From any point P on the spiral, draw a line toward the center of the spiral. P is constant, the curve is an equiangular spiral. A special case of equiangular spiral is the circle, where the constant angle is 90 Degrees. Equiangular Spiral Family Equiangular spiral is the cross section of Nautilus and various other shells. One can also find it in the arrangement of seeds in sunflower, pine cones, and other growths.
Formulas Let alpha be the constant angle.
Suppose there are n bugs each at a corner of a n sided regular polygon. Each bug crawls towards its next neighbor with uniform speed. The figure on the left shows the trace of four bugs, resulting four equiangular spirals of 45 degree. The figure on the right has six objects forming a chasing chain. Each line is the direction of movement and is tangent to the equiangular spirals so formed.