MHB TikZ Challenge 2 - Function Graph

[I like Serena]

Who can make the most impressive, interesting, or pretty TikZ picture?

This second challenge is to create a function graph.
We can use vanilla TikZ, or the pgfplots package, or... well... that's up to you!
If it's not immediately obvious, please mention what makes your picture special.

Please post your submission in this thread.
This thread will be closed after 2 weeks.
After that we will have 2 weeks to vote on what we think is the best TikZ contribution for this challenge.

Only 1 submission of a picture is allowed, and it is not allowed to change the picture after submission.
Any change to the picture itself will disqualify it.
(I'm leaving some wiggling room for editing the description.)
See http://mathhelpboards.com/tikz-pictures-63/tikz-announcement-22140.html for more information on how to create and post TikZ pictures.
To help create pictures we can use this http://35.164.211.156/tikz/tikzlive.html.

 

[I like Serena]

\begin{tikzpicture}[scale=1.5]
\usetikzlibrary{arrows}
\draw[help lines] (-3.5,-3.5) grid (3.5,3.5);
\draw[<->, >=stealth'] (-3.5,0)--(3.5,0) node

{$x$};
\draw[<->, >=stealth'] (0,-3.5)--(0,3.5) node[above] {$y$};
\draw[ultra thick,blue,samples=200,domain=125:-35] plot(\x:{3*sin(\x)*cos(\x)/(sin(\x)^3+cos(\x)^3)})
node[above right] {$x^3+y^3-3axy=0$};
\draw[dashed] (1.5, 0) -- (1.5,1.5) -- (0,1.5);
\draw[dashed] (-3,2) -- (2,-3);
\draw[dashed] (-2,-2) -- (2,2);
\foreach \x/\xtext in {-3/-3a,-2/-2a,-1/-a,1/a,1.5/\frac 32a,2/2a,3/3a}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north,fill=white] {$\xtext$};
\foreach \y/\ytext in {-3/-3a,-2/-2a,-1/-a,1/a,1.5/\frac 32a,2/2a,3/3a}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east,fill=white] {$\ytext$};
\node[above,align=center,font=\bfseries] at (current bounding box.north) {Folium of Descartes};
\end{tikzpicture}
This picture uses:

1. greg1313's method to add a title,
2. lfdahl's method to add tick labels,
3. MarkFL's method to add axis labels,
4. Evgeny.Makarov's method to add neat arrow heads.

I like this picture because it represents the summum as I know it of function analysis (finding zeroes, extremes, singularities, asymptotes, and symmetries).

My credo, there's nothing wrong with stealing as long as we do it right (and learn from it)! (Bigsmile)​

 

[I like Serena]

Time is up.

Since there is only 1 submission, there's no point in voting.
Hopefully there will be more contributors next time.

Thread closed.