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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}
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