

Show HN: A Sierpinski Valentine in 4 equations - harmonium1729
https://www.desmos.com/calculator/9ed6k6wexp

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

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

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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...](https://www.overleaf.com/latex/examples/the-first-six-levels-of-
the-sierpinski-triangle/gqwmqrhmphxv)

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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)

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

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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 (2 _pi_ (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.

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harmonium1729
Yeah - I think it'd take some serious chops to construct this from scratch
(note: it wasn't me! author: twitter.com/teachwithcode). But I've been having
a blast deconstructing the equations.

Here's a fun intermediate step (circles instead of hearts), with a few of the
numbers parametrized as sliders:

[https://www.desmos.com/calculator/irg4qa2s4h](https://www.desmos.com/calculator/irg4qa2s4h)

[disclaimer: I work at desmos]

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

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lion_del
Very cool!

