Distribution of Nearest Neighbor

dist_2d.m

% number of random points to generate
number = 500;
x_dim = 100;
y_dim = 100;

% generate points
points = rand(number,2) * [x_dim 0; 0 y_dim];

% list of nearest neighbors
nearest_neighbors = nan(1, number);

% get nearest neighbor to each point
idx = 1:number;
for i = idx
    others = (idx ~= i);
    nearest_neighbors(i) = min(sqrt(sum(((ones(number - 1, 1) * points(i, :)) - points(others, :)) .^ 2, 2)));
end

% create a scatter plot
f_s = figure;
scatter(points(:, 1), points(:, 2));
xlim([0 x_dim]);
ylim([0 y_dim]);

% create a histogram
f_h = figure;
hist(nearest_neighbors);
ylabel('Distance to nearest neighbor');
title('Histogram');