0xDE's recent toot on cavatappi-like surfaces reminded me of a helical surface I devised a few years ago that had ridges on it. I thought it might be a good way to test the new surface-styling features of the recently released Mathematica 12.3...

(A similar question could be asked regarding the totient function and the golden ratio.)

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@christianp's question reminded me of something I've always been curious about: has anyone ever came up with a formula that involved both the prime-counting function and the constant associated with the circle? If so, how was the possible notational clash addressed?

Not everything intuitive is true; not everything true is intuitive.

My housing situation isn't very good. That being said, I don't complain, since I know from experience that things could be much, much worse.

I was playing around with the blancmange/Takagi function (en.wikipedia.org/wiki/Blancman), thanks to a recent posting by @esoterica. I particularly liked this 3D version.

I got off a ~ two-week span of illness and my larynx is still too sore that I can only barely whisper. Thankfully, people I communicate with have been sufficiently understanding about me not being able to participate verbally.

...and this is a slight modification of the function I previously plotted.

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I had the thought that visualizing the Padua points (en.wikipedia.org/wiki/Padua_po) in the complex plane would lead to nice-looking domain coloring plots. I was not disappointed.

This is why I'm always keen to give back and help other people whenever I possibly can, and always strive to write things that are educational, funny, or hopefully both. I feel like I owe the Internet my knowledge of how the world is put together.

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Somewhat recently, I noticed a bunch of people having the sentiment that the Internet is making people dumber. I thought to offer the counterpoint that the Internet taught me far more things than all my formal education did; I would estimate that ~80% of the knowledge I use for work is stuff I learned from the Internet.

Every once in a while, you see interesting sequences of events in your timeline (c.c. @ColinTheMathmo, @marianom):

I did not know until today that you can build a diamond structure solely from integer lattice points.

Software defaults are often a prime example of "pleasing nobody by trying to please everybody".

(I also now have a way to do a hyperbolic Voronoi diagram, but I haven't yet tried to implement the hyperbolic version of Lloyd's algorithm with it.)

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Since @11011110 recently boosted that Lloyd toot I made a while back, I should also state that Lloyd's algorithm also looks mesmerizing when done on a sphere.

This page by Robert FerrΓ©ol (mathcurve.com/surfaces.gb/gour) features Goursat surfaces that have icosahedral symmetry. I've always wondered if it's possible to get a surface that looks like a rounded version of the truncated icosahedron, but I have not been successful in tweaking the formula from that page.

I'm on a domain coloring kick again. Elliptic functions tend to make for interesting patterns.

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