It could happen again that the same pattern is arranged at a different place / time. And that pattern would consider itself the original. And it is a matter of subjectivity as to whether that is held to be true or not.
Everything else rather depends on what one views as "I".
Personally I tend to think of "I" as the memories.
But what other people tend to think of as "me" would be a consciousness within my physical body.
E.g. if I became unconscious and lost all my memories, then would I retain the same sense of "I"? In people who have such memory issues, where they can not retain long-term memory, the answer tends to be no... each time they awake they think it is the first time they have been so, and they take some convincing otherwise.
But my friends would consider me to still be "me"... since to them I am a consciousness within a body. They may think my personality has changed, or that I am not the same person, but they would still think it is "me", even if that "me" has changed.
Likewise if I retained all the memories and characteristics that I currently do, but woke up in the body of a machine (able to see, hear etc as I currently do, but clearly in a mechanical body)... then "I" would still think it is me, but now located in the machine body.
My friends might take more convincing, but might see "me" as the personality, the characteristics of mind that I previously had.
However, if we combine the two - and "I" lose all my memories and am transplanted into the body of a machine... I would suggest that neither "I" nor my friends / family would think that it is "me"/"I"... that it is a distinctly different "person", and that "I" had died.
So I think the personal sense of "I" is memory-dependent. Without those continuing memories on which to root our sense of "I", I do not think there is a sense of "I" at all. "I" is a sense of continuation... and with nothing to provide input to the nature of that continuation there can be no "I".
The sense of "me" that others see is more rooted in the continuation of the physical aspects that the other person experiences of "me".
I'd also suggest you watch this:
Youtube -
https://www.youtube.com/watch?v=8Biv_8xjj8E - from about 28mins onward.
Very interesting, regarding the sense of separation between the mind and body, and how the mind can be convinced it is located elsewhere other than behind one's own eyes.