Graphics, Figures & Tables ⇒ Diagrams in the complex Plane, Markov Maps

[tomosparry]

Hi,

I'd like to add in several diagrams into a LaTeX document I'm doing. The diagrams fall into two types:

1. diagrams of isolated points, discs and half planes in the complex plane
2. diagrams of Markov maps (these are maps of the unit interval into itself, where the unit interval is split into a finite partition; the point is I'd like vertical and horizontal lines highlighting the partition. As for what the function does, it will be any piecewise smooth map, with the discontinuities happening at the partition points)

Any help with any of those would be greatly appreciated.

Thanks very much.

[Stefan Kottwitz]

Hi tomosparry,

welcome to the board!

I would use TikZ for that. Here's an example, written by Martin Scharrer, copied from texample.net: Circle in the complex plane with TikZ.

Code: Select all

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \begin{scope}[thick,font=\scriptsize]
    % Axes:
    % Are simply drawn using line with the `->` option to make them arrows:
    % The main labels of the axes can be places using `node`s:
    \draw [->] (-5,0) -- (5,0) node [above left]  {$\Re\{z\}$};
    \draw [->] (0,-5) -- (0,5) node [below right] {$\Im\{z\}$};

    % Axes labels:
    % Are drawn using small lines and labeled with `node`s. The placement can be set using options
    \iffalse% Single
    % If you only want a single label per axis side:
    \draw (1,-3pt) -- (1,3pt)   node [above] {$1$};
    \draw (-1,-3pt) -- (-1,3pt) node [above] {$-1$};
    \draw (-3pt,1) -- (3pt,1)   node [right] {$i$};
    \draw (-3pt,-1) -- (3pt,-1) node [right] {$-i$};
    \else% Multiple
    % If you want labels at every unit step:
    \foreach \n in {-4,...,-1,1,2,...,4}{%
        \draw (\n,-3pt) -- (\n,3pt)   node [above] {$\n$};
        \draw (-3pt,\n) -- (3pt,\n)   node [right] {$\n i$};
    }
    \fi
    \end{scope}
    % The circle is drawn with `(x,y) circle (radius)`
    % You can draw the outer border and fill the inner area differently.
    % Here I use gray, semitransparent filling to not cover the axes below the circle
    \path [draw=none,fill=gray,semitransparent] (+1,-1) circle (3);
    % Place the equation into the circle:
    \node [below right,darkgray] at (+1,-1) {$|z-1+i| \leq 3$};
\end{tikzpicture}
\end{document}

complex-plane.png (20.91 KiB) Viewed 3187 times

Browse the TikZ Example Gallery to see more examples, and have a look at the TikZ manual.

Stefan

[tomosparry]

Thanks very much, I'll give it a try!