The compact group of 2-adic integers (black points), with selected elements labeled by the corresponding character on the Pontryagin dual group (the discrete Prüfer 2-group) (colored discs).
Counter-clockwise from the right, the labeled elements are 0, 4, 2, −3, 1, −1/7, −1/3, 1/3, 1/7, −1, 3, −2, and −4. Open the SVG directly in your browser to get tooltips on group elements.
Each colored disc is tied to a 2-adic integer, x∈Z2{\displaystyle x\in \mathbb {Z} _{2}}, and it represents the corresponding character on the Prüfer 2-group, χx:Z(2∞)→R/Z{\displaystyle \chi _{x}:\mathbb {Z} (2^{\infty })\to \mathbb {R} /\mathbb {Z} }, defined by χx(q)=xq{\displaystyle \chi _{x}(q)=xq}. The circle group R/Z{\displaystyle \mathbb {R} /\mathbb {Z} } is represented by a color wheel where 0 = red.

For details on the embedding of the 2-adic integers, 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 Υs(∞){\displaystyle \Upsilon _{s}^{(\infty )}}, defined in Definition 3 and depicted in Figure 1.
Own work
Melchoir