Displaying circles in sequence from the same central point

Question

I would like to draw concentric circles that are displayed in sequence.

When applying the following code, the circles appear to move from the top edge downwards as each circle is displayed.

How to avoid this and make them displayed on top of each other from the same centre coordinate as in this diagram.

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{tkz-fct}
\usetikzlibrary{fadings}
\begin{document}
\begin{frame}[fragile,t]
\frametitle{}
\begin {center}
\begin{tikzpicture}[scale=.9, transform shape]
  \only<1,5>
{
\node[circle, outer color=yellow!60!green, inner color=white, minimum width=5cm] (radial) at (4,0) {};
\fill[pattern=dots,pattern color = black] (3.6,-.4) -- + +(.8,0) -- ++ (0,.8) -- ++(-.8,0) -- cycle;
}
  \only<4-5>
{
\node[circle, outer color=green!80!purple, inner color=purple, minimum width=4cm] (radial) at (4,0) {};
}
  \only<3-5>
{
\node[circle, outer color=purple, inner color=purple!20!red, minimum width=3cm] (radial) at (4,0) {};
}
  \only<2-5>
{
\node[circle, outer color=purple, inner color=purple!50!black, minimum width=2cm] (radial) at (4,0) {};
}
\end{tikzpicture}
\end {center}
\end{frame}
\end{document}

Answer 1

a rude solution is add to each slide invisible circle with minimum size of the greatest one:

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usetikzlibrary{fadings, patterns}

\begin{document}
\begin{frame}[fragile,t]
\frametitle{Circles \dots}
\begin {center}
\begin{tikzpicture}[scale=.9,
circ/.style args = {#1/#2/#3}{circle,outer color=#1, inner color=#2, minimum width=#3,
                              node contents={}},
                    ]
  \only<1,5>
{
\node[circ=yellow!60!green/white/5cm];
\fill[pattern=dots,pattern color = black] (-0.4,-0.4) rectangle + (0.8,0.8);
}
  \only<4-5>
{
\node[circle, minimum size=5cm] {};
\node[circ=green!80!purple/purple/4cm];
}
  \only<3-5>
{
\node[circle, minimum size=5cm] {};
\node[circ=purple/purple!20!red/3cm];
}
  \only<2-5>
{
\node[circle, minimum size=5cm] {};
\node[circ=purple/purple!50!black/2cm];
}
\end{tikzpicture}
\end {center}
\end{frame}
\end{document}

note:

• coordinates in tikzpicure are relative to picture, not to slide. therefore in your case at (4,0) gives the same result as at (0,0) or if you omit explicit notation of coordinates.

• for determining coordinate on absolute position on slide, you need to use remember picture, overlay:

  \documentclass{beamer}
  \beamertemplatenavigationsymbolsempty
  \usepackage{tikz}
  \usetikzlibrary{calc, fadings, patterns,
                  overlay-beamer-styles}
  
  \begin{document}
  \begin{frame}[fragile,t]
  \frametitle{Circles \dots}
  \begin{tikzpicture}[remember picture,overlay,
  circ/.style args = {#1/#2/#3}{circle,outer color=#1, inner color=#2, minimum width=#3},
                      ]
    \only<1,5>
  {
  \node[circ=yellow!60!green/white/5cm] (center) at (current page.center) {};
  \fill[pattern=dots,pattern color = black]
      ($(current page.center)+(-0.4,-0.4)$) rectangle + (0.8,0.8);
  }
    \only<4-5>
  {
  \node[circ=green!80!purple/purple/4cm] at (center) {};
  }
    \only<3-5>
  {
  \node[circ=purple/purple!20!red/3cm] at (center) {};;
  }
    \only<2-5>
  {
  \node[circ=purple/purple!50!black/2cm] at (center) {};;
  }
  \end{tikzpicture}
  \end{frame}
  \end{document}
  

Answer 2

A less rude solution with the beamer-overlay-styles library.

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usetikzlibrary{overlay-beamer-styles} %<-added
\usepackage{pgfplots}
\usepackage{tkz-fct}
\usetikzlibrary{fadings}
\begin{document}
\begin{frame}[fragile,t]
\frametitle{Circles with the \texttt{overlay-beamer-styles} library}
\begin {center}
\begin{tikzpicture}[scale=.9, transform shape]
\node[visible on=<{1,5}>,circle, outer color=yellow!60!green, inner color=white, minimum width=5cm] (radial) at (4,0) {};
\fill[visible on=<{1,5}>,pattern=dots,pattern color = black] (3.6,-.4) -- + +(.8,0) -- ++ (0,.8) -- ++(-.8,0) -- cycle;
\node[visible on=<{4-5}>,circle, outer color=green!80!purple, inner color=purple, minimum width=4cm] (radial) at (4,0) {};
\node[visible on=<{3-5}>,circle, outer color=purple, inner color=purple!20!red, minimum width=3cm] (radial) at (4,0) {};
\node[visible on=<{2-5}>,circle, outer color=purple, inner color=purple!50!black, minimum width=2cm] (radial) at (4,0) {};
\end{tikzpicture}
\end {center}
\end{frame}
\end{document}