Show HN: A Sierpinski Valentine in 4 equations

[jwmerrill]

You can send this graph as a valentine, or make your own at http://mathogram.desmos.com/

Disclosure: I'm one of the engineers at Desmos.

[JohnHammersley]

This is very cool - both Desmos itself and the Sierpinkski Valentine example! In case you're more familar with LaTeX, you can also create similar visualizations in LaTeX using the 'lindenmayersystems' libary and TikZ. Here's a quick example: https://www.overleaf.com/latex/examples/the-first-six-levels...

[darklajid]

Unsupported browser.

Desmos works best on your version of Android if you use the Chrome Browser.

(Close page in Aurora, no clue what "Desmos" is but I don't care by now)

[splike]

How the heck do people come up with these equations? Is it purely mathematical knowledge, knowing what functions look like when plotted?

[electronvolt]

I think it's a combination of playing around and math chops.

Without any mathematical knowledge, you probably couldn't come up with something like the s(i,k,o) function (which, as far as I can tell from just looking/playing around with them briefly, seems to be the function responsible for the tessellation offset), and you might not have thought to define a system like (x=X(N,t), y=Y(N,t), 0<t<1).

Without a nontrivial amount of playing around, you probably wouldn't have found the exact constants used, like (2pi(3^i)), .2/(2^i), etc.--but knowing how altering those affects the end result takes some mathematical knowledge, so it's more guided investigation than random guessing.

[azeirah]

By playing around, usually.

See https://www.youtube.com/watch?v=Zkx1aKv2z8o Specifically from 4:30 to 7~

[meta_pseudo]

There are iterated function systems (IFS) for constructing such fractals, Sierpinski gasket is in fact quite common.

[joshu]

can i extract an svg of this? that would let me CNC it.

[lion_del]

Very cool!