So you want to be a computer animator like the pros? Or maybe you just want to start making your own computer animations now? Well, you're going to need a few things first.
You don't need a super computer to run most 3D modeling or landscape generation applications today. You just need a decent Pentium II or equivalent, like a K6-2. Of course it depends on just how complicated of a scene or animation you are planning on rendering. You are going to need a much higher CPU, or possibly two CPUs in one computer, if you are plannng on rendering multiple objects at a time with detailed beach scene with blowing sand clouds and raging waves under a blaring sun.
Along with a decent CPU, there comes the issue of RAM. For a decent rendering time you're going to want a lot of RAM. For a decent computer animation computer you need at least 128MB. More and faster RAM decreases the rendering time a lot but again it depend on what the scene or animation contains.
Next, you are going to need a rendering program. These can be a bit expensive. They can rang from Metacreations' Ray Dream Studio($349) to mega-industry sellers like SGI's Maya Unlimited($16000). But a very decent affordable 3D program would be Calagari's TrueSpace series($300-600). If you are just starting out it's even wiser to choose a cheaper renderer like Byte by Byte's Soft F/X Pro for learning the basics before you go spending your first born for a professional renderer liable to confuse to death.
Also you will need an Operating System that multitasks well and can use multiple processors if you have one. Many of the programs support Windows NT, SGI's OS, or sometimes Mac's OS.