It took me longer than I'd like to figure out how to (cleanly) roll a hyperbola on a straight line, but it worked out. I should try writing up the math behind this later...

I was able to find my old code for plotting the Wente torus (en.wikipedia.org/wiki/Wente_to) in Mathematica again, after losing it in a disk failure. It's really nice to see it again.

More fun with tori. Here's my conception of an ouroboros, by suitably modifying the usual parametric equations of a torus.

I don't know why I never tried experimenting with Villarceau circles before. Even the simple operation of uniformly spacing them on their corresponding torus makes for a nice woven appearance.

I forgot that I did this cartoon of a circle rolling on a parabola years ago. I should really find time to modernize it.

Quite a while ago, @11011110 wrote about the Wankel rotor. That reminds me that I should really find the time to clean up my write-up on the Bernoulli-Euler double generation theorem for cycloidal curves.

I made a domain coloring plot of one of the functions I'm currently studying. It looks quite mesmerizing.

Going back to basics. I've always been impressed by situations where two seemingly unrelated things give rise to the same result. In this case, two different curve families generate the same envelope: a nephroid.

I redid one of Kitaoka Akiyoshi's illusions in Mathematica a few days ago (picture might cause a little dizziness in sensitive individuals): community.wolfram.com/groups/-

Now, this one's a domain coloring plot for Ramanujan's \(L\)-series associated with his \(\tau\) function done in Mathematica. This took **two** days.

Numerically evaluating Dirichlet series can sometimes be difficult. Here's a domain coloring plot for Riemann \(\zeta\) done in Mathematica, which took about 10 minutes.

I'm still on a domain coloring kick. Here's a plot corresponding to an iterated rational function related to the symmetries of the icosahedron (cf. the Doyle-McMullen iteration).

...and here is the corresponding domain coloring plot of the Dixon elliptic function \(\operatorname{cm}(z,\alpha)\) for fixed \(z\) and varying \(\alpha\):

Show more
Mathstodon

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!