  For a three-dimensional lattice in magnetic fields we have shown that the
hopping along the third direction, which normally tends to smear out the Landau
quantization gaps, can rather give rise to a fractal energy spectram akin to
Hofstadter's butterfly when a criterion, found here by mapping the problem to
two dimensions, is fulfilled by anisotropic (quasi-one-dimensional) systems. In
3D the angle of the magnetic field plays the role of the field intensity in 2D,
so that the butterfly can occur in much smaller fields. The mapping also
enables us to calculate the Hall conductivity, in terms of the topological
invariant in the Kohmoto-Halperin-Wu's formula, where each of $\sigma_{xy},
\sigma_{zx}$ is found to be quantized.
