in reply to Re^3: Randomly biased, random numbers.
in thread Randomly biased, random numbers.

generate a piecewise-linear function (or spline) in each dimension with steps taken from the PRNG, then generate uniform random points and apply the function to them.

That's sounds like a real possibility -- or rather looks like it having done a search for "spline" and seen a few images. I'm imagining sticking a few (2 or 3 or 4 decided at random) sticks, of random length, into a square of ground at randomly chosen points; and then draping a tarpaulin over them. The height of the tarpaulin at any given point then "influences" the randomly generated xy pairs such that they tend to concentrate around the sticks.

I haven't a clue how I'd go about it though :( (Offers?:)

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Re^5: Randomly biased, random numbers.
by educated_foo (Vicar) on Dec 06, 2013 at 04:55 UTC
    You more or less have it.
    I haven't a clue how I'd go about it though :( (Offers?:)
    For my standard consulting rate? ;-)

    Basically, you want to take a uniform distribution between 0 and M, and map it to a non-uniform one between 0 and N, so that X+I < X+J when I < J. One way to do this is to generate a step-functionpiecewise linear function, then translate values through that step function. In Matlab, it looks something like this for a 10-step function: 

    fx = [0,cumsum(unifrnd(0,1,1,10))];
tmp=unifrnd(1,10,1,1e5);
ix=floor(tmp);
dx=rem(tmp,1);
values = (fx(ix) + (fx(ix+1)-fx(ix)).*dx)./fx(end-1);

    [download]
    Using a spline would be more complicated, but would be smoother.
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      In Matlab, it looks something like this for a 10-step function:

      Great, thanks. Now all I gotta do is translate that from matlab, a lingo I am not familiar with.

      Darn it. Fell at the first hurdle. I cannot sense of your parameters to unifrnd()?

      With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
        Sorry -- it's much terser than Perl for math. 
        unifrnd(MIN, MAX, ROWS, COLUMNS); # uniform random numbers in [MIN,MAX
+)
cumsum(VECTOR) = #cumulative sum of vector
# .OP = element-wise application of OP to operands

        [download]
[reply]
[d/l]

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