  The Hofstadter butterfly of lattice electrons in a strong magnetic field is a
cornerstone of condensed matter physics, exploring the competition between
periodicities imposed by the lattice and the field. In this work we introduce
and characterize the Weyl butterfly, which emerges when a large magnetic field
is applied to a three-dimensional Weyl semimetal. Using an experimentally
motivated lattice model for cold atomic systems, we solve this problem
numerically. We find that Weyl nodes reemerge at commensurate fluxes and
propose using wavepackets dynamics to reveal their chirality and location.
Moreover, we show that the chiral anomaly -- a hallmark of the topological Weyl
semimetal -- does not remain proportional to magnetic field at large fields,
but rather inherits a fractal structure of linear regimes as a function of
external field. The slope of each linear regime is determined by the difference
of two Chern numbers in gaps of the Weyl butterfly and can be measured
experimentally in time of flight.
