Why am I missing streamlines?

I'm trying to plot 3D streamline data but appear to be missing a section where the streamlines split off. Am I doing something wrong in my code or is this to do with the starting points I've chosen for stream3 to take?

xvals = linspace(-2,2,20);
yvals = linspace(-2,2,20);
zvals = linspace(-2,2,20);
[X,Y,Z] = meshgrid(xvals,yvals,zvals); %creates coordinate grid

%creates a symbolic expression for the Bfield By + iBx
syms Bfield(B0,x,y,a,b,c,d)
Bfield(B0,x,y,a,b,c,d) = -B0*( ((b*a^2 + 2*a*c*(x+1i*y) - (x+1i*y)^2 + 0.5*a^2)/sqrt((x+1i*y)^2 - a^2)) + 2*a*d*1i);

%defines 3d field
B = Bfield(1,X,Y,1,0.5,0,0);
Bx = sign(X).*imag(B) - 0.5*X ;
By = sign(X).*real(B);
Bz = 0.5*Z;

%defines test starting points for streamlines
i = 1:1:40;
sy = [ones(1,i(end))*0.001 ones(1,i(end))*-0.001];
sx = [0.1*sin(2*pi*i/i(end))+1 0.1*sin(2*pi*i/i(end))-1];
sz = [0.4*cos(2*pi*i/i(end)) 0.4*cos(2*pi*i/i(end))];

%finds streamline data back along spine of null and finds new starting
%points at the end of the spine
spineint = stream3(X,Y,Z,-Bx,-By,-Bz,sx,sy,sz);
length = size(spineint);
no = length(1,2);
sx = 0;
sy = 0;
sz = 0;

for j = 1:1:no
    streamlines = spineint{1,j};
    rc = size(streamlines);
    r = rc(1,1);
    sx(j) = streamlines(r,1);
    sy(j) = streamlines(r,2);
    sz(j) = streamlines(r,3);
end

%plots streamlines with starting points at end of the spine
figure
streamline(stream3(X,Y,Z,Bx,By,Bz,sx,sy,sz))
xlabel('x');
ylabel('y');
zlabel('z');
view(3);

This is the figure I'm getting using my code.

I am expecting to get something similar to this although not in the same orientation.

I'd appreciate any help you can give me. Thanks!