Golden circles

This is from my tweet here. It’s based on a drawing by Diego Rattaggi.

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\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{intersections}
\let\phi\varphi
\begin{document}
\begin{tikzpicture}[nodes = {execute at begin node=$, execute at end node=$}]
  \pgfmathsetmacro\r{(1+sqrt(5))/2}
  \draw [name path=c1] circle(\r) node{\phi=\frac{1+\sqrt{5}}{2}};
  \draw [name path=c2,fill=green!15] (0,\r+\r^2) circle(\r^2)  node{\phi^2};
  \draw [name path=c3] (0,\r^3-\r) circle(\r^3);
  \path [name path=l] (-\r^3,\r) -- (\r^3,\r);
  \draw [name intersections={of=l and c3, name=l0}] 
        (l0-1) -- (l0-2);
  \path [name path=l1] (-\r^3,\r+1) -- (\r^3,\r+1);
  \path [name path=c4] (0,\r+\r^2) circle(\r^2+1);
  \draw [name intersections={of=l1 and c4, name=c},fill=blue!10] 
        (c-1) circle (1) node {1};
  \draw [fill=blue!10] (c-2) circle (1) node {1};
  \path [name path=l4] (-\r^3,\r-1) -- (\r^3,\r-1);
  \path [name path=c8] (0,0) circle(\r+1);
  \draw [name intersections={of=l4 and c8, name=c9},fill=blue!10] 
        (c9-1) circle (1) node {1};
  \draw [name intersections={of=l4 and c8, name=c9},fill=blue!10] 
        (c9-2) circle (1) node {1};
  \path [name path=c5] (0,\r+\r^2) circle(\r^2+\r^-2);
  \path [name path=l2] (-\r^3,\r+\r^-2) -- (\r^3,\r+\r^-2);
  \draw [name intersections={of=l2 and c5, name=c6},fill=orange!10] 
        (c6-1) circle (\r^-2) node [font=\scriptsize] {\phi^{-2}};
  \draw [fill=red!10] (c6-2) circle (\r^-2) node [font=\scriptsize] {\phi^{-2}};
  \path [name path=c7,dotted] (0,\r+\r^2) circle(\r^2+1/5);
  \path [dotted,name path=l3] (-\r^3,\r+1/5) -- (\r^3,\r+1/5);
  \draw [name intersections={of=l3 and c7, name=c8}] 
        (c8-1) circle (1/5) node[font=\tiny] {\frac{1}{5}};
  \draw [] (c8-2) circle (1/5) node[font=\tiny] {\frac{1}{5}};
  \path [name path=l5] (-\r^3,\r-\r/5) -- (\r^3,\r-\r/5);
  \path [name path=c10] (c9-1) circle(1+\r/5);
  \draw [name intersections={of=l5 and c10, name=c11},fill=yellow!30] 
 
 
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