August 21st
340 notes

spring-of-mathematics:

Chaos Theory & The Beautiful Geometry of Double Pendulum

  • Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, sociology, physics, engineering,etc…. In a scientific context, the word chaos has a slightly different meaning than it does in its general usage as a state of confusion, lacking any order. Chaos, with reference to chaos theory, refers to an apparent lack of order in a system that nevertheless obeys particular laws or rules.

Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions. These systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as follows: “Chaos: When the present determines the future, but the approximate present does not approximately determine the future.” (pg 68).

  • Chaotic behavior can be observed in many natural systems, such as weather and climate. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.

See more at: Chaos theory on Wikipedia & What is chaos theory? on WhatIs.com.

A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions.

August 21st
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August 21st
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tierradentro:

The Persistence of Memory" (detail), 1931, Salvador Dalí.

August 21st
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August 21st
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ryandonato:

Light show projections by Tony Martin

August 21st
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August 20th
9,061 notes

Trainspotting (1996), dir. Danny Boyle

August 20th
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August 20th
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August 20th
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“We had to save you because you’re the mockingjay, Katniss,” says Plutarch. While you live, the revolution lives.”

August 20th
1,775 notes

Let eet Go - Heavina BabyMenzel
Video by thatspyisascout

August 20th
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August 20th
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The fact that Harry Potter was going out with Ginny Weasley seemed to interest a great number of people, most of them girls, yet Harry found himself newly and happily impervious to gossip over the next few weeks. After all, it made a very nice change to be talked about because of something that was making him happier than he could remember being for a very long time, rather than because he had been involved in horrific scenes of Dark Magic. - Harry Potter and the Half-Blood Prince

August 20th
1,944 notes

I’m lying on the moon…

August 19th
68,559 notes

heisenbergchronicles:

the boys are back (x)