Neko Time!!! =^_^= matthen

Last week I spend some days in Cambridge performing some experiments at the university,l and as always happens when I go to Cambridge, I learn something new.

This time I came across Matt Henderson blog.

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Matt has a mathematics degree by Cambridge University, and he is now working on his PhD on statistical dialogue systems.

He is an unstoppable explorer. His blog is full of experiments and nice mathematical simulations. And here I want to show you which are the ones I like the most. Who knows, maybe a collaboration between us could be possible in the future.

So, here they are.

Aggregation.

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Basically, if you have particles moving randomly and they are able to become added to a seed, then these random patterns appear. They are close related to chemical reactions and electrical transport. Nice post, with code, and a link to.. Agregation images by Andy Lomas.

Gingerbreadman.

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Gingerbreadman is a chaotic map. Basically, you select random points in the plane and using very simple equations, you transform the points into new ones. If you repeat it enough times, a figure appears that looks like a Gingerbreadman. And I like this one because I also explore it myself. Remember this?

Iterated Function Systems.

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Iterated function systems is a technique to build fractals using transformations of points. It’s similar to the Gingerbreadman map, but with a set of equations that alternate randomly. And I also explore it! Remember the 100 posts post?

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Double pendulum.

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This was the post that bring me to the blog. The double pendulum is an example of a quite simple chaotic system, it’s only two pendulums linked. In the image on top we can see 2 double pendulums, what the animation want to show is that quite similar initial conditions can evolve into very different evolutions. (I’m working in a nice post about this, but I’m not telling anything more now).

Functors.

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This is an applet to play with iterated functions systems. This one uses the geometrical approach for defining the functions used for performing the iteration. I like it, is quite good. Unfortunately, it’s difficult to repeat successfully patterns.

Create GIF animations with Mathematica.


I don’t like Mathematica, I prefer Matlab or Python, but… who knows, this could be useful.

Animated Optical Illusions.

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I saw this effect long ago in a book. I like it. I never had enough time to make anything. But here you can see how it works.

Designing Galleries.

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In this post what he wants to show is the importance of designing of buildings. Basically, a good design can help to build a museum where you can visit exactly once each room without crossing with other visitors. Or… if it is a mall, how to design it to make people walk several times into the same point (increasing the showing of that particular shop).

Soap film holes.

The film doesn’t belongs to the blog, but is so amazing…

Shepard scale.

I like this one, is my first sound illusion. Basically, you feel like the scale is getting higher, but it is not.

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A Tautochrone (or Brachistochrone if you focus on other property) is a curve where no matter you put a ball on it, it always takes the same time to get to the botom point. I saw many times the Brachistochrone and never realize that it also has this property. I can think of quite funny experiments now for it.

Quine.

f[x_] := Print[StringJoin[x, FromCharacterCode[{91, 34}],x,FromCharacterCode[{34, 93}]]];
f[“f[x_]:=Print[StringJoin[x,FromCharacterCode[{91, 34}],x,FromCharacterCode[{34, 93}]]];f”]

A quine is a piece of code which is able to print itself. I heard about it before, but it’s the first time I saw one for Mathematica.

And thats all. If you want more, visit his blog. Hope you like it!

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