I saw tomoq’s star-shaped plot on X (Twitter), together with a pretty big implicit function definition:
How to plot this?
An easy way is to consider the left side as a function z=f(x,y) in three dimensions, and that equation would be a contour line at height z=1. So, let’s plot it together with contour lines at different heights, to see how they run.
Run the files with -enable-write18 or –shell-escape or similar option enabled, because contour plots run the external gnuplot program in the background. The won’t run withe the online compiler TeXlive.net here, for security reasons.
% !TEX lualatex
\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}[
declare function = {
f(\x,\y) = x^6 + y^6 + 3*x^4*y^2 + 3*x^2*y^4
- 5*x^4*y + 10*x^2*y^3 - y^5; } ]
\begin{axis}[
axis lines = middle,
domain = -2:2,
samples = 80,
samples y = 80,
enlargelimits ]
\addplot3 [
contour lua =
{ levels = {0.001, 0.1, 1, 4, 8, 16, 32},
labels = false} ]
{ f(x,y) };
\addplot3 [surf,
thick, colormap/violet,
opacity = 0.2 ]
{ f(x,y) };
\end{axis}
\end{tikzpicture}
\end{document}
To get the final two-dimensional plot, we can choose a viewing angle from above, and plot only the contour line at height level 1.
We can generate this star-shaped plot with pgfplots choosing a contour plot with LuaLaTeX: https://t.co/jglaLYpRSf pic.twitter.com/T5LrV19CP4
— LaTeX.org (@TeXgallery) January 31, 2025
% !TEX lualatex
\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}[
declare function = {
f(\x,\y) = x^6 + y^6 + 3*x^4*y^2 + 3*x^2*y^4
- 5*x^4*y + 10*x^2*y^3 - y^5; } ]
\begin{axis}[
axis lines = middle,
domain = -2:2,
samples = 80,
samples y = 80,
enlargelimits,
view = {0}{90} ]
\addplot3 [
thick,
contour lua =
{ levels = {1},
labels = false} ]
{ f(x,y) };
\end{axis}
\end{tikzpicture}
\end{document}