plotting the sequence x_n using tikz

Question

I want to plot the sequence

• x_1 = \sin(pi root(2))

• x_2 = \sin(pi root(6))

• x_3 = \sin(pi root(12))

In short my x_n = sin( pi root(n^2 + n)). I want to plot this as an animation as n goes to infinity. Can i have the command line arguments for plotting this animation using TikZ package

Answer 1

Is this the kind of thing you want:

I've used pgfplots in a standalone file as follows

% arara: pdflatex
% !arara: indent: {overwrite: on}
\documentclass[tikz]{standalone}

\usepackage{pgfplots}

\begin{document}


\foreach \n in {3,4,...,30}
{
    \begin{tikzpicture}
        \begin{axis}[
                xmin=0,xmax=30,
            ymin=-1.2,ymax=1.2]
            \addplot[samples at={1,2,...,\n},only marks]expression{sin(deg(pi*sqrt{x^2+x}))};
        \end{axis}
    \end{tikzpicture}
}
\end{document}

And then used the command

convert -delay 10 -loop 0 -density 300 myfile.pdf myfile.gif

with ImageMagick installed. You'll see this technique demonstrated in a few other answers on the site- How to convert pstricks animation to GIF file? for example.

---

If you plan to have a lot of these animations, then you might like to make an arara rule, something like the following

!config
# Make animated .gif file from .pdf
# author: Chris Hughes
# last edited by: cmh, May 25th 2013
# requires arara 3.0+
#
# Sample usage: 
#
# % arara: animate
# % arara: animate: {density: 200}
# % arara: animate: {density: 200, delay: 20}
#
# This rule is really just a shortcut for commands like the following
#
#  convert -delay 10 -loop 0 -density 300 myfile.pdf myfile.gif
#
# which will output myfile.gif
#
identifier: animate
name: animate
commands: 
- <arara> convert -delay @{delay} -loop @{loop} -density @{density} "@{ getBasename(file) }.pdf" "@{ getBasename(file) }.gif"
arguments:
- identifier: delay
  flag: <arara> @{parameters.delay}
  default: 10
- identifier: loop
  flag: <arara> @{parameters.loop}
  default: 0
- identifier: density
  flag: <arara> @{parameters.density}
  default: 300