Without having clear technical goals, I'm just going to assume that no technical requirements exist for shape or density. I'm going to treat this as a rudimentary dithering operation.
% image size
s = 320;
% generate some gaussian profile or something?
sg = s*0.15; % gaussian shape parameter
os = 0.05; % background noise
R = linspace(-s/2,s/2,s);
prof = exp(-(R.^2 + R.'.^2)/(2*sg^2));
prof = prof*(1-os) + os;
% create random mask
mask = rand(s);
% binarize profile by comparing gray levels to mask
out = mask <= prof;
imshow(out)
