What is the math behind Bitcoin's elliptic curve?

[Bitcoin]

What is the math behind Bitcoin's elliptic curve?

I have seen many videos regarding the math behind the bitcoin elliptical curve but none of them show the public key generation. They are just defining few steps. I need the complete math behind the elliptical curve in which the generation of the public key is defined. Actually, I would like to see a visualization of the public key generation, could someone give me a link which explains the math behind elliptical curve?

What I understand that is k * n times G is equal to the public key but my question remains the same. If kn times G (where every point of G we get from point multiplication and point addition ) then at every multiplication of kG will result a different value then how can we combine them to get the public key?

Source: What is the math behind Bitcoin's elliptic curve?