在整数格上绘制定向随机游走

Question

你能帮我画出随机环境中的随机游动吗？我如何在网格上画出有向随机游动，例如

或者用不同的颜色。我认为方法几乎相同。但我不知道如何开始。我学会了如何绘制二叉树。

提前感谢您的帮助和时间。

Answer 1

TikZ 示例：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{calc}

\pgfmathsetseed{3}

\begin{document}
  \begin{tikzpicture}

    % Coordinate axes
    \begin{scope}[
      semithick,
      ->,
      >={Stealth[]},
    ]
      \draw (0, -3.5) -- (0, 3.5);
      \draw (0, 0) -- (6.5, 0);
    \end{scope}

    % Ticks
    \draw[node font=\small]
      \foreach \y in {-3, ..., 3} {
        (0, \y) +(.25em, 0) -- ++(-.25em, 0)
        node[left] {$\y$}
      }
    ;

    % Random walk
    \draw[thick]
      (0, 0)
      \foreach \x in {1, ..., 6} {
        -- ++(1, {2*greater(rnd, .5) - 1})
      }
    ;

    % Random points
    \foreach \x in {1, ..., 6} {
      \foreach \y in {-3, ..., 3} {
        \pgfmathsetmacro\sy{random(0, 1)}%
        \node[
          circle,
          fill=white,
          draw,
          inner sep=0pt,
        ]
          at (\x, \y)
          {$\ifcase\sy -\else +\fi$}
        ;
      }
    }
  \end{tikzpicture}
\end{document}

第二个图的示例：

\documentclass{article}
\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{calc}

\pgfmathsetseed{3}

\begin{document}
  \begin{tikzpicture}[
    x=7.5mm,
    y=7.5mm,
  ]

    % Grid
    \draw[thin]
      \foreach \x in {0, ..., 10} {
        (\x, -6) -- (\x, 6)
      }
      \foreach \y in {-5, ..., 5} {
        (0, \y) -- (11, \y)
      }
    ;  

    % Coordinate axes
    \begin{scope}[
      semithick,
      ->,
      >={Stealth[]},
    ]
      \draw (0, -6.5) -- (0, 6.5);
      \draw (0, 0) -- (11.5, 0);
    \end{scope}

    % Random walk
    \draw[thick]
      (0, 0)
      \foreach \x in {1, ..., 10} {
        -- ++(1, {2*greater(rnd, .5) - 1})
      }
    ;  

    % Random points
    \tikzstyle{dot1} = [fill=white, draw];
    \tikzstyle{dot2} = [fill=lightgray, draw];
    \tikzstyle{dot3} = [fill=gray];
    \tikzstyle{dot4} = [fill=darkgray, draw];
    \tikzstyle{dot5} = [fill=black];
    \foreach \x in {1, ..., 10} {
      \foreach \y in {-5, ..., 5} {
        \pgfmathsetmacro\sy{random(1, 5)}%
        \path[dot\sy] (\x, \y) circle[radius=2mm];
      }
    }
  \end{tikzpicture}
\end{document}