  Explicit formulas are obtained for a family of continuous mappings of p-adic
numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space
\~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for
which the Cantor set and the Sierpinski triangle are images of the unit balls
in $\Qn{2}$ and $\Qn{3}$. In each of the families, the subset of the embeddings
is found. For these embeddings, the Hausdorff dimensions are calculated and it
is shown that the fractal measure on the image of $\Qp$ coincides with the Haar
measure on $\Qp$. It is proved that under certain conditions, the image of the
$p$-adic solenoid is an invariant set of fractional dimension for a dynamic
system. Computer drawings of some fractal images are presented.
