  Fractals such as the Cantor set can be equipped with intrinsic arithmetic
operations (addition, subtraction, multiplication, division) that map the
fractal into itself. The arithmetics allows one to define calculus and algebra
intrinsic to the fractal in question, and one can formulate classical and
quantum physics within the fractal set. In particular, fractals in space-time
can be generated by means of homogeneous spaces associated with appropriate Lie
groups. The construction is illustrated by explicit examples.
