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Added Stern-Brocot-Tree

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Martin Thoma 2013-10-01 12:12:01 +02:00
parent e0923f1d09
commit 23569bea72
4 changed files with 94 additions and 0 deletions
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tikz/stern-brocot-tree/stern-brocot-tree.tex Normal file
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\documentclass[tikz]{standalone}
\usepackage{forest}
\makeatletter
\pgfmathdeclarefunction{strrepeat}{2}{%
\begingroup
\pgfmathint{#2}\pgfmath@count\pgfmathresult
\let\pgfmathresult\pgfutil@empty
\pgfutil@loop
\ifnum\pgfmath@count>0\relax
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult#1}%
\advance\pgfmath@count-1\relax
\pgfutil@repeat
\pgfmath@smuggleone\pgfmathresult
\endgroup}
\makeatother
\tikzset{
Stern Brocot at/.style={at/.pgfmath={
strcat("([rotate around=180:(!", strrepeat("#1",\SBLevel),")] !",
strrepeat("#1",\SBLevel-1),"2)")}},
Stern Brocot at*/.style n args={3}{
at/.pgfmath={strcat("(!",strrepeat("#1",#2),"-| SB@#3)")},
append after command/.expanded={\ifnum#2<\SBLevel(\noexpand\tikzlastnode)
edge[densely dotted] (SB@#3@\the\numexpr\SBLLoop+1\relax)\fi}}}
\begin{document}
\begin{forest}
Stern Brocot*/.style n args={2}{
content=$\frac{#1}{#2}$,
edge=densely dotted,
if={level()<\SBLevel}{append={[,Stern Brocot*={#1}{#2}]}}{}},
Stern Brocot/.style n args={5}{
/utils/exec=\edef\SBLevel{#5},@Stern Brocot={#1}{#2}{#3}{#4}},
@Stern Brocot/.style n args={4}{
/utils/exec=\edef\SBTop{\number\numexpr#1+#3\relax}%
\edef\SBBottom{\number\numexpr#2+#4\relax},
content/.expanded=$\frac{\SBTop}{\SBBottom}$,
if/.expanded={level()<\SBLevel}{% true
append={[,@Stern Brocot={#1}{#2}{\SBTop}{\SBBottom}]},
append={[,Stern Brocot*={\SBTop}{\SBBottom}]},
append={[,@Stern Brocot={\SBTop}{\SBBottom}{#3}{#4}]}
}{}}% false (empty)
[,Stern Brocot={0}{1}{1}{0}{4}]
%
\coordinate[Stern Brocot at=1] (SB@left) coordinate[Stern Brocot at=3] (SB@right);
\foreach \SBLLoop in {\SBLevel, ..., 0}
\path node[Stern Brocot at*={1}{\SBLLoop}{left}] (SB@left@\SBLLoop) {$\frac01$}
node[Stern Brocot at*={3}{\SBLLoop}{right}] (SB@right@\SBLLoop) {$\frac10$};
\end{forest}
\end{document}