I'm not clear on what counts as a "copy" in the case of code.
If I read your code, that was MIT licensed, implement a similar logic on my own and use no code fragments from the original author, does that constitute a "copy" without attribution to the original author and therefore a violation of the MIT license if I release the code under my own copyright?
Reading code and then writing it down from memory, whenever you're writing down the exact code or not, can be considered "derived work" and thus could be subject to copyright (IANAL, but as far as I can recall the definitions of derived work and fair use remain fuzzy and subject to interpretation; in this specific case, and particularly if the resulting code keeps a similar structure, I would find it quite hard to claim fair use of the original work).
Your best approach to ensure that the work cannot be considered derived work is to use the clean room design technique: have one person read the code and produce functional specifications, then someone else who've never even glanced at the original code write his own implementation, thus ensuring no code from the original work can even accidentally taint the resulting project.
This of course offers no protection from patent infringements if the algorithm is covered by valid patents.
You're okay to independently and entirely re-implement an existing algorithm, and then copyright your code, as long as the algorithm isn't patented.
For example, the lzw compression algorithm used by gif was patented (the patent expired ~2004). And therefore, (a) you couldn't copyright an independently-written gif generator or viewer, and (b) you couldn't even write one without copyrighting it, and just give the code away.
And assuming no patent, then to be completely safe about copyright violation, you'd be best off reading a textbook discussion of the algorithm in a cleanroom-like fashion, e.g., https://en.wikipedia.org/wiki/Clean_room_design , rather than poring over already-copyrighted code for long hours.
IANAL.
The terms of MIT license state:
Permission is hereby granted [...] to modify [and] sublicense [...] copies of the Software, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
If you memorized the entire text of the original program, and then wrote a similar program that did not include any of the original text ("portions of the Software"), then in my opinion the attribution requirement would no longer apply and you could put your own name on the reimplementation and not credit the original authors.
Your reimplementation would still be a derived work of the original program.
