Let $X\subset \mathbb{C}^{n}$ be a domain. You can assume that it is nice (e.g. bounded convex balanced ). Let $\{x\_n\}$ be a sequence of points that does not have a limit point in $X$.


Let $D$ be the (unit) disc on the plane.



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> Is there a holomorphic $\varphi:D\to X$ such that $\varphi(D)$ contains an infinite number of $x\_n$?
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> 


Of course there are further questions: can we catch all the points? Or maybe all but finite number?



How many points of a sequence can we catch with an analytic disc?
The answer to your quesiton is yes.


In particular in [Discs in Stein manifolds containing given discrete sets](https://www.fmf.uni-lj.si/%7Edrinovec/research/SteinMZ.pdf) B. Drinovec Drnovšek proves that given a discrete subset $S$ of a connected Stein manifold $M$ (every domain of holomorphy in $\mathbb{C}^m$ is if this kind) there is a proper holomorphic map $f:D \rightarrow M$ such that $S\subset f(D)$. Moreover if dim $M\geq$3 the map f can be chosen to be an embedding.


