Refurio Anachro

Will do, @PetraSchwer@mathstodon.xyz! There are a few. Just this week I was quite surprised to see a philosopher friend keep asking about topos theory, because they wanted to understand how to get countable reals! That was fun. I'll have to get them read some nice intro. Of course, for leymen it has to be extra leisurely, so I expect to lend a hand.

@PetraSchwer@mathstodon.xyz

Reading is also writing

Ha! I like this one!

I have some promising laypersons to try your nice guide on.

Oh wow, that's much closer to what pops out when you overlay wave trains aligned along the edges of a pentagon, than I would have expected! https://www.shadertoy.com/view/4cXBz2 @johncarlosbaez@mathstodon.xyz

It uses three.js and the code is quite readable, even if somewhat long-ish, @otte_homan@theblower.au. Nice work, @jasonhise@mathstodon.xyz! @johncarlosbaez@mathstodon.xyz

I made a thing!

Benoit, a tiny GLSL 3.0 ES fragment shader loader, and compressor for the web!

https://codeberg.org/refurio/benoit

It's shadertoy compatible, and can load their export files! No mouse, textures, or audio yet. Baseline is 770 bytes for a trivial shader. I made a bet with myself to get my Julibob Tunnel study under 1k, and I got down to 1046 bytes...! Still, that should settle it for now, mine is shorter than yours!

#glsl

What if both portals were shaped like the orange one in the last example. I have watched your work for a while, and I think I have developed an intuition by now. It's still so much fun to look at your results. @optozorax@mathstodon.xyz

Got another opportunity to show the C² Julia Loop installation yesterday. This is just after setting up, later on people came to dance to dub music. Most didn't interact with the installation, but those who did seemed to have lots of fun! It's great to see people discover the boundary of the Mandelbrot set with their hands, because that's where you get the best pictures.

https://www.shadertoy.com/view/sfXSzM

This is such a rewarding motif! Since the idea is so incredibly simple, I feel shy to take too much credit. Someone else must have tried to make a video loop with a complex square function in between long before me, right? Anyways, there is stuff to learn. How to set up lighting to get nice images, or that it's a good idea to turn off auto exposure. Adding color shifting was a good idea, and making it slowly rotate by itself kept things interesting enough so I could leave to take a leak. There are certainly more clever things to try. Or maybe add some way to make it react to audio signals.

#mandlebrot #installation

Ha, and I thought it was about characters! @mei @amy

I can now see why quaternionic mandelbrots give a doughy appearance, with almost all bulbs gone! No antennas either. It's because solutions of approximations of the quaternionic Mandelbrot polynomial are continuous! The full polynomial is infinite, so it's less surprising we get uncountably many solutions. @hallasurvivor

The following is in analogy to i²=-1 from complex numbers. I know that imaginary quaternions can be written using any orthonormal basis. Which means they are spherically symmetric. In fact, the symmetries cover the unit sphere twice! So we can take any solution and rotate it continuously. Since I still felt surprised I wanted to get my hand on some of them: Take any point (a,b) on the unit cirle. It means a²+b²=1. Expanding (ai+bj)² we get a²i²+abij+abji+b²k². Now, also by definition, i²=j²=-1 and ij=-ji. So we can simplify to get -a²-b², which is what we wanted: Using a subspace of just two imaginary dimensions we get a circle of solutions! I think we can simply use general imaginary unit quaternions and do the algebra. Appealing to symmetry seems odd at this point, because symmetry alone already solves the problem. @hallasurvivor

Gorgeous! DrFlopine just did something physalis related in #revision2026 live coding semifinals on a bonzomatic. @bleuje@mathstodon.xyz

I recently made a shader to illustrate the complex square function using a camera: https://www.shadertoy.com/view/scsGDH The line goes like this: "can we make fractals using a video loop? Look at this!" and I would hold my phone at them, showing their face gruesomely distorted and duplicated... And then, after remarking that they can see everything twice, I'd ask them to go to the restroom with me, because I'd like to show them something in the mirror... I have actually tried this in bars. It was a lot of fun. I didn't get into trouble, because I'm a nice guy, ymmv. @robinhouston

That's because it's the volume, not the radius of a black hole that's proportional to its mass!

That's a typo. The radius of a black hole is proportional its mass. It's density is one over the square of either, whereas the density of a gas is constant.

@johncarlosbaez@mathstodon.xyz @mc@mathstodon.xyz @jonasfrey@mathstodon.xyz

Feynman a fraud? An insecure guy making up stories? Are the books about him all lies? Watch Angela Colliers video linked upthread! Thank you, @acollierastro@mastodon.social, watching you debunk thr Feynman legends was such fun! There's record of Leonard Susskind scratching at the legend as well. He says he was good friends with him, and at one occasion (I can't remember the link, it's a celeb lecture on Youtube) he hinted at Feynman having a severe alcohol addiction. He obviously didn't want to put him in too much of a bad light, but he kept putting his tongue in his cheek remembering him.