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+%%
+%% Ein Beispiel der DANTE-Edition
+%%
+%% 2. Auflage
+%%
+%% Beispiel 15-04-82 auf Seite 813.
+%%
+%% Copyright (C) 2016 Herbert Voss
+%%
+%% It may be distributed and/or modified under the conditions
+%% of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%%
+%% See http://www.latex-project.org/lppl.txt for details.
+%%
+%%
+%% ====
+% Show page(s) 1
+%%
+%%
+\documentclass[]{exaarticle}
+\pagestyle{empty}
+\setlength\textwidth{352.81416pt}
+\usepackage[T1]{fontenc}
+%StartShownPreambleCommands
+\usepackage{pgfplots,luacode} \pgfplotsset{width=7cm,compat=1.8}
+\begin{luacode}
+ function weierstrass(x0, x1, n, a, b, epsilon)
+ local dx = (x1-x0)/n; x = x0
+ local y, k, dy
+ local out=assert(io.open("tmp.data","w")) -- external data file
+ while (x <= x1) do
+ y = 0; k = 0
+ repeat
+ dy = math.pow(a,k) * math.cos(math.pow(b,k)*math.pi*x)
+ y = y + dy; k = k + 1
+ until (math.abs(dy) < epsilon)
+ out:write(x, " ", y, "\string\n")
+ x = x + dx
+ end
+ out:close()
+ end
+\end{luacode}
+%StopShownPreambleCommands
+\begin{document}
+\begin{tikzpicture}
+ \directlua{weierstrass(-2,2,5000,0.3,5,1.e-12)}%
+ \begin{axis}[axis lines=middle, domain=-2:2]
+ \addplot [thin, line join=round] table {tmp.data}; %% read data
+ \coordinate (legend) at (axis cs:0,2);
+ \end{axis}
+ \node at (legend){$\displaystyle f(x)=\sum_{n=0}^\infty a^n \cos(b^n\pi x)$};
+\end{tikzpicture}
+\end{document}