English: The 2-adic integers (black points), with the numbers 1, 2, 4, 8, 16, and 0 labeled.

The 2-adic integers are laid out in a (non-isometric) topological embedding of Z₂ into the complex plane:

${\displaystyle [\ldots d_{2}d_{1}d_{0}]\mapsto e^{2\pi i[d_{0}]/2}+ce^{2\pi i[d_{1}d_{0}]/2^{2}}+c^{2}e^{2\pi i[d_{2}d_{1}d_{0}]/2^{3}}+\cdots }$

where c is a small scale factor. For details on this map, see Chistyakov, D. V. (1996), “Fractal geometry for images of continuous embeddings of p-adic numbers and solenoids into Euclidean spaces”, in Theoretical and Mathematical Physics, volume 109, issue 3,

DOI:10.1007/BF02073866, pages 1495–1507 The particular mapping used is ${\displaystyle \Upsilon _{s}^{(\infty )}}$, defined in Definition 3 and depicted in Figure 1 (with a larger scale factor).