plot 4d data

I'm trying to draw (plot) the swallowtail catastrophe surface. I am completely stuck because I'm definitely not a mathematician. The surface has the potential:

V(x) = F(x,u,v) = x^5 + ux^3 + vx^2+wx so it should be given by this implicit equation:

5x^4 + 3ux^2 + 2vx+w = 0 But I don't know how to implement this

Answer 1

[KSSV]

Refer this link: http://mathworld.wolfram.com/SwallowtailCatastrophe.html

N = 50 ;
u = linspace(-2,2,N) ;
v = linspace(-0.8,0.8) ;

[U,V] = meshgrid(u,v) ;

X = U.*V.^2+3*V.^4 ;
Y = -2*U.*V-4*V.^3 ;
Z = U ;

surf(X,Y,Z) ;