http://www.smbc-comics.com/comic/genera
Alt text
You can tell if it’ll be a cartoonist by seeing if it cries whenever anyone comes in its room and/or turns on the lights.
Bonus panel
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How is a function continuous everywhere but not differentiable anywhere? Thats like an oxymoron almost. Is every point a step function, a corner? Im so confused…so many questions.
In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is also an example of a fractal curve.
The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. Weierstrass’s demonstration that continuity did not imply almost-everywhere differentiability upended mathematics, overturning several proofs that relied on geometric intuition and vague definitions of smoothness.
Animation based on the increasing of the b value from 0.1 to 5. ☝️
I dislike this very much! My engineer brain never studied fractals, and was told that functions that are continuous everywhere will be differentiable…this is so counterintuitive! I find it funny that the first fractals were literally introduced to show that this assumption was not universally true. Basically, the mathematical equivalence of trolling 🤣
Its a type of fractal, I think. A pretty famous one too, though I don’t remember anything about it besides that it exists.
