Zufällige Anordnung von Kreisen in Tikz

[MC3330]

Hallo,

ich suche ein Möglichkeit, wie ich eine vorgegebenen Anzahl von Kreisen in einem Viereck zufällig verteilen kann. Dabei soll es möglich sein einen Mindestabstand einzustellen, damit es nicht zu Überlappungen kommt. Ich habe das Paket poisson gefunden, das ziemlich genau das macht, was ich möchte. Leider verstehe ich noch nicht, wie ich da die Anzahl an Kreisen vorgeben kann.

Ich wäre über Verbesserungen oder auch Tipps zu anderen Ansätzen Dankbar.

Minimalbeispiel

\documentclass[12pt,listof=totoc,bibliography=totoc,pointlessnumbers]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[obeyspaces]{url}
\usepackage[utf8]{inputenc}
\usepackage{lmodern} 
\usepackage{poisson} 
\usepackage{tikz}
\usetikzlibrary{math}


\tikzset{plaettchenvoll/.style={line width = 0.2 mm,draw,fill=gray!80,circle,minimum width = 3.25mm},
}%\\
\begin{document}
	\begin{tikzpicture}
		\xdef\mylist{\poissonpointslist{5}{5}{0.7}{3}}  % Sparse, fast
		\draw (-0.5,-0.5)--(5.5,-0.5)--(5.5,5.5)--(-0.5,5.5)--cycle;
		\foreach \x/\y[count=\i from 0]in \mylist {
				\node[plaettchenvoll,fill=blue!\i] at(\x,\y) {};
		}
	\end{tikzpicture}
\end{document}

poisson.sty

\directlua{dofile("poisson.lua")}
\newcommand{\poissonpointslist}[4]{
    \directlua{poisson_points_list(#1,#2,#3,#4)}
}

poisson.sty

-- This is a lua implementation of the algorithm described in
-- http://devmag.org.za/2009/05/03/poisson-disk-sampling/
--
-- The structure of the algorithm is exactly the same than in 
-- the mentioned article. Its pseudo-code snippets were translated
-- to Lua.
--
-- One detail worths an explanation, though. The article uses a 2D matrix
-- called grid to store coordinates of points. In the article, it is
-- assumed that grid elements can be accesed via grid[point], being point
-- some structure with a pair of x and y integers, so grid[point] should
-- be equivalent to grid[x,y] or grid[x][y]. This grid is assumed to be
-- initially dimensioned and filled by nils.
--
-- In my implementation the grid is dynamic, and it is an associative array
-- indexed by string keys in the form grid["(x,y)"]. The function gridToString()
-- can be used to convert a Point to its string form, so the grid is indeed
-- accesed like this: grid[gridToString(p)] being p a Point with integer
-- coordinates (which in fact is found via imageToGrid, like in the article)

-- UTILITY FUNCTIONS (used in the article, without giving implementation)
-- =====================================================================

-- RandomQueue stores values and gives them in random order
RandomQueue = {}
function RandomQueue.new ()
    return {last=-1}
end

function RandomQueue.push(q, item) 
    local last = q.last + 1
    q.last = last
    q[last] = item
end

function RandomQueue.pop(q)
    if (RandomQueue.empty(q)) then 
        return nil
    end
    local index = math.random(0,q.last) 
    -- A random index is generated. The last element
    -- is swaped with this random item, and the new
    -- last item is popped.
    local last = q.last
    item = q[index]
    q[index] = q[last]
    q[last] = nil
    q.last = last -1
    return item
end

function RandomQueue.empty(q)
    return q.last==-1
end

function RandomQueue.print(q)
    -- For debugging. Not used
    local t = {}
    for i=0, q.last do
        table.insert(t, string.format("(%f,%f)", q[i].x, q[i].y))
    end
    print (string.format("RandomQueue %d elem: %s", q.last+1, table.concat(t, " ")))
end

-- Point stores a coordinate pair
Point = {}

function Point.new(x,y)
    return {x=x, y=y}
end

-- Determines if a point is inside the rendered rectangle
function inRectangle(point, width, height)
  return (point.x>0 and point.y>0 and point.x