Helix type cumulative distribution in Tikz

Question

I wrote the following codes. I am trying to obtain helix (as in DNA) type of structure on which everything - intersection points etc - can be seen explicitly. Whatever I do I am getting really ugly shapes. I have played angles, curvatures etc. Any help would be great! Some codes are not active, my apologies for that.

\documentclass{article}
\usepackage{tikz,subfigure}
\usetikzlibrary{intersections,calc}

\newdimen\XCoord
\newdimen\YCoord

\newcommand*{\ExtractCoordinate}[1]{\path (#1); \pgfgetlastxy{\XCoord} {\YCoord};} %

\newcommand*{\LabelCurrentCoordinate}[2]{\fill[#1] ($(\XCoord, \YCoord)$) circle (2pt) node [right] {#2}} %

\begin{figure}
\centering
\begin{tikzpicture}[ultra thick, scale=1]
\draw (0,0) -- +(10,0) node[pos=0,left]{\tt\color{black}1};

\draw (0,-10)-- +(10,0) node[pos=0,left]{\tt\color{black}0};

\draw [red,line width=2pt, name path= curve 1] (0,-10) -- (1,-10) to [out=0,in=180] (3,-8) to[out=0,in=270] (5,-6) to[out=90,in=180] (7,-4) to [out=0,in=180] (9,-2) to [out=0,in=180] (9.8,0) to (10,0);


 \draw [blue, line width=2pt, name path= curve 2] (0,-10) -- (0.2,-10) to [out=0,in=270] (4,-8) to[out=-270, in=180] (6,-6) to [out=0,in=160](8,-2) to[out=-20,in=270] (9.8,0) -- (10,0);

 \fill[name intersections={of=curve 1 and curve 2,total=\t}]
 \foreach \s in {2,...,\t}{(intersection-\s) circle (3pt)
node[above left] {$E$\s}};

\end{tikzpicture}
\end{figure}
\end{document}

Answer 1

To get a nice repeating structure (as mentioned in @KevinC's comment), use plot functionality in tikz.

I defined an \ampl command to set the amplitude of the sine waves we'll be plotting (0.5 in this example). You may want to adjust this if you change the scale or number of cycles.

The number of cycles to plot is set using the \cycles command (3 for this example). The total number of intersections (including the first one, which you do not label) will be 2*\cycles + 1.

The option samples=80 tells tikz to plot 80 points for each plot over the domain (domain=0:10). The value of samples can be adjusted to obtain less smoothness if desired.

I also converted your usage of \tt (deprecated) to the current texttt{} syntax.

The Code

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections,calc}

\newcommand\ampl{0.5} % amplitude of sine variation
\newcommand\cycles{3} % number of cycles to plot

\begin{document}
\begin{tikzpicture}[
  line width=2pt,
  domain=0:10, % plot functions from x=0 to x=10
  samples=80,  % sample 80 times over domain (adjust for smoothness)
]

  % draw helix
  \draw[red,name path=curve 1] plot (\x,{\x+\ampl*sin(36*\cycles*\x)});
  \draw[blue,name path=curve 2] plot (\x,{\x-\ampl*sin(36*\cycles*\x)});

  % draw ``axes''
  \draw (0,10)-- +(10,0) node[pos=0,left]{\texttt{1}}; % \tt is deprecated
  \draw (0,0) -- +(10,0) node[pos=0,left]{\texttt{0}}; % use \texttt{<content>} instead

  % draw intersection nodes
  \fill[name intersections={of=curve 1 and curve 2,total=\t}]
  \foreach \s in {2,...,\t}{(intersection-\s) circle (3pt) node[above left] {$E$\s}};
\end{tikzpicture}
\end{document}

The Output

Edit

Another method, using the answer from here. This one eliminates the "skewness" in the sine waves and doesn't depend on the intersections library.

The Code

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.pathmorphing}

\newcommand\ampl{0.5cm} % amplitude of sine variation
\newcommand\cycles{7} % number of cycles to plot
\pgfmathsetmacro\finish{2*\cycles+1} % final intersection point

\tikzset{/pgf/decoration/.cd,
    number of sines/.initial=10,
    angle step/.initial=10,
}
\newdimen\tmpdimen
\pgfdeclaredecoration{complete sines}{initial}
{
    \state{initial}[
        width=+0pt,
        next state=move,
        persistent precomputation={
            \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/angle step}}%
            \let\anglestep=\pgfmathresult%
            \let\currentangle=\pgfmathresult%
            \pgfmathsetlengthmacro{\pointsperanglestep}%
                {(\pgfdecoratedremainingdistance/\pgfkeysvalueof{/pgf/decoration/number of sines})/360*\anglestep}%
        }] {}
    \state{move}[width=+\pointsperanglestep, next state=draw]{
        \pgfpathmoveto{\pgfpointorigin}
    }
    \state{draw}[width=+\pointsperanglestep, switch if less than=1.25*\pointsperanglestep to final, % <- bit of a hack
        persistent postcomputation={
        \pgfmathparse{mod(\currentangle+\anglestep, 360)}%
        \let\currentangle=\pgfmathresult%
    }]{%
        \pgfmathsin{+\currentangle}%
        \tmpdimen=\pgfdecorationsegmentamplitude%
        \tmpdimen=\pgfmathresult\tmpdimen%
        \divide\tmpdimen by2\relax%
        \pgfpathlineto{\pgfqpoint{0pt}{\tmpdimen}}%
    }
    \state{final}{
        \ifdim\pgfdecoratedremainingdistance>0pt\relax
            \pgfpathlineto{\pgfpointdecoratedpathlast}
        \fi
   }
}

\begin{document}
\begin{tikzpicture}[
  line width=2pt,
  domain=0:10, % plot functions from x=0 to x=10
  samples=80,  % sample 80 times over domain (adjust for smoothness)
]

  % draw helix
  \draw[red,decorate,decoration={complete sines,number of sines=\cycles,amplitude=\ampl}] (0,0) -- (10,10);
  \draw[blue,decorate,decoration={complete sines,number of sines=\cycles,amplitude=-\ampl}] (0,0) -- (10,10);

  % draw ``axes''
  \draw (0,10)-- +(10,0) node[pos=0,left]{\texttt{1}}; % \tt is deprecated
  \draw (0,0) -- +(10,0) node[pos=0,left]{\texttt{0}}; % use \texttt{<content>} instead

  % draw intersection nodes
  \foreach \s in {2,3,...,\finish} {
    \fill ({10*(\s-1)/(\finish-1)},{10*(\s-1)/(\finish-1)}) circle (3pt) node[above left] {$E$\s};
  }
\end{tikzpicture}
\end{document}

The Output

Answer 2

Just for typing exercise with PSTricks.

\documentclass[preview,border=24pt]{standalone}
\usepackage{pst-plot,pst-eucl,pgfmath}

\psset{algebraic,plotpoints=100,PosAngle=135}
\def\f#1{x+sin(2*Pi*x/2+#1*Pi)/3}

\begin{document}
\begin{pspicture}(6,6)
    \psplot[linecolor=red]{0}{6}{\f0}   \psplot[linecolor=blue]{0}{6}{\f1}
    \foreach \x[count=\i from 2] in {1,...,6}{\pstGeonode(\x,\x){E_\i}}
    \psset{yunit=6}
    \multido{\i=0+1}{2}{\uput[180](0,\i){\i}\psline(0,\i)(6,\i)}
\end{pspicture}
\end{document}