You seem to have ambiguous requirements. First, you want equidistribution for a packing structure, which would suggest closest packing or quasirandom sequences, as you have tried.
But then you are disturbed by the packing structure, because it gives a perceivable pattern, so you wish to randomize it, but under some unspecified condition of equidistribution (your "electrostatic repulsion" algorithm). You obviously have some constraints on selection you have not quantified yet. E.g., circles of unspecified radii cannot overlap. You should also realize that any distribution of centers under such constraints will always exhibit structure due to the constraints. Is your problem simply to give an appearance of randomness to the casual observer, or something more definite? You also need to say something about the packing density involved. On the face of it, you with At 06:22 AM 4/26/2008, baptiste Auguié wrote: >Dear list useRs, > >I have to generate a random set of coordinates (x,y) in [-1 ; 1]^2 >for say, N points. At each of these points is drawn a circle (later >on, an ellipse) of random size, as in: > > > > N <- 100 > > > > positions <- matrix(rnorm(2 * N, mean = 0 , sd= 0.5), nrow=N) > > sizes<-rnorm(N, mean = 0 , sd= 1) > > plot(positions,type="p",cex=sizes) > > >My problem is to avoid collisions (overlap, really) between the >points. I would like some random pattern, but with a minimum >exclusion distance. In looking up "Numerical recipes in C", I found >out about some Sobol quasi-random sequences, which one can call from >the gsl package, > > > > library(gsl) > > > > g <- qrng_alloc(type="sobol",dim=2) > > qrng_get(g,n= N) ->xy > > > > plot((xy),t="p",cex=0.5) > >but this does not look very random: I clearly see some pattern >(diagonals, etc...), and even the non-overlapping condition is not >impressive. > >One (painful) way I can foresee is to check the distance between each >symbol and the others, and move the overlapping ones in a recursive >manner. Before delving into this, I wanted to check I'm not >overlooking something in the rgl quasi-random sequences, or missing a >more obvious way to generate such patterns. Perhaps solving an >electrostatic problem with a potential both attractive at long >distances and repulsive at short distances is a better way? I have a >vague recollection of hearing that somewhere to position points >evenly on a sphere. > > >Thanks for any comment / suggestion, > >Baptiste > > >_____________________________ > >Baptiste Auguié > >Physics Department >University of Exeter >Stocker Road, >Exeter, Devon, >EX4 4QL, UK > >Phone: +44 1392 264187 > >http://newton.ex.ac.uk/research/emag >http://projects.ex.ac.uk/atto > >______________________________________________ >R-help@r-project.org mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >and provide commented, minimal, self-contained, reproducible code. ================================================================ Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail: [EMAIL PROTECTED] Least Cost Formulations, Ltd. URL: http://lcfltd.com/ 824 Timberlake Drive Tel: 757-467-0954 Virginia Beach, VA 23464-3239 Fax: 757-467-2947 "Vere scire est per causas scire" ================================================================ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.