将 Spirograph 代码与嵌套的多个 \foreach 循环相结合

Question

我使用了以下代码来回答这个问题将比例与颜色和旋转变化结合起来

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\begin{document}
\tikzset{pics/spiro/.style={code={
\tikzset{spiro/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro/##1}} 
\draw[trig format=rad,pic actions]
 plot[variable=\t,domain=0:2*pi*\pv{nRotations}, samples=90*\pv{nRotations}+1, smooth cycle] 
(
{(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
{(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})}
);
}},
spiro/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,nRotations/.initial=1}
\begin{frame}[t] 
\frametitle{Spiro`6,-1.5,1`- - foreach} 
\begin{center}
\vskip -.8cm
\begin{tikzpicture}[line width=.06cm]
\foreach \scl/\clr in {.8/10,.6/30,.4/50,.2/70} 
{
(0,0) \pic[draw,blue,outer color=blue!80,inner color/.expanded=blue!\clr,scale=\scl]{spiro}; 
}
\end{tikzpicture} 
\end{center} 
\end{frame}
\begin{frame}[t] 
\frametitle{Spiro`6,-1.5,1`- foreach} 
\begin{center}
\vskip -.8cm
\begin{tikzpicture}[line width=.06cm]
\foreach \scl/\clr/\clra in {.8/100/80,.7/80/70,.6/70/60,.5/60/50,.4/50/40,.3/40/30,.2/30/20,.1/20/10} 
%    \foreach \scl/\clr/\clra/\clrb in {.8/100/90/80,.7/90/80/70,.6/80/70/60,.5/70/60/50,.4/60/50/40,.3/50/40/30,.2/40/30/20,.1/30/20/10} 
{
(0,0) \pic[draw/.expanded=blue!\clr,fill/.expanded=blue!\clra,scale=\scl]{spiro}; 
%    (0,0) \pic[draw/.expanded=blue!\clr,outer color/.expanded=blue!\clra,inner color/.expanded=blue!\clrb,scale=\scl]{spiro}; 
}
\end{tikzpicture} 
\end{center} 
\end{frame}
\begin{frame}[t] 
\frametitle{Spiro`6,-1.5,1`- foreach} 
\begin{center}
\vskip -.8cm
\begin{tikzpicture}[line width=.06cm]
\foreach \scl/\rotate/\clr/\clra in {.8/0/100/80,.7/10/80/70,.6/20/70/60,.5/30/60/50,.4/40/50/40,.3/50/40/30,.2/60/30/20,.1/70/20/10} 
{
(0,0) \pic[draw/.expanded=blue!\clr,fill/.expanded=blue!\clra,scale=\scl,rotate/.expanded=\rotate]{spiro}; 
}
\end{tikzpicture} 
\end{center} 
\end{frame}
\end{document}

但我不知道如何将它应用于以下代码：

通过旋转来改变绘制和填充颜色的比例

\begin{frame}[t]
\frametitle{Spiro`6,-1.5,1`- - - -}
\begin{center}
\vskip -1.cm
\begin{tikzpicture}[line width=.8mm]
\draw
(0,0) pic[scale=.8, purple!80, rotate=0, fill=purple!60]{spiro}
(0,0) pic[scale=.7, red!80, rotate=10, fill=red!60]{spiro}
(0,0) pic[scale=.6, orange!80, rotate=20, fill=orange!60]{spiro}
(0,0) pic[scale=.5, yellow!80, rotate=30, fill=yellow!60]{spiro}
(0,0) pic[scale=.4, green!80, rotate=40, fill=green!60]{spiro}
(0,0) pic[scale=.3, cyan!80, rotate=50, fill=cyan!60]{spiro}
(0,0) pic[scale=.2, blue!80, rotate=60, fill=blue!60]{spiro}
(0,0) pic[scale=.1, violet!80, rotate=70, fill=violet!60]{spiro}
;
\end{tikzpicture}
\end{center}
\end{frame}

产生

Answer 1

您只需要循环颜色，就可以从计数器中得出比例和旋转角度。

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\tikzset{pics/spiro/.style={code={
\tikzset{spiro/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro/##1}} 
\draw[trig format=rad,pic actions]
 plot[variable=\t,domain=0:2*pi*\pv{nRotations}, samples=90*\pv{nRotations}+1, smooth cycle] 
(
{(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
{(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})}
);
}},
spiro/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,nRotations/.initial=1}
\begin{document}

\begin{frame}[t]
\frametitle{Spiro`6,-1.5,1`- foreach}
\begin{center}
\vskip -1.cm
\begin{tikzpicture}[line width=.8mm]
\draw foreach \Col [count=\Y starting from 0] 
    in {purple,red,orange,yellow,green,cyan,blue,violet}
    {pic[scale=.8-0.1*\Y, \Col!80, rotate=\Y*10, fill=\Col!60]{spiro}};
\end{tikzpicture}
\end{center}
\end{frame}
\end{document}