[EM] High Order Numerical Cubature2.0
Daniel Carrera
dcarrera at gmail.com
Sat Feb 5 13:55:29 PST 2022
Hello Forest,
On Sat, Feb 5, 2022 at 2:00 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:
> This is a slight revision of the original with some clarifications to
> prevent all posible misunderstandings! (Sure)
>
> In particular, if G is a set of points and V is a set of vectors, let G+V
> be the set obtained by displacing each point of G by every vector of V:
>
> G+V={g+v| (g,v) in G×V)},
>
> where G×V is the Cartesian product of G and V.
>
> So in general (when there are no double representations of points) the
> number of points in this kind of sum will be the same as #(G×V), wich is
> just (#G)*(#V).
>
Aha! I think this added the clarity that I needed. Now I understand what
you're saying. To make sure we are on the same wavelength, I wrote a script
to plot a schematic of how I understand your algorithm to work, followed by
the first few generations up to G(6). Here is the plot:
https://postimg.cc/zV34pv0F
Unfortunately, it doesn't seem to be space-filling. It looks like you have
reinvented Sierpiński's gasket.
Let me know if I misunderstood the algorithm again.
Cheers,
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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