Schematic representation of log-periodic spiral arms and the main parameters used. The thick blue spiral has a pitch angle ψ₁ = 10°. As an example of the effect that an increase of an arm’s pitch angle has, while leaving the other two parameters fixed, we plotted a log-periodic spiral with ψ₂ = 2 × ψ₁ (blue dashed line). A circle is obtained if ψ = 0, as indicated by the gray dot-dashed line. As indicated in the figure, the pitch angle is the angle between the tangent to the spiral arm and a perfect circle, providing a measure of how tightly wound the spiral arm is. The thick green spiral has the same pitch angle as the blue one, but a larger reference radius, R_ref. The four Galactic quadrants are indicated by roman numerals I-IV at the corners of the plot. The azimuthal angle, β, is measured starting from the Sun-Galactic center direction, and increasing in the direction of Galactic rotation, as indicated here.