A few easy ones

Knot
            x=-y;  
            y=x*x*x-x-y;
            
Insect
            x=y;
            y=y*y+x+y; 
            
Eshape
             x=-y; 
             y=x+y+1/y;  
             
Square
             x=-0.999776*y;  
             y=x;  
           
Triangle
             x=-0.999776*y;  
             y=x-y; 
             
Hexagon
             x=-0.999776*y;  
             y=x+y;  
             
Square/Circle
             x=-0.999776*y;  
             y=x+0.1*y; 
4 spirals
             x=.004*x+y;   
             y=(-1./y - y)/x; 
Pentagon
             x=x*0.6 -y;   
             y=0.1*x*y +x; 
Diagonal
             x=.001*y+y; 
             y=x;  
Circle of circles
             x=y; 
             y=-0.288/y +0.5*y - x;            
Chaotic oval
             x = x/y -x;  
             y = x*x - 0.24; 
Chaotic shell
             x = x*y + 0.357057*x -y; 
             y = x + y; 

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Maintained by Giuseppe Zito : Giuseppe.Zito@cern.ch