borrowing heavily from concepts of self-organisation, well known in physics; by which non-uniformity may arise from uniform homogeneous states, and outlined the reaction-diffusion theory of morphogenesis. Reaction–diffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space.

Independently, around the same time a Russian biophysicist Boris Belousov discovered a reaction-diffusion system, now called the Belousov-Zhabotinsky reaction. Where Turing had proposed mathematical models, here was already a demonstration of the self-organizing tendencies of the non linear systems which he had proposed. Here’s a video of a BZ cocktail evolving

From a uniformly homogeneous solution – spirals, spots and expanding rings are formed. And no two instances of the same experiment will get you the exact same results. The equations that govern these reactions are so expressive that you can actually come up with results that show stripes and hexagons! Try it out yourself in this applet.

These two works are considered by some as the founding work on chaos theory. In a nutshell, Chaos theory deals with highly nonlinear and usually self looped systems that despite being fully deterministic, are subject to abrupt and seemingly random change. It is clear in this case –  In spite of explicitly and deterministically defined rules, the reaction-diffusion yields a uniquely different result every time. The source of all this chaos is, well…, in the source itself. The non-linearity of the system greatly magnifies even immeasurably small changes in the initial state. So, the next time you round up a value from 0.506127 to 0.506, be warned! As a sidenote, the phrase “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?“, is not a misunderstanding of chaos theory. It is in fact the title of the talk presented by Edward Lorenz at AAAS, 1972 on chaos theory. The title was the result of inferences from a run of the simulation he had built, when he changed one of the values of atmospheric conditions as stated above.

If you are interested in learning more about Chaos theory, there is a fantastic one hour program on BBC. No, it does not have equations ( well, maybe just one )

  1. Well, thats not entirely true! We have fingerprints. And they are beautiful and unique, but not colorful or macro. Guess that still qualifies as dull.
  2. This is interesting because, man is the only mammal; excluding those that are aquatic, that has no fur, check out the February 2010 edition of Scientific American

Further reading

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A new kind of a Game

It doesn’t look visually enticing, but I am pretty sure its darn good. No, I have not played the game yet.

NERO

Now, I wasn’t expecting to write a post on a game, any time soon. Not even on DotA. But this is just too good a game for me to resist. I have been quite intrigued by the concept of Evolutionary Computation. One lazy Sunday, I started looking for more stuff on Evolutionary Computation. I found a lot. Particularly, a post-doctoral researcher’s blog. Julian Togelius. He’s published a paper on solving Sudoku using Genetic Algorithms. Serious stuff that! One of his other papers have been judged as one of the top ten AI game innovations of the year. This dude was one of the organisers of a Simulated Car Racing Championship atWCCI 2008. It seems there are not a lot of games available that actually use the latest Learning Techniques.

It was very funny in the beginning when I looked at the games’ graphics( WCCI ). Not a ‘Need for Speed’ then. On further reading, I found more on the rules of the game. From a programmer’s stand point, I thought, not very easy to program a controller. All the various cases. How could it adapt?? Perhaps learn?? Neural Networks then?? Neural Networks are to put it very very simple terms, like a brain. ( Please note that this is a gross over-estimation, it resembles the brain only in that it can learn new stuff. It is not even close to the functioning of a brain ). Perhaps neural networks would have been the answer if the same question had been put forth a few years ago. Today, ANNs alone will not suffice!!

Genetic Algorithms are now used to train Neural Networks. OK. Imagine you are given the job of teaching something to someone. If you couple GA with ANN, it’d something like, you just have to tell the person, how well he has learnt the subject, and he’ll keep improving all by himself. ( Of course, this is another gross over-estimation. If this is very non-technical please refer to one of the links given in the side )

It just got more interesting after that. I learnt that one of the Car controllers was evolved using rtNEAT( real time NeuroEvolving Augmenting Technologies ) developed by Kenneth O Stanley at University of Texas at Austin. NEAT not only evolves the best neural network of a given structure, it also evolves the best structure for the purpose. Fantastic stuff. As I kept reading, link after link. I get here. The page gives a detail overview of how NERO is played and how it is being developed. Please do read it. Its an interesting read. You’ll start wondering what kind of games will be the next big trend.

I have added on my links lists some of the more interesting blogs I have found during my research. Anyone interested in AI, please do have a look at these pages. I definitely plan on writing more posts on my own discoveries on the Web about AI, more particularly, Evolutionary Computing. And next time, I hope I try to convey more technically what I actually wish to convey. Cheers.

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