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Imagine you wanted to measure the coastline of Great Britain. You might remember from calculus that straight lines can make a pretty good approximation of curves, so you decide that you’re going to estimate the length of the coast using straight lines of the length of 100km (not a very good estimate, but it’s a start). You finish, and you come up with a total costal length of 2800km. And you’re pretty happy. Now, you have a friend who also for some reason wants to measure the length of the coast of Great Britain. And she goes out and measures, but this time using straight lines of the length 50km and comes up with a total costal length of 3400km. Hold up! How can she have gotten such a dramatically different number?

It turns out that due to the fractal-like nature of the coast of Great Britain, the smaller the measurement that is used, the larger the coastline length will be become. Empirically, if we started to make the measurements smaller and smaller, the coastal length will increase without limit. This is a problem! And this problem is known as the coastline paradox.

By how fractals are defined, straight lines actually do not provide as much information about them as they do with other “nicer” curves. What is interesting though is that while the length of the curve may be impossible to measure, the area it encloses does converge to some value, as demonstrated by the Sierpinski curve, pictured above. For this reason, while it is a difficult reason to talk about how long the coastline of a country may be, it is still possible to get a good estimate of the total land mass that the country occupies. This phenomena was studied in detail by Benoit Mandelbrot in his paper “How Long is the Coast of Britain" and motivated many of connections between nature and fractals in his later work.

Vídeo

Muhahahajaaj XD

(Fuente: cause-every-tear-is-a-waterfall)

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#fail

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:3 :3

(Fuente: tijgertjerawr)

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Tritón en alta resolución (NASA/Daniel Machacek).

Vía.

Texto Mundo/s

Uno.

Enorme.

Todo.

Entero.

Orbe.

Completo.

Diminuto,

Frágil.

Soñando.

Torpe.

Humano.

Muchos.

Participando con Sindel y amigos.

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El polo norte de Saturno visto por la Cassini el 4 de mayo de 2014 (NASA/JPL).

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`Veneto, Italy`
Enlace http://clientsfromhell.net/post/95548445446/client-my-fiance-and-i-are-unhappy-with-the»

Client: My fiancé and I are unhappy with the engagement photos you sent us.

Me: What’s wrong with them?

Client: We’re wearing sweat pants in them!

Me: But that’s what you wore to the shoot. I asked you on the day if you wanted to change into something more appropriate and you said no.

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Burning sky by FuT

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El vigilante del castillo

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Esta semana que he empezado de nuevo a trabajar he andado practicando lo de “recordar es volver a vivir”, a base de fotos de las vacaciones. Y me he dado cuenta de que el breve paso por el “Jardín del Ángel” (Plaza del Ángel, en lo alto de la Calle Huertas de Madrid, junto al Hotel Palacio Tepa), una tienda de todo y nada malo, debía verse reflejado también en este blog. Ved por qué:

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También después de otra subida a mediodía, pero en Guetaria (en lo alto de su “Ratón”), encontré otra declaración de optimismo vital:

Nada mejor que un jardín ;-)

{ 23 – VIII } Un jardín de optimismo Esta semana que he empezado de nuevo a trabajar he andado practicando lo de “recordar es volver a vivir”, a base de fotos de las vacaciones.
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Es que no sabéis nada xD

via Anx-Tumblr.
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(Fuente: malaclasecl)

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