Is emulating someone else's work a copyright violation? ex. I make something looks very much like a zygote figure, except I make it completely on my own.

No. But why would you go to the trouble of making something that looks just like something you've already got?

The point is, I don't want to pay for the object in question. So if I make my own equivalent, will people get on my case?

If you make something look too much like a copyrighted object or graphic you MIGHT get in trouble. It all depends on how close the two things look alike and how aggresive the copyright holder is. If its done for personal use you may be alright.

Zygote has a copyright on the MESH itself. If you're creating an original mesh, you should have no problems. After all, what are the odds of you creating a mesh with the same polygon count? If they WERE to come complaining, it'd be easy enough to prove it's an original!

If you are really worried about it, save a few work in progress files as you make your figure to help prove that you did the work.

wyrwulf is right. Make a backup with dates and your fine.