  We study the geometric properties of Cantor subshifts in the Besicovitch
space, proving that sofic shifts occupy exactly the homotopy classes of
simplicial complexes. In addition, we study canonical projections into
subshifts, characterize the cellular automata that are contracting or isometric
in the Besicovitch or Weyl spaces, study continuous functions that locally look
like cellular automata, and present a new proof for the nonexistence of
transitive cellular automata in the Besicovitch space.
