[EM] High Order Numerical Cubature2.0

[Forest Simmons]

Nice graphics! We should call it "shingles".

I wonder if you could do the same thing for an  equilateral triangle ...
say with vertices at (-1,0), (1, 0) and (0, sqrt(3)).

El sáb., 5 de feb. de 2022 1:55 p. m., Daniel Carrera <dcarrera at gmail.com>
escribió:

> 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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