# Logarithmic Spiral

Logarithmic Spiral

The logarithmic spiral is plotted with the origin in red. It can be expressed in polar coordinates as or parametrically as:

r(θ)=ab

θ

x(θ)=abcos(θ)

θ

y(θ)=absin(θ)

θ

Each small black point represents the spiral's point for a different angle . Specifically, 80 black points are plotted for each completed round (). The big black point represents the "initial point" corresponding to . The big blue point highlights the point for the specific angle selected with the control.

(x(θ),y(θ))

θ

Δθ=2π

θ=0

Select "fixed axes" to restrict the range of in the plot to . Without "fixed axes", the same spiral can be seen resized; the unit line segment along the axis shows the scale.

x

[-1,1]

x