How to show rows of randomly colored circles

Question

I would like to have 5 rows of randomly colored circles. Here is my MWE:

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\setbeamersize{text margin left=10mm,text margin right=5mm} 
\setbeamertemplate{frametitle}[default][center]
\usepackage{tikz}

\newcommand{\tikzcircle}[2][red,fill=red]{\tikz[baseline=-0.5ex]\draw[#1,radius=#2] (0,0) circle ;}%


\begin{document}
\begin{frame}{The counting problem}
\foreach \x in {1,2,...,100}  {\tikzcircle{2pt}}
\end{frame}

\end{document}

I am not sure how to pick the colors at random or how to get the circles to wrap so they fill the space the text would normally fill.

If possible, it would be great if I could pick colors randomly with replacement from a set whose size I can specify. E.g pick the colors randomly with replacement from a set of 10 colors.

Answer 1

You can start with something like this. Code for \randomcolor was taken from Generate random color in way that works with both pdflatex and lualatex

\documentclass{beamer}

\beamertemplatenavigationsymbolsempty
\setbeamersize{text margin left=10mm,text margin right=5mm} 
\setbeamertemplate{frametitle}[default][center]
\usepackage{tikz}

\newcommand{\randomcolor}{%
    \pgfmathsetmacro{\R}{random(0,10000)/10000}%
    \pgfmathsetmacro{\G}{random(0,10000)/10000}%
    \pgfmathsetmacro{\B}{random(0,10000)/10000}%
    \definecolor{randomcolor}{rgb}{\R,\G,\B}%
}

\newcommand{\tikzcircle}[1]{\randomcolor\tikz[baseline=-0.5ex]{\fill[randomcolor,radius=#1]circle;}}%


\pgfmathsetseed{\number\pdfrandomseed} % seed for random generator


\begin{document}

\begin{frame}{The counting problem}

\foreach \j in {1,2,...,5} {\foreach \i in {1,2,...,10} {\tikzcircle{.05\textwidth}}\\}

\end{frame}
\end{document}

Update: limited colors

Following code shows an alternative to select colors from a limited set. The set is defined into a TikZ array and the color is selected with a random index.

\documentclass{beamer}

\beamertemplatenavigationsymbolsempty
\setbeamersize{text margin left=10mm,text margin right=5mm} 
\setbeamertemplate{frametitle}[default][center]
\usepackage{tikz}

\def\mycolors{{"red","green","blue","brown","pink","violet","orange","cyan","yellow"}}
    
\newcommand{\tikzcircle}[1]{%
    \pgfmathsetmacro{\mycolorindex}{random(0,8)}%
    \pgfmathsetmacro{\mycolor}{array(\mycolors,\mycolorindex)}%
    \tikz[baseline=-0.5ex]{\fill[\mycolor,radius=#1]circle;}}%

\pgfmathsetseed{\number\pdfrandomseed} % seed for random generator

\begin{document}

\begin{frame}{The counting problem}

\foreach \j in {1,2,...,5}{\foreach \i in {1,2,...,10}{\tikzcircle{.05\textwidth}}\\}

\end{frame}
\end{document}

Answer 2

Try to play with the parameters of the random number generator, while keeping the same seed.

For example

\documentclass{beamer}

\beamertemplatenavigationsymbolsempty
\setbeamersize{text margin left=10mm,text margin right=5mm} 
\setbeamertemplate{frametitle}[default][center]
\usepackage{tikz}

\newcommand{\randomcolor}{%
    \pgfmathsetmacro{\R}{random(0,1)/2}%
    \pgfmathsetmacro{\G}{random(0,1)/2}%
    \pgfmathsetmacro{\B}{random(0,1)/1}%
    \definecolor{randomcolor}{rgb}{\R,\G,\B}%
}

\newcommand{\tikzcircle}[1]{\randomcolor\tikz[baseline=-0.5ex]{\fill[randomcolor,radius=#1]circle;}}%


%\pgfmathsetseed{\number\pdfrandomseed} % seed for random generator


\begin{document}

\begin{frame}{The counting problem}

\foreach \j in {1,2,...,5}{\foreach \i in {1,2,...,10}{\noindent\tikzcircle{.05\textwidth}}\\}

\end{frame}
\end{document}
    

will produce 2x2x2 = 8 different colors. (R= 0 or 0.5, etc.)