Constructing Weierstrass' function. Continuous, nowhere differentiable, unbounded variation, no intervals of increase or decrease. Fractal dimension 3/2. All things it has in common with mathematical Brownian motion

second time I've written this animation from scratch, as the first was lost when I destroyed my laptop by spilling diet Coke on it, so may as well post it here

It is Hölder continuous with exponent 1/2. Unlike Brownian motion, which is only locally Hölder continuous for exponents 1/2-ε

“Science doesn’t tell us why the Big Bang happened, how the singularity occurred in the first place, or why it exploded when it did. It tells us there is objective scientific evidence that it occurred. So, what exactly was the Big Bang?” – Book III The Enigmatic Mystery

I learned recently that estimating the Hoelder continuity properties of these functions is surprisingly simple (compared to the care that is required for the negative results); really fun stuff!

indeed (fixed typos and relinked)

Thanks for the nightmares ! 🫣

this next vid looks like it will be epic!

€_n~ix1+n|¥+|-z{{^am+b-C}

I don't understand it. But it sure is cool!