Logarithmic Spiral

a

1

b

0.73613

angle φ

1

rounds

2

fixed axes

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

r(θ)=a

θ

b

or parametrically as:

x(θ)=a

θ

b

cos(θ)

,

y(θ)=a

θ

b

sin(θ)

.

Each small black point represents the spiral's point

(x(θ),y(θ))

for a different angle

θ

. Specifically, 80 black points are plotted for each completed round (

Δθ=2π

). The big black point represents the "initial point" corresponding to

θ=0

. The big blue point highlights the point for the specific angle selected with the control.

Select "fixed axes" to restrict the range of

x

in the plot to

[-1,1]

. Without "fixed axes", the same spiral can be seen resized; the unit line segment along the

x

axis shows the scale.

Loreto Llorente