# Distribute a given number of equally sized rectangles along a spiral path with minimum distance between adjacent rectangle edges constant

I would like to generate a set of x,y coordinates according to which thumbnails (i.e. rectangles) should appear along a spiral path so that the minimum distance between the edges of adjacent thumbnails is constant. This is to ensure that the icons are nicely displayed along the spiral so that none of them overlap or are spread too far from each other.

Given is: the number of points to generate, the dimensions of the rectangles (same for all), the minimum distance between the edges and necessary parameters for the spiral.

Here's an illustration with an approximation of what I'm trying to achieve (only in my case the rectangles all have the same size and the minimum distance between neighbouring rectangles should be constant):

What algorithm or formula should I use to do that?