Question

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

enter image description here

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

enter image description here

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 ^[1], but that uses manually inserted font commands.

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

mwibrow

[1] https://tex.stackexchange.com/questions/82867/create-elegant-display-of-digits-and-symbols/82877#82877

Answer 1

The text effects along path (in PGF 3.0) can do this quite easily (if a bit slowly):

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{decorations.text}
\begin{document}
\begin{tikzpicture}[
  decoration={
    reverse path,
    text effects along path,
    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.},
    text effects/.cd,
      text along path,
      character count=\i, character total=\n,
      characters={scale=1-\i/\n}
    }
]
\draw [decorate] (0,0) 
    \foreach \i [evaluate={\r=(\i/2000)^2;}] in {0,5,...,2880}{ -- (\i:\r)}; 
\end{tikzpicture}
\end{document}

For PGF versions before 3.0, see the edit history where a simple hack is described.

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}

enter image description here

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

enter image description here

\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}