Ever since I learned about complex valued functions I've been wondering if there was a better visualization for them. Obviously we can't visualize four dimensions, but I was wondering if it would be useful to model them as vector fields. After all, a complex valued function is essentially a mapping from $\mathbb{R}^2$ to $\mathbb{R}^2$. Are there useful aspects of seeing it this way, and what benefits do other visualizations have over this?

  • 1
    $\begingroup$ It would be hard to visualize the branch cuts in this way. $\endgroup$ – mastrok Jun 16 '16 at 4:44

Yes, for some purposes this can be useful, as described (much better than I could do here) in Chapters 10 and 11 in the book Visual Complex Analysis by Tristan Needham.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.