利萨如曲线的改进

Question

我正在进行以下 MWE 工作：

\documentclass[border=5pt,tikz]{standalone}
\usepackage{bookman}
\usetikzlibrary{backgrounds}
\tikzset{
    io/.style={
        fill=black,circle,inner sep=.5pt
    },
    every node/.style={io}
}
\begin{document}
    \begin{tikzpicture}
        \foreach \x in {0,1,...,359}
        {
%           \node at ({sin(3*\x)},{sin(2*\x)}) {};
            \draw ({sin(3*\x)},{sin(2*\x)}) -- ({sin(3*\x+3)},{sin(2*\x+2)});
            \draw[opacity=.5] ({sin(3*\x)},{sin(2*\x)}) -- ({sin(3*(\x+30))},{sin(2*(\x+30))});
                \draw[white] ({sin(3*\x)},{sin(2*\x)}) -- ({sin(3*(\x+1))},{sin(2*(\x+1))});
        }
        \begin{pgfonlayer}{background}
            \fill[top color=green!30,bottom color=yellow!30] (current bounding box.north west) rectangle (current bounding box.south east);
        \end{pgfonlayer}
            \node[fill=none,black,rotate=-36,above left] at ({sin(3*182)},{sin(2*182)}) {\tiny Ti\emph{\textcolor{green!50}{k}}Z};
    \end{tikzpicture}
\end{document}

输出如下：

我的问题是：如何改进代码？