Macs now have them again. OLED screens made them create animated login screens. (At least I think that's what happened.)

And definitely re-post worthy!

Thanks! Macroexpanded:

Factorizer - https://news.ycombinator.com/item?id=10776019 - Dec 2015 (30 comments)

Animated Factorisation Diagrams - https://news.ycombinator.com/item?id=4788224 - Nov 2012 (72 comments)

Animated Factorization Diagrams - https://news.ycombinator.com/item?id=4713048 - Oct 2012 (2 comments)

Same. I loved this unique insight that the visualization provided. It definitely unlocked something in my brain for how I should think about that shape.

If anyone is curious, 6561 (3^8) is the highest pure Sierpinski available in the animation since it caps at 10K.

It would function pretty well as a waiting animation too.

Kind of makes me wish that there were recognizable shapes for primes bigger 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) that didn't just look like circles. Because my favorite part about this is how you can see at a glance what the factors are. Except for primes 7 or greater I find myself cheating and looking at the top left for which prime it is.

Is there some non-regular polygon that would be more distinctly recognizable to use for 7, 11, etc?

I believe it's called prime factorization. Each number is placed in a group of numbers (or group of groups, etc...)

E.g. 24 -> 2 * 3 * 4 = Two groups of (three groups of (four items))

Also try this for the archived version of that explanation -> https://web.archive.org/web/20130206023100/http://mathlesstr...

1. Set var factors to the prime factors of the integer

2. Sort factors in ascending order

3. Set var diagram to a single dot

4. Foreach factor in factors

4.1. Set var diagram to factor copies of diagram aranged in a circle

But it's not CRUD data visualization, it's a custom animation. Why use a heavy library if the browser draws circles just fine?

I don't know what you mean by that, but for an example, 16=2^4 and is therefore arranged as a grid, whereas 17 is prime, and must therefore be arranged as 17 dots on a circle.

That's the difference between the additive view of the world and the multiplicative one. A lot of number theory involves trying to bridge that gap, and even this simplest view of numbers can rapidly fling you into the mathematical unknown. The "simplest hard problem", the Collatz conjecture, can be viewed as coming from this space. You either take a step in multiplicative space, or a step in multiplicative space and then additive space, and ask a very simple question about where those steps can take you.

And that's all it takes to end up at an unsolved problem in math.

You can spend a lifetime on this simple observation that "the jumps between neighbors are so dramatic", just trying to reconcile the complex relationships between the additive view of the world and the multiplicative one.

And we haven't even done anything like bring in complex numbers, or rationals, or introduce exponentiation!