Loxodrome Art

loxodrome specification

parameter a

1.33

bearing angle start

θ

min

0.4

bearing angle range

θ

range

0.86

loxodrome appearance

number of curves m

2

4

8

16

32

64

color scheme

BrightBands

curve thickness

3

The parametric equation of a loxodrome on the unit sphere can be expressed as

(x,y,z)=

cos(t)((4a)

θt



)

4+

2

a

2θt



,

sin(t)((4a)

θt



)

4+

2

a

2θt



,1-

8

4+

2

a

2θt



. This family of curves is parametrized by

a

and

θ

. In this Demonstration, you can continuously vary the parameter

a

and see

m

curves obtained by using values of the parameter

θ

spaced evenly from

θ

min

to

θ

range

.

Varying the parameter

a

or the number of curves

m

, or changing the range of the bearing angle

θ

, yields some interesting artistic images.