Quantum Octahedral Fractal via Random Spin-State Jumps

sharpness of spin direction

Quantum jumps of spin 1/2 states on the Bloch sphere are realized by Möbius transformations. Chaos games produced by a random sequence of six noncommuting transformations centered at the vertices of the octahedron result in a fractal pattern on the sphere. The parameter

k

,

0<k<1

, defines the sharpness of the spin-direction measurements.