# Draw a “super-twisting” curve TIKZ

I am trying to draw the "twisted" curve in the pic:

I am not an expert in Tikz, and I have written the following latex code:

\documentclass{standalone}
\pagestyle{empty}
\usepackage{tikz}
\usepackage{verbatim}
\usetikzlibrary{shapes,arrows}
%\usetikzlibrary{knots}
%\renewcommand{\baselinestretch}{2}
\pagestyle{plain}

\begin{document}

% SET ARROW STYLE WITH TIP IN THE MIDDLE OF THE LINE
\tikzset{->-/.style={decoration={
markings,
mark=at position -0.3 with {\arrow{>}}},postaction={decorate}}}

\tikzset{line/.style={->,shorten <=0.4cm,shorten >=0.4cm}}

\centering
\resizebox{\textwidth}{!}{%

\begin{tikzpicture}[auto, node distance=5cm,>=latex']

% DRAW AXIS
\draw[->](-2,0)--(3,0);
\draw[->](0,-2)--(0,4);
\node at(3.2,0)(x){\large$x$};
\node at(0.25,4)(xy){\large$\dot{x}$};

% DRAW CURVES
\draw[->-] (0,3) .. controls (-0.001,2)  and (1.9,-1) .. (0,-0.5);
\draw[-] (0,-0.5) .. controls (-0.1,-0.08) and (-0.3,-0.2)  .. (-0.25,0);
\draw[-] (-0.25,0) .. controls (-0.1,0.4) and (0,0)  .. (0.05,0);
\draw[-] (0.05,0) .. controls (0.1,-0.2) and (0.05,-0.2)   .. (0,-0.03);

\node at(0.2,0.2)(x){\large$0$};

\end{tikzpicture}
}%
\end{document}


but what I get is something a little bit different from what I want:

I could improve my code? Thank you!

I modified slightly your code. There were unneeded commands that I erased and I modified the points of the curve to fit the model.

Notation remark. 0 is a real number. I think you need the letter O to denote the origin.

The code:

\documentclass[margin=1cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, decorations.markings}

\begin{document}

% SET ARROW STYLE WITH TIP IN THE MIDDLE OF THE LINE
\tikzset{%
->-/.style={%
decoration={
markings,
mark=at position .65 with {\arrow[scale=1.2]{stealth}}
},
postaction={decorate}
},
>=stealth
}

\begin{tikzpicture}
% DRAW AXIS
\draw[->] (-1, 0) -- (2, 0) node[above right] {$x$};
\draw[->] (0, -1.5) -- (0, 4) node[left] {$\dot{x}$};

% DRAW CURVE
\draw[blue, thick, ->-] (0, 3)
to[out=270, in=90] (1, 0)
.. controls +(0, -.4) and (.8, -1.1) .. (.4, -1.1)
.. controls +(-.2, 0) and (0, -.8) .. (0, -.5)
.. controls +(0, .3) and (-.2, -.2) .. (-.2, 0)
.. controls +(0, .2) and (0, .25) .. (0, 0);

\path (0, 0) node[above right] {$O$};
\end{tikzpicture}

\end{document}

• Thank you so much, Daniel. I really appreciated your help. Just a question, which is the meaning of plus sign after thr controls commands? – michele_ub Oct 17 '20 at 20:05
• My pleasure. As for +(a,b), it represents a relative coordinate with respect to the previous point; if the previous point is (x,y), then its significance is (x,y)+(a,b). In fact, I should have written ++(a,b), but in this case, it makes no difference. – Daniel N Oct 17 '20 at 21:37
• Ok, now everything is clear! – michele_ub Oct 17 '20 at 22:17