# TiKZ plot x^a* cos(ln(x))

I wanted to plot the function X^(-1.5)*cos(ln(X)) I can do successfully X^(1.5)*cos(ln(X)), but if I put a negative exponent the code does not work.

I wanted to plot a function that increases close to the wall with the oscillations wavelength increasing as well. Could someone help? Thanks!

\draw[-stealth] (0,-2) -- (0,2);

\draw[-stealth] (0,0) -- (5,0);

\draw [scale=0.5,domain=10:0,smooth,variable=\x,blue]    plot (\x, { 0.1*cos(1200* ln(\x))*(\x)^(1.5) });

\draw [scale=0.5,domain=10:0,smooth,variable=\x,black]    plot (\x, {  0.1*\x^(1.5) });

\draw [scale=0.5,domain=10:0,smooth,variable=\x,black]    plot (\x, {  -0.1*\x^(1.5) });


• May I recommend pgfplots for that, and not to extend the domain all the way down to 0? – marmot Jan 31 at 23:35
• Please complete your code, so it is compilable. - starting with \documentclass ... and ending with \end{document} – hpekristiansen Jan 31 at 23:36
• Using algebra to rewrite as cos(ln(x))/x^(1.5) works for me. – DJP Feb 1 at 0:14
• When dealing with unbounded, infinite frequency function plots, maybe TikZ, pgfplots, LaTeX aren’t the greatest tools. If you don’t mind using high resolution bitmap plot, I’d suggest producing your graph using GrafEq. See this gallery for GrafEq’s capability (in particular the “infinite frequency plot”) and also this awesome plot. – Ruixi Zhang Feb 1 at 6:09

You can use modify the @marmot code using cos(ln(x))/x^(1.5) as I suggested above. To make the graph a little more pleasing to the eye, I have a template that I use:

\documentclass{standalone}
\usepackage[dvipsnames]{xcolor}%declare color here to avoid color clash with tikz
\usepackage{pgfplots}% This uses tikz
\pgfmathdeclarefunction{f}{1}{%
\pgfmathparse{.1/x^(1.5)}%
}
\pgfmathdeclarefunction{g}{1}{%
\pgfmathparse{0.1*cos(1200*ln(x))/x^1.5}%
}
\pgfmathdeclarefunction{h}{1}{%
\pgfmathparse{-.1/x^(1.5)}%
}
\tikzset{Line Style1/.style={smooth,thick, dashed,samples=400}}
\tikzset{Line Style2/.style={smooth,thick, samples=800}}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
%grid = both,%grid for major ticks (every integer) and minor ticks
minor tick num=4,% number of hor/vert lines in a box
every major grid/.style={Red!30, opacity=1.0},%set the color for major grid
every minor grid/.style={ForestGreen!30, opacity=1.0},%set the color for minor grid
height= 1\textwidth,%compress height: eg height=0.5\textwidth
width = 1\textwidth,%compress width: eg width=0.5\textwidth
thick,
black,%Set the color of the main axes and numbers
scale=1.0,
axis lines=center,
domain=0:4
samples=500,
line join=bevel,
xmin=0,
xmax=2,
ymin=-4,
ymax=4,
%xticklabels=\empty,% remove % at beginning of line to remove x labels
%yticklabels=\empty,% remove % at beginning of line to remove x labels
major tick length=0pt,% Increase number adds tick mark and increases distance of numbers from the x/y axis
minor tick length=0pt,% Increase number adds minor tick marks
%xtick=\empty,
%ytick=\empty,
]
\addplot[Line Style2, color=Peach, domain=.01:2] (\x,{f(\x)}); %color names determined by dvipsnames
\addplot[Line Style2, color=NavyBlue, domain=0.05:2] (\x,{g(\x)});% in the xcolor package
\end{axis}
\end{tikzpicture}
\end{document}


The output running in Gummi is shown below:

As you approach the y-axis from the right, you'll need to adjust the values of the domains to make the plot pleasing to your eye: the closer you go to 0 the more chaotic the graph becomes. So much so that it will look like a solid blue area, rather than a curve. Set at .05 the graph doesn't look so messy yet.

Here is some pgfplots code producing this plot.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[domain=0.01:10,no marks,axis lines=middle,smooth,
xmax=12,xlabel=$\eta$,xtick=\empty,ytick=\empty]
\end{axis}
\end{tikzpicture}
\end{document}


It is also possible to draw this with TikZ, and I assume @DJP will provide you with a code.

If you want the thing to become larger towards the wall, you could use

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[domain=0.01:10,no marks,axis lines=middle,smooth,
xmax=12,xlabel=$\eta$,xtick=\empty,ytick=\empty,ymin=-4.5,ymax=4.5]