This is not a question but I just wanted to share some nice code I was able
to write to create the Sierpinski carpet.
Nothing new probably but it seemed pretty cool to me,
I also formatted it in a fancy way to match the graph result:
https://www.desmos.com/geometry/wrr3yzgz90
(This is for a lesson I’m gonna be giving about fractals …)
wow :).
(not because I saw you had no replies and replied something stupid to you, definitely not)
Kind of necro-posting but how did you do that?
so, we use recurrence:
s(0) is a triangle T
g(n, k) shrinks the set s towards the k-th vertex of triangle T
g(n,k) = dilate(s(n-1), T.vertices[k], .5)
s(n) joins what you get from shrinking s towards the three vertices:
s(n) = (g(n,1), g(n,2), gt(n,3))
finally you want to build s(5).
For a more clear explanation see: ifs.
In other words:
start with a triangle, shrink it towards one vertex, then towards the other vertex and then towards the other vertex.
You get a new set.
Now repeat the process with this new set.
Yep! I have absolutely no idea what any of that means, especially dilate.
It’s probably because I never use the geometry tool (I know it’s very powerful thought)
ok, just to get you started:
dilate(X, p, 1/2) means something very easy:
for any point of the set X, connect it to p, and take the point half way in that line.
So you get a copy of X scaled by a factor 1/2 …
Oh! I see. very cool! I think I get it. It’s like midpoint in the calculator, but you can also do 1/3, 1/4 ...
Yes … and you can also do times 2 …
Ohhh, and the g(n, k) = {...} , .5) just does it half way each time!