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Summary

A (non-isometric) depiction of the 4-adic integers,

${\displaystyle [\ldots d_{2}d_{1}d_{0}]\mapsto e^{2\pi i[d_{0}]/4}+ce^{2\pi i[d_{1}d_{0}]/4^{2}}+c^{2}e^{2\pi i[d_{2}d_{1}d_{0}]/4^{3}}+\cdots }$

where c is a small scale factor. The integers −1 = …333 through 6 = 12 are labeled, as are 33 and 333.

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; analogues for p=2, 3, and 6 are displayed in Figure 1.

Created by Melchoir (talk)

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