Numbers stations are mysterious shortwave radio channels of indiscernible origin that exist in countries all across the world and have been reported since World War 1. They are identifiable by the unusual contents of their broadcasts: seemingly random sequences of numbers, words, letters, tunes, and Morse code, usually spoken by artificially generated voices of women and children.

The most common theory regarding the purpose of these bizarre stations is that they’re used by governments the world over to secretly transmit encrypted commands and messages to spies. That said, even though numbers stations have been discovered all over the globe and in any number of different languages, no government has ever officially acknowledged their existence. While the espionage theory is a logical one, with no official confirmation of their purpose the jury is still out.

One particularly odd station, UVB-76, has existed since the late 1970s and has broadcast a simple, repetitive buzzing tone 24 hours a day ever since. On very rare occasions, however, listeners have reported a Russian voice interrupting the buzz to read out sequences of numbers and words, always in a consistent format — this happened once in 1997, once in 2002, once in 2006, 56 times in 2010, and 14 in 2011. As with all numbers stations, its true purpose is and will probably remain unknown, but the increase in frequency of whatever it’s doing is certainly odd.

You can listen to well over 100 recordings of numbers stations for free on archive.org but be forewarned that they’re all kind of, well, eerie. They feel like something you shouldn’t be listening to, which stands to reason since apparently you’re not supposed to know they exist.

Yankee

Hotel

Foxtrot

dotroom:

Around the black hole

matthen:

If a mathematician wants to cross a road, they will think carefully about their optimal path. The total distance of the path should be minimised, but they prefer walking on the sidewalk to the road. If there is no extra discomfort from being on the road, the best path is a straight line, but as it increases it is better to cross the road more directly.  The resulting path is exactly the same as a ray of light refracting through a block of glass [with relative refractive index equal to the ratio of these ‘discomfort levels’]. Fermat’s principle says that light will want to spend less time in the glass (on the road), as it actually travels more slowly in the glass. [video] [code] [more]

matthen:

A gingerbreadman drawn using chaos. Points are chosen at random, then repeatedly moved to new locations according to a simple rule [the new y coordinate is the old x one, and the new x is 1 - the old y + |the old x|]. This rule is called the gingerbreadman map, of course. The trajectories shown are chaotic, showing complex behaviour from such a simple rule. Hexagonal areas seem to build up the picture. [detailed version] [more] [code]

matthen:

In 1952 Alan Turing, a british mathematician, logician, cryptanalyst, and computer scientist, wrote a paper which remains influential in computational biology today. He explained how stripes might form on a snake’s skin [and other patterns on animals], using the dispersion of two chemicals; an activator [red] and an inhibitor [yellow]. The activator causes the colouration, and the inhibitor inhibits it. Turing wrote a pair of equations which say that concentrations of the activator cause creation of more inhibitor, but that the inhibitor diffuses and spreads out more quickly than the activator. As shown in the animation, this causes the activator to form peaks with surrounding basins of inhibitor. The concentrations of the two chemicals quickly converge to a stripey pattern where the red activator is periodically in higher concentration than the yellow inhibitor. [video] [more] [code]

mechanicalreproductions:

whippit

mechanicalreproductions:

braid

mathani:

Did you know that you can specify animated GIF’s individual after-frame delay in Mathematica? This is true, look for "DisplayDurations" export property for GIF format in help. Why would one want to do this? GIF above for example has 60 frames, 30 for each color decay (imitating radioactive decay), with time delays exponentially distributed.

buzzfeed:

You can change the direction this train is moving just by thinking about it.

this kind of of effect is sort of present in some intothecontinuum gifs if you try.
also see: the wagon wheel effect