Visualizing the basin of attraction of a multistart problem

Hello everyone,

I am dealing with multistart and a basin of starting points for lsqcurvefit. Particularly, lsqcurvefit needs to evaluate a 3-variable function. I am giving a (3 entries) vector x0 has initial guess and multistart is generating a set of 500 initial points. The code is a simple generalization to 3D of the one on the matlab page: visualizing the basin of attraction and it is working fine. What i want to do now is to visualize the basins of atteaction for the solutions in a similar fashion as it is done in the last section of that same matlab page (Visualize the basin of attraction). Since in my problem i have a 3 dimensional space i am finding difficulties in coding it and visualizing it. I have been suggested to look into: Plot 3-D Solutions and Their Gradients, particularly Contour Slices Through 3-D Solution, which seems a good idea. In particular, since the starting points generated by multistart do not lie on the same plane, i think i would need to have slices on a curve grid. Can anyone help me in writing the code?

Thank you