Text spirals with TikZ

Question

I just ran across this, and I'm curious about whether it can be replicated in TeX...

Ideally one would have the spiral getting tighter and tighter as one got to the centre, as in

I know TikZ has the ability to fit text along a path, but I'm not sure how one might make text get smaller and smaller. The closest I can find is create elegant display of digits and symbols, but that uses manually inserted font commands.

Edit: I got what I wanted using mwibrow's answer:

Answer 1

Overrated or not, it is the case that tikz cannot do this by default. Also, somewhat annoyingly it isn't possible to use \lipsum[1] as an argument for text key in the text along path decoration (which I concede is entirely my fault).

A proper solution would take a bit more work, so here's a crude - but servicable - hack:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.text}

\makeatletter

\let\pgf@lib@dec@text@dobox@original=\pgf@lib@dec@text@dobox%

\def\pgf@lib@dec@text@dobox{%
    \pgf@lib@dec@text@dobox@original%
    \ifpgfdecorationtextalongpathscaletext%
    \pgfmathparse{\pgf@lib@dec@text@endscale+(\pgf@lib@dec@text@startscale-\pgf@lib@dec@text@endscale)*\pgfdecoratedremainingdistance/\pgfdecoratedpathlength}%
    \setbox\pgf@lib@dec@text@box=\hbox{\scalebox{\pgfmathresult}{\box\pgf@lib@dec@text@box}}%
    \fi%
}
\newif\ifpgfdecorationtextalongpathscaletext
\def\pgf@lib@dec@text@startscale{1}
\def\pgf@lib@dec@text@endscale{1}

\pgfkeys{/pgf/decoration/.cd,
    text path start scale/.code={%
        \pgfdecorationtextalongpathscaletexttrue%
        \def\pgf@lib@dec@text@startscale{#1}%
    },
    text path end scale/.code={%
        \pgfdecorationtextalongpathscaletexttrue%
        \def\pgf@lib@dec@text@endscale{#1}%
    }
}
\begin{document}    
\begin{tikzpicture}[
    decoration={
    reverse path,
    text along path,
    text path start scale=1.5,
    text path end scale=0,
    text={Lorem ipsum dolor sit amet, consectetur adipisicing elit, 
    sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. 
    Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris
    nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in
    reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla
    pariatur. Excepteur sint occaecat cupidatat non proident, sunt
    inculpa qui officia deserunt mollit anim id est laborum.}}
]
\draw [decorate] 
    (0,0) 
    \foreach \i [evaluate={\r=(\i/2000)^2;}] in {0,5,...,2880}{ -- (\i:\r)}; 
\useasboundingbox (-2.75,-2.75) rectangle (2.75,2.75); 
\end{tikzpicture}    
\end{document}

Answer 2

run with latex->dvips->ps2pdf

\documentclass[12pt]{article}
\usepackage{pst-plot}
\usepackage{pst-text}
\usepackage{lipsum}

\pagestyle{empty}
\begin{document}
\large
\begin{pspicture}(-3.8,-5)(4.5,4.5)
\pstextpath{%
  \parametricplot[linestyle=none,plotpoints=5000,algebraic,unit=0.25]
    {0}{200}{t^2*sin(t)/200 | t^2*cos(t)/200}}{\lipsum[1]}%
\end{pspicture}

\end{document}

it is also possible to increase the fontsize, but then we have to handle every character.

\documentclass[pstricks]{standalone}
\usepackage[T1]{fontenc}
\usepackage{mathptmx}
\usepackage{pst-plot}
\usepackage{pst-text}

\newdimen\MyDim \MyDim=30pt
\makeatletter
\def\doPerChar#1#2\@nil{%
    \CharacterAction{#1}%
    \ifx\relax#2\relax\else\doPerChar#2\@nil\fi}
\def\perChar#1{\doPerChar#1\@nil}
\def\CharacterAction#1{%
  \fontsize{\MyDim}{1.1\MyDim}\selectfont#1%
  \global\advance\MyDim by -0.175pt}
\makeatother

\pagestyle{empty}
\begin{document}

\begin{pspicture}(-3,-3)(3,3)
\pstextpath{%
  \parametricplot[linestyle=none,plotpoints=5000,algebraic,unit=0.2]
    {50}{0}[/A 5e-3 def ]{A*(cos(t)+t^2*sin(t)) | A*(sin(t)-t^2*cos(t))}}{\perChar{Now~we~write~some~nensense~text~here~to~write~it~on~%
        an~involute~only~to~see~what~happens~with~this~nonsense~text~%
        in~this~nonsense~example!}}
\end{pspicture}

\end{document}