如何绘制层次矩阵模式？

Question

如何绘制像这样的分层矩阵图案（是否使用 TikZ）？以及如何在两个矩形矩阵的乘积之间添加一个小的方阵？

是否有可能创建一个可以在层次结构的下一级重复使用的构建块，而无需重复相同的代码？

我认为构建模块可能是这样的：

\documentclass[border=3mm]{standalone}
\usepackage{tikz}

\begin{document}
  \begin{tikzpicture}[baseline={(0, 1.75cm)}]
    \draw (0,0) rectangle (4,4);
    \filldraw [ fill={gray} ] (0,2) rectangle (2,4);
    \filldraw [ fill={gray} ] (2,0) rectangle (4,2);
    
    \filldraw [ fill={gray} ] (0.1,1) rectangle (0.4,1.8);
    \filldraw [ fill={gray} ] (0.5,1.5) rectangle (0.8,1.8);
    \filldraw [ fill={gray} ] (0.9,1.5) rectangle (1.7,1.8);
    
    \filldraw [ fill={gray} ] (2.1,3) rectangle (2.4,3.8);
    \filldraw [ fill={gray} ] (2.5,3.5) rectangle (2.8,3.8);
    \filldraw [ fill={gray} ] (2.9,3.5) rectangle (3.7,3.8);
  \end{tikzpicture}}
\end{document]

Answer 1

描述

• pic为两个矩形 ( rectangles) 和正方形 ( x0)定义s
• 进一步的图片 xi 用递归方式定义\defxi
• 该比例用作递归的参数

代码

\documentclass[border=3mm]{standalone}

\usepackage{tikz}

\tikzset{
    x0/.pic={
        \draw[fill={gray}] (0,0) rectangle (1,1);
    },
    rectangles/.pic={
        \draw[fill={gray}] (0.1,0.8) rectangle (.3,.2);
        \draw[fill={gray}] (0.4,0.8) rectangle (.9,.6);
    },
    every pic/.style={transform shape},
}

\newcommand{\defxi}[1]{
    \tikzset{
        x#1/.pic={
            \draw[scale=##1] (0,0) rectangle (1,1);
            \pic[scale=.5*##1] at (0,.5) {x\the\numexpr#1-1\relax=##1};
            \pic[scale=.5*##1] at (.5,0) {x\the\numexpr#1-1\relax=##1};
            \pic[scale=.5*##1] at (0,0) {rectangles};
            \pic[scale=.5*##1] at (.5,.5) {rectangles};
        }
    }
}

\defxi{1}
\defxi{2}
\defxi{3}
\defxi{4}

\begin{document}
\begin{tikzpicture}
    \foreach \i in {0, ..., 4} {
        \pic at (\i*1.2,0) {x\i=1};
    }
\end{tikzpicture}
\end{document}

结果

Answer 2

我已经调整了我的递归代码这个多边形相关的答案drawDist。我删除了有关和的全部长篇大论，shiftDist因为它们让事情变得比本来的更复杂。

两个矩形的线宽随着每个更深的层次而减半。这是通过

line width=.4pt/2^(\pgfkeysvalueof{/tikz/flakes/level'}-1)

基本上/tikz/flakes/level'是一个计数器，随着我们越深入，计数就会增加（而level计数越低）。默认线宽thin为 0.4pt，我在这里将其用作起始线宽。

代码

\documentclass[tikz]{standalone}
\usepgfkeyslibrary{ext.pgfkeys-plus}
\makeatletter
\pgfqkeys{/handlers}{
  .foreach/.code={\let\pgfkeys@exp@call@\pgfkeys@exp@call
    \foreach\pgf@keys@temp in{#1}{\expandafter\pgfkeys@exp@call@\expandafter{\pgf@keys@temp}}}}
\makeatother
\newcommand*\flakesset{\pgfqkeys{/tikz/flakes}}
\newcommand*\flakescreate[1][]{\begingroup\flakesset{#1,start}\endgroup}
\flakesset{% adapted from https://tex.stackexchange.com/a/685124
  .code=\flakesset{#1}, tikz/.code=\tikzset{#1},
  level/.initial=0, level'/.initial=0, item/.initial=0,
  start item/.initial=0, end item/.initial=3,
  item list/.initial={\pgfkeysvalueof{/tikz/flakes/start item},...,\pgfkeysvalueof{/tikz/flakes/end item}},
  start/.style={level'=0, item=0, tikz=flakes/at start/.try, __do=0},
  __do/.style={
    /utils/TeX/ifnum={\pgfkeysvalueof{/tikz/flakes/level}=0}{__place={#1}}{
      level/.--, level'/.++, before split={#1},
      __split/.foreach/.expanded={\pgfkeysvalueof{/tikz/flakes/item list}}}},
  __split/.code={%
    \pgfkeyssetevalue{/tikz/flakes/item}{#1}%
    \tikzset{flakes/before do={#1}}%
    \flakesset{__do={#1}}%
    \tikzset{flakes/after do/.try={#1}}},
  __place/.code={\path[flakes/styling={#1}](0,0)to[flakes/path={#1}](0,0);},
  before split/.style={
    level \pgfkeysvalueof{/tikz/flakes/level}/.try={#1},
    level \pgfkeysvalueof{/tikz/flakes/level'}'/.try={#1}}}

%% Here starts your definitions
\flakesset{
  hiermatrix/.style={
    /tikz/my test/.style n args={3}{/utils/TeX/if=##1{##2}{##3}},
    before do/.style 2 args={
      shift={(##1.5,##2.5)}, scale=.5,
      my test={##1##2}{% if ++ or -- place the drawing and stop recursions
        /tikz/flakes/__place={##1##2},
        /tikz/flakes/__do/.code=}{}},
    styling/.style={
      my flakes,
      my test={##1}{line width=.4pt/2^(\pgfkeysvalueof{/tikz/flakes/level'}-1)}{}},
    item list={++, -+, --, +-},
    path/.style={
      my test={##1}{% if ++ or -- draw two rectangles with border
        to path={
          (-1,-1) edge[to path=rectangle(\tikztotarget),thin,path only,draw] (1,1)
          (-.75, -.5) rectangle ++(.25, 1.125) ++(right:.2) rectangle +(1, -.25)},
      }{% otherwise just a rectangle
        to path={(-1, -1) rectangle (1, 1)}}}}}
\begin{document}
\tikz[my flakes/.style={draw=black, fill=lightgray}]
  \matrix[
    column sep=5mm,
    nodes={node font=\bfseries\sffamily,
       node contents=(\pgfkeysvalueof{/tikz/flakes/level})},
    cells={flakes/level/.expanded=\inteval{\pgfmatrixcurrentcolumn-1}}
  ]{
    \path[my flakes] (-1,-1) rectangle (1,1); & \flakescreate[hiermatrix]
                  & \flakescreate[hiermatrix] & \flakescreate[hiermatrix] \\
    \node[]; & \node[]; & \node[]; & \node[];\\};
\end{document}

输出