Logarithmic spiral
The derivative r'(θ) is proportional to the parameter b.  In other words, it controls how "tightly" and in which direction the spiral spirals.  In the extreme case that b = 0 (ɸ = π/2) the spiral becomes a circle of radius a.  Conversely, in the limit that b approaches infinity (ɸ → 0) the spiral tends toward a straight line.  The complement of ɸ is called the pitch.