An equation that generates a beautiful or unique shape for motivating students in mathematics 
Could anyone here provide us an equation that generates a beautiful or unique shape when we plot? For example, this is old but gold, I found this equation on internet:
  $$
\large\color{blue}{ x^2+\left(\frac{5y}{4}-\sqrt{|x|}\right)^2=1}.
$$
  When I plot on Wolfram Alpha, the output is



The reason why I post this question is not only for fun or the sake of curiosity but it is also to motivate my students and kids around me to like and to learn mathematics more enthusiastic because motivating students to be enthusiastically receptive is one of the most important aspects of mathematics education. A good teacher should focus attention on the less interested students as well as the motivated ones. I have learnt from my $3$-year experience on teaching that the good strategies for increasing students motivation in mathematics are enticing the class with a “Gee-Whiz” mathematical result and using recreational subjects that consist of puzzles, games, paradoxes, experiments, and pictures/ video animations. We all know, 'a picture is worth a thousand words'.

Here is a way to generate bunches of intriguing (most often) periodic curves drawn by adding unit length complex numbers of the form
$$e^{2\pi i m} \ \ \ \text{with} \ \ \ m:=\dfrac{n}{a}+\dfrac{n^2}{b}+\dfrac{n^3}{c}$$ 
for $0 \le n < abc$, where $a,b,c$ are fixed positive integers.
Here are displayed some of them with the corresponding values of $a,b,c$ :

Please note that two same curves like the hourglass-like shapes in position 1 and 3 can sometimes be generated with different values of $a,b,c$.
Here is the Matlab program that has generated these 25 curves :

clear all;close all;
set(gcf,'color','w');axis equal off;hold on
for P=1:5
   for Q=1:5;
      V=ceil(9*rand(1,3));a=V(1);b=V(2);c=V(3);L=a*b*c;
      S=zeros(1,L+1);
      for n=0:L;
         m=n/a+(n^2)/b+(n^3)/c;
         S(n+1)=exp(2*pi*i*m);
      end
      S=cumsum(S);
      M=mean(S);S=S-M;R=max(abs(S));S=S/R;
      shi=3*(P+i*Q);
      plot(shi+S);
      text(real(shi),-1.5+imag(shi),num2str(V),'horizontalalignment','center');
   end;
end;


Remarks : 
1) This idea comes from the explained logo one can find here : https://math.stackexchange.com/users/119775/david
2) About spirographs, one can use the following splendid simulation : https://nathanfriend.io/inspirograph/
