Show HN: A Sierpinski Valentine in 4 equations
1–10 of 12 posts
Re: Show HN: A Sierpinski Valentine in 4 equations
#2How the heck do people come up with these equations? Is it purely mathematical knowledge, knowing what functions look like when plotted?
Re: Show HN: A Sierpinski Valentine in 4 equations
#3You 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.
Re: Show HN: A Sierpinski Valentine in 4 equations
#4How the heck do people come up with these equations? Is it purely mathematical knowledge, knowing what functions look like when plotted?
By playing around, usually.
See https://www.youtube.com/watch?v=Zkx1aKv2z8o Specifically from 4:30 to 7~
Re: Show HN: A Sierpinski Valentine in 4 equations
#5How 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), 0Without 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.
Re: Show HN: A Sierpinski Valentine in 4 equations
#6How 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 Without a nontrivial amou…
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]
Re: Show HN: A Sierpinski Valentine in 4 equations
#7This 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...
Re: Show HN: A Sierpinski Valentine in 4 equations
#8You 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.
[deleted]
Re: Show HN: A Sierpinski Valentine in 4 equations
#9How the heck do people come up with these equations? Is it purely mathematical knowledge, knowing what functions look like when plotted?
There are iterated function systems (IFS) for constructing such fractals, Sierpinski gasket is in fact quite common.
Re: Show HN: A Sierpinski Valentine in 4 equations
#10can i extract an svg of this? that would let me CNC it.