Plotting random points in matlab

Hello everyone, I have this figure which is shown below. I am getting a certain pattern of points every time i run my simulation. I mean, although the points are different every time but there is always some pattern in these points. Why is this, i don't know.

[José-Luis]

Sorry, but unless you give some more details, we are limited to venturing wild guesses. Also, this is not really a Matlab question.

[Aftab Ahmed Khan]

Hi, i have this function for generating these points. And i want to have random points but not having any pattern in it.

function [posxy] = position(r, n, h)

ms = 10 * r;                                         
ms = ms + 4 * sum(fix(sqrt(r^2-[1:r-1].^2)));

if n > ms
    error('n exceeds the number of position.');
end

posxy = zeros(n,3);

for ii=1:n
    while 1
        xx  = (r*rand) * sign(sin(2*pi*rand));                 
        yy  = (r*rand) * sign(cos(2*pi*rand));
        if xx^2+yy^2 <= r^2 & (xx~=0 | yy~=0)                       
            if length(find(posxy(:,1)==xx & posxy(:,2)==yy)) == 0   
                break
            end
        end
    end
    posxy(ii,[1 2]) = [xx yy];
    if h == 1
        while 1
            posxy(ii,3) = round(50*rand) / 10;
            if 1 <= posxy(ii,3) & posxy(ii,3) <= 4
                break
            end
        end
    end
end

[Aftab Ahmed Khan]

Also, what is "rand" in this code. I can't see anywhere its value then how it can be used here.

[Star Strider]

The rand function returns uniformly-distributed pseudorandom numbers on the interval (0,1).

[Aftab Ahmed Khan]

Then why i am not getting something like this. I am again using the rand function.

[Star Strider]

That is because xx and yy are scaled, so that the radius component is always on the interval (0,r) and the quadrant is defined by the sign of the sin and cos (respectively) of different random numbers, this time on the interval (0,2*pi), so those parts of the calculation are defined on the interval (-1,1).

The end result is that xx and yy are each independently defined on the same interval for both the radius and angle compoents, but are different because the values returned by rand are different. Here, it looks as though they will always end up on an angle that is some odd integer multiple of (pi/4) radians, with varying radii.

Those explain posxy(:,1:2). I don’t understand posxy(:3).

Answer 1

[Star Strider]

Computer-generated random numbers aren’t really ‘random’ in the mathematical sense of ‘randomness’ because they depend on deterministic algorithms and finite word lengths to compute them. These also depend on where the random number generator starts (the ‘seed’ number). The term used to describe numbers generated by these algorithms is ‘pseudorandom’ for that reason.

MathWorks explains it better than I can, because they wrote the algorithms. See Random Numbers in MATLAB and Why Do Random Numbers Repeat After Startup? for details.

[Aftab Ahmed Khan]

Hi star,

I got this now for my starting question. There is no pattern in it now compare to my starting question. I achieved this by removing the sign function from below two lines of code. Can you explain to me what this function does over here. I understand what sign function does, but what does it do over here ?

   xx  = (r*rand) * sign(sin(2*pi*rand));                 
          yy  = (r*rand) * sign(cos(2*pi*rand));

[Star Strider]

Here, the sign function forces the angle the radii are plotted against to always be an odd integer multiple of (pi/4) radians (45°).

Removing the sign function allows the angle to be defined randomly on the interval (0,2*pi).