As expected, when considering the particles as having completely random magnetic moments, we get the following distribution of hits :

If we also widen the uncertainty in the X direction, we get somthing like this :

If we use the simplified model, in which the spin can only take "up" or "down" values, along the Z axis, we get a flat distribution that looks like this :

But if we go further and measure the spin continuesly along the axis tangent to the field in its current position, we get a more interesting distribution, which is very similar to the original experimental result :

The point in the middle represents a possible, yet very rare event, in which the spin flips, because the field slightly changed, and the path becomes no longer monotonic.
If we allow a little more uncertainty in the Z axis, we get the following :

For comparison, I added also the original result, obtained by Stern and Gerlach :

Finally, I also captured a short video of the simulation, which is shown here in a .GIF format :

And can also be downloaded in a .MPG format, with also better quality and smaller file size.

In addition, the same movie with a little better quality in .MP4 format, but requiers a browser that supports HTML5.

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