Show HN: A Sierpinski Valentine in 4 equations

https://www.desmos.com/calculator/9ed6k6wexp

by harmonium1729 • 11 years ago

72 10 11 years ago

splike• 11 years ago

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

azeirah• 11 years ago

By playing around, usually.

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

electronvolt• 11 years ago

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.

harmonium1729• 11 years ago

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

[disclaimer: I work at desmos]

meta_pseudo• 11 years ago

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

jwmerrill• 11 years ago

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• 11 years ago

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...

joshu• 11 years ago

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

darklajid• 11 years ago

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)

lion_del• 11 years ago

Very cool!

Show HN: A Sierpinski Valentine in 4 equations

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