7 ms·

Show HN: A Sierpinski Valentine in 4 equations

72 points by harmonium1729 12y ago

splike 12y ago
How the heck do people come up with these equations? Is it purely mathematical knowledge, knowing what functions look like when plotted?
- azeirah 12y ago
  By playing around, usually. See https://www.youtube.com/watch?v=Zkx1aKv2z8o https://www.youtube.com/watch?v=Zkx1aKv2z8o Specifically from 4:30 to 7~
- electronvolt 12y 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 12y 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 https://www.desmos.com/calculator/irg4qa2s4h [disclaimer: I work at desmos]
- meta_pseudo 12y ago
  There are iterated function systems (IFS) for constructing such fractals, Sierpinski gasket is in fact quite common.
jwmerrill 12y ago
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.
- deleted 12y ago
  [deleted]
JohnHammersley 12y 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-of-the-sierpinski-triangle/gqwmqrhmphxv https://www.overleaf.com/latex/examples/the-first-six-levels...
joshu 12y ago
can i extract an svg of this? that would let me CNC it.
darklajid 12y 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 12y ago
Very cool!

72 points by harmonium1729 12y ago

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

azeirah 12y ago
By playing around, usually. See https://www.youtube.com/watch?v=Zkx1aKv2z8o https://www.youtube.com/watch?v=Zkx1aKv2z8o Specifically from 4:30 to 7~
electronvolt 12y 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 12y 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 https://www.desmos.com/calculator/irg4qa2s4h [disclaimer: I work at desmos]
meta_pseudo 12y ago
There are iterated function systems (IFS) for constructing such fractals, Sierpinski gasket is in fact quite common.

jwmerrill 12y ago

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.

deleted 12y ago
[deleted]

JohnHammersley 12y 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-of-the-sierpinski-triangle/gqwmqrhmphxv https://www.overleaf.com/latex/examples/the-first-six-levels...

joshu 12y ago

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

darklajid 12y 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 12y ago

Very cool!