H-tree and b-tree

The H-tree got his name because of its repeating pattern which looks like the letter "H". It is also called H-fractal, it's a space-filling curve with a Hausdorff dimension of 2.

A binary tree is a tree where each node has no more than two child nodes.

The example shows how to build up a tree recursively using a foreach loop. It uses the tree stuff already in TikZ. With a slight modification, the routine for drawing the H-tree can be adapted to a full binary tree.

Edit and compile if you like:

% H-tree and B-tree
% Author: Andrew Stacey
\documentclass{article}
\usepackage{tikz}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength{\PreviewBorder}{10pt}%
\tikzset{
  htree leaves/.initial=2,
  sibling angle/.initial=20,
  htree level/.initial={}
}

\makeatletter

\def\htree@growth{%
  \pgftransformrotate{%
    (\pgfkeysvalueof{/tikz/sibling angle})*(-.5-.5*\tikznumberofchildren
      +\tikznumberofcurrentchild)}%
  \pgftransformxshift{\the\tikzleveldistance}%
  \pgfkeysvalueof{/tikz/htree level}%
}
\tikzstyle{htree}=[
  growth function=\htree@growth,
  sibling angle=180,
  htree level={
    \tikzleveldistance=.707\tikzleveldistance
    \pgfsetlinewidth{.707*\the\pgflinewidth}
  }
]

\tikzstyle{btree}=[
  growth function=\htree@growth,
  sibling angle=60,
  htree level={
    \tikzleveldistance=.55\tikzleveldistance
    \pgfsetlinewidth{.707*\the\pgflinewidth}
  }
]

\long\def\ge@addto@macro#1#2{%
  \begingroup
  \toks@\expandafter\expandafter\expandafter{\expandafter#1#2}%
  \xdef#1{\the\toks@}%
  \endgroup}

\newcommand{\htree}[2][]{%
  \def\htree@start{\noexpand\coordinate}
  \def\htree@end{}
  \foreach \l in {0,...,#2} {
    \g@addto@macro\htree@start{child foreach \noexpand\x in {1,2} {\iffalse}\fi}
    \g@addto@macro\htree@end{\iffalse{\fi}}
    \global\let\htree@start\htree@start
    \global\let\htree@end\htree@end
  }
  \edef\htree@cmd{\htree@start\htree@end;}
  \begin{scope}[htree,#1]
  \htree@cmd
  \end{scope}
}

\makeatother

\begin{document}
\begin{tikzpicture}[
  rotate=90,
  yscale=.5,
  level distance=3cm,
  line width=8pt,
]
\htree{7}
\htree[btree,yshift=-12cm,xshift=-3cm]{7}
\end{tikzpicture}
\end{document}