  The ground-state phase diagram is mapped out for an alternative anisotropic
extension of quantum spin-1 ferromagnetic biquadratic model, which accommodates
twelve distinct phases: three degenerate fractal phases, six Luttinger liquid
phases and three symmetry-protected trivial phases. It is found that distinct
types of quantum phase transitions are involved between them. In particular,
one type arises from an instability of a Luttinger liquid towards a degenerate
fractal phase, and the other type describes spontaneous symmetry breaking with
type-B Goldstone modes from one degenerate fractal phase to another degenerate
fractal phase, with the fractal dimension $d_f$ being identical to the number
of the type-B Goldstone modes, both of which turn out to be one. In addition,
quantum phase transitions from the Luttinger liquid phases to the
symmetry-protected trivial phases are identified to be in the
Kosterlitz-Thouless universality class, with central charge being one.
