[math-fun] good deterministic algorithmic point sets without repeated distances?
In the plane (or some other low dimensional space) I want a good infinite point set that has "density 1." What does "good" mean? Well, "more uniform than random" in some vague sense, such as sphere packing, sphere covering, and providing good estimates of integrals via sums. BUT, what I also want, is the set has no repeated distances. So lattices are undesirable. Random point sets will not repeat a distance (with probability 1) so they are great, except they fail to be good in the sense of the previous paragraph, while lattices can be quite good in that sense. Another thing I want is an easy, algorithmic description of the point set, and it should be deterministic. The question is how to get the best of both worlds. I admit, I am being vague here. Ideas are solicited.
How about lattice points plus small random vectors. Brent On 11/12/2013 9:16 PM, Warren D Smith wrote:
In the plane (or some other low dimensional space) I want a good infinite point set that has "density 1."
What does "good" mean? Well, "more uniform than random" in some vague sense, such as sphere packing, sphere covering, and providing good estimates of integrals via sums.
BUT, what I also want, is the set has no repeated distances. So lattices are undesirable. Random point sets will not repeat a distance (with probability 1) so they are great, except they fail to be good in the sense of the previous paragraph, while lattices can be quite good in that sense.
Another thing I want is an easy, algorithmic description of the point set, and it should be deterministic.
The question is how to get the best of both worlds.
I admit, I am being vague here. Ideas are solicited.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2014.0.4158 / Virus Database: 3629/6830 - Release Date: 11/12/13
participants (2)
-
meekerdb -
Warren D Smith