There does not appear to be any way to change the thickness of the plotted surface.
The best I can come up with is the revised figure(2) that plots two slightly scaled versions of the same surface together, so one is slightly smaller than the other. I only changed that one plot, not the ones following it.
(If that does not do what you want, I will delete my Answer.)
[x,y,z] = meshgrid(0:rate:x_period, 0:rate:y_period, 0:rate:z_period);
f = cos(frequency*x).*sin(frequency*y) + cos(frequency*y).*sin((frequency*z)+pi/2) + cos((frequency*z)+pi/2).*sin(frequency*x);
fv = isosurface(x,y,z,f,'verbose');
d = x_period/(2*(x_period*frequency/pi)) - 0.1;