Show HN: A Sierpinski Valentine in 4 equations(desmos.com)
desmos.com
Show HN: A Sierpinski Valentine in 4 equations
https://www.desmos.com/calculator/9ed6k6wexp
6 comments
[deleted]
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...
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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)
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)
How the heck do people come up with these equations? Is it purely mathematical knowledge, knowing what functions look like when plotted?
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.
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.
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]
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]
By playing around, usually.
See https://www.youtube.com/watch?v=Zkx1aKv2z8o Specifically from 4:30 to 7~
See https://www.youtube.com/watch?v=Zkx1aKv2z8o Specifically from 4:30 to 7~
There are iterated function systems (IFS) for constructing such fractals, Sierpinski gasket is in fact quite common.
can i extract an svg of this? that would let me CNC it.
Very cool!
Disclosure: I'm one of the engineers at Desmos.