I really wish I could pin individual threads in Mastodon (or #glitch) for when I'm following a (or several) interesting conversations.

Folks, get Siobhan Roberts' book "Genius At Play" to learn more about his life, and about his many other results, in game theory, and his work with Martin Gardner, Elwyn Berlekamp and Richard Guy... Invented notations for polyhedra, worked on octonions and number theory, and even published on free will. As he had to, I must end somewhere, but his work lives on! Farewell!

*Programming in 2D text*

This evening I'm thinking of two ideas I've thought about several times before, but never together.

The first: Arjun Nair's https://github.com/batman-nair/IRCIS, an esoteric language (art for art's sake) that comes with a cool visualizer. Maybe all languages should.

The second is Dave Ackley's https://movablefeastmachine.org, a tiled processor for very finely grained distributed computation. Programming it is like playing with a cellular automaton.

Category theory is a very high level tool. Take, for example, the idea of 'universal constructions'. I'd link Wikipedia, but its article comes up with a cat-theoretic description of the idea, which needlessly complicates things. It's a basic technique: Given some constraints, find the most general object (algebra, ...) that satisfies them. It's about interpreting things. It's nonconstructive. Commutative diagrams aren' programs, they're more like equations to be solved.

This is the second time I read about a problem becoming easier in hyperbolic space. I forgot the other one, I'll have to hunt for it! I can see what's happening with TSP here - there must be more problems like this! Thanks for inspiring!

Square packing: http://www.adamponting.com/square-packing/

Adam Ponting found a way to cover arbitrarily large (e.g. as measured by inradius) contiguous patches of the plane by distinct squares of sizes from \(1\) to \((2n+1)^2\), for any \(n\). Via https://demonstrations.wolfram.com/PontingSquarePacking/ and http://www.mathpuzzle.com/

@freemo \ x_{n+1} = r x_n(1 - x_n) \ is a simple enough population model. Lets try simulating it! Oh no...

new blog post summarizing the recent stuff on mating Julia sets that I've been playing with

https://mathr.co.uk/blog/2020-01-16_slow_mating_of_quadratic_julia_sets.html

I think I solved it!

Animated slow mating of p=-1+0i with q=-0.122+0.75i via inverting the pullback, which gives a series of functions like (az^2+b)/(cz^2+d); starting from the pixel coordinates in equirectangular projection I compute the initial z and apply all the collected functions in reverse order, colouring white if the final output |z| > R for some large R.

Next step will be trying to draw the Julia sets in the halves of the sphere.

Userland is an experimental graphical environment which can run shell commands (pipes, really) in a spreadsheet!

Have a look at this thread for a demo video and a link to fork with a Dockerfile:

@RefurioAnachro yes it's on my https://code.mathr.co.uk , needs a few of my other libraries too. but it's a bit work-in-progress, and I haven't pushed the most recent progress yet. only tested on debian

Turns out it was much simpler to just clamp the potentially huge wake image coordinates to +/-10 in mpfr_t before converting to lower-range double for cairo filling.

The image is roughly +/-1 in that coordinate frame, depending on aspect ratio - clamping may break appearance with very wide images, left a #FIXME note in the code for later.

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Thinking Outside the Plane: https://www.metafilter.com/183649/Thinking-Outside-the-Plane

Interesting roundup of 3d solutions to 2d problems, starting with Tarski's plank problem: Can you cover a diameter-\(n\) disk with fewer than \(n\) unit-width strips?

Sadly, they missed the 3d proof of Desargues' theorem: https://en.wikipedia.org/wiki/Desargues%27s_theorem#Three-dimensional_proof

There's also a 2d-3d connection with Miquel's six-circle theorem but I think it goes the other way: https://11011110.github.io/blog/2006/03/22/miquels-six-circles.html

Automatic annotation progress update:

✅ child bulbs of a mu-unit

✅ filaments of a mu-unit (done, this post)

❎ child islands of a mu-unit

❎ embedded Julia set filaments (next on the list)

❎ embedded Julia set islands

❎ embedded Julia set hubs

Mu-unit is Robert Munafo's terminology: https://www.mrob.com/pub/muency/muunit.html

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I didn't know that Philip Glass had composed a piece of music for Sesame Street, and its about geometry!

https://m.youtube.com/watch?v=19hRQfZdTr4

- g+ blog archive
- https://refurioanachro.github.io/g-viewer/

Higher maths is cool – come and see invisible worlds with me!

Joined Apr 2017