フラクタル図形を描画するfractal.sty

fractal.sty

\RequirePackage{pgf}
\RequirePackage{tikz}
\RequirePackage{calc}

\newcounter{deep}

\newlength{\treeBold}
\def\Tree#1#2#3#4#5{{
  \pgfmathsetmacro{\xA}{#1}
  \pgfmathsetmacro{\yA}{#2}
  \pgfmathsetmacro{\R}{#3}
  \pgfmathsetmacro{\Degree}{#4}
  \setcounter{deep}{#5}
  \setlength{\treeBold}{\value{deep} pt}

  \pgfmathsetmacro{\xB}{\xA - \R*cos(\Degree)}
  \pgfmathsetmacro{\yB}{\yA + \R*sin(\Degree)}
  \draw[line width=\treeBold] (\xA, \yA) -- (\xB, \yB);
  \ifnum \value{deep}=1
  \else
  \pgfmathsetmacro{\newR}{0.8*\R}
  \pgfmathrandominteger{\a}{0}{60}
  \pgfmathsetmacro{\newAngleLeft}{\Degree+\a}
  \pgfmathrandominteger{\a}{0}{60}
  \pgfmathsetmacro{\newAngleRight}{\Degree-\a}
  \Tree{\xB}{\yB}{\newR}{\newAngleLeft}{#5-1}
  \Tree{\xB}{\yB}{\newR}{\newAngleRight}{#5-1}
  \fi
}}

\def\circleR#1#2#3#4{{
\pgfmathsetmacro{\xA}{#1}
\pgfmathsetmacro{\yA}{#2}
\pgfmathsetmacro{\R}{#3}
\setcounter{deep}{#4}

\draw[ultra thin] (\xA, \yA) circle (\R);

\pgfmathsetmacro{\newR}{\R/2}

\ifnum \value{deep}=1
\else
\circleR{\xA - \newR}{\yA}{\newR}{#4-1}
\circleR{\xA + \newR}{\yA}{\newR}{#4-1}
\fi
}}

\def\Koch#1#2#3#4#5{{
  \pgfmathsetmacro{\X}{#1}
  \pgfmathsetmacro{\Y}{#2}
  \pgfmathsetmacro{\R}{#3}
  \pgfmathsetmacro{\Degree}{#4}

  \pgfmathsetmacro{\newR}{\R / 3}
  \pgfmathsetmacro{\xA}{\X + \newR*cos(\Degree)}
  \pgfmathsetmacro{\yA}{\Y + \newR*sin(\Degree)}
  \pgfmathsetmacro{\xB}{\X + 2*\newR*cos(\Degree)}
  \pgfmathsetmacro{\yB}{\Y + 2*\newR*sin(\Degree)}
  \pgfmathsetmacro{\xC}{\X + 3*\newR*cos(\Degree)}
  \pgfmathsetmacro{\yC}{\Y + 3*\newR*sin(\Degree)}
  \pgfmathsetmacro{\xD}{\xA + \newR*cos(\Degree+60)}
  \pgfmathsetmacro{\yD}{\yA + \newR*sin(\Degree+60)}
  \setcounter{deep}{#5}

  \ifnum \value{deep}=1
    \draw[ultra thin] (\X, \Y) -- (\xA, \yA);
    \draw[ultra thin] (\xA, \yA) -- (\xD, \yD);
    \draw[ultra thin] (\xD, \yD) -- (\xB, \yB);
    \draw[ultra thin] (\xB, \yB) -- (\xC, \yC);
  \else
    \Koch{\X}{\Y}{\newR}{\Degree}{#5-1}
    \Koch{\xB}{\yB}{\newR}{\Degree}{#5-1}
    \Koch{\xA}{\yA}{\newR}{\Degree+60}{#5-1}
    \Koch{\xD}{\yD}{\newR}{\Degree-60}{#5-1}
  \fi
}}


\def\gasket#1#2#3#4{{
  \pgfmathsetmacro{\xA}{#1}
  \pgfmathsetmacro{\yA}{#2}
  \pgfmathsetmacro{\R}{#3}
  \pgfmathsetmacro{\xB}{\xA+\R/2}
  \pgfmathsetmacro{\yB}{\yA+\R*sqrt(3)/2}
  \pgfmathsetmacro{\xC}{\xA+\R}
  \pgfmathsetmacro{\yC}{\yA}
  \setcounter{deep}{#4}
  \draw[ultra thin] (\xA,\yA) -- (\xB,\yB) -- (\xC,\yC) -- (\xA,\yA);
  \ifnum \value{deep}=1
  \else
  \gasket{\xA}{\yA}{\R/2}{#4-1}
  \gasket{\xA+\R/4}{\yA+\R*sqrt(3)/4}{\R/2}{#4-1}
  \gasket{\xA+\R/2}{\yA}{\R/2}{#4-1}
  \fi
}}