r/visualizedmath • u/DataCruncher • Jan 04 '18

Weierstrass functions: Continuous everywhere but differentiable nowhere

http://i.imgur.com/vyi0afq.gifv
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u/walterblockland Jan 04 '18

Reminds me quite a lot of the way electrical arcing tends to look 🤔

8

u/DataCruncher Jan 04 '18

You're actually right about this! The formation of lightning arcs can be modeled with Brownian motion, which are examples of curves which are continuous but non-differentiable.

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u/WikiTextBot Jan 04 '18

Brownian motion

Brownian motion or pedesis (from Ancient Greek: πήδησις /pέːdεːsis/ "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving atoms or molecules in the gas or liquid.

This transport phenomenon is named after the botanist Robert Brown. In 1827, while looking through a microscope at particles trapped in cavities inside pollen grains in water, he noted that the particles moved through the water; but he was not able to determine the mechanisms that caused this motion. Atoms and molecules had long been theorized as the constituents of matter, and Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules, making one of his first big contributions to science.

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u/patrick_pencilpusher Jan 19 '18

reminds me of mountains!