Java3D is not really intended for huge point clouds. It is intended for controlled scene graphs, whereas for clouds with large dots, you usually want to make fairly direct OpenGL calls.
You better go with jMonkeyEngine (which has its own cloud / particle subsystem) or LWJGL (this is what jMonkeyEngine uses under the hood and will give you low-level access to OpenGL)
All of the above can be used in applets (the user will probably have to approve the removal of Applet security restrictions in order to allow their own OpenGL access), although I would recommend WebStart as an alternative if you are trying to do something more complex.
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