WOLFRAM|DEMONSTRATIONS PROJECT

Elliptical Spheres

​
function parameters:
α
m
embedding parameters:
x-direction Re/Im ratio
y-direction Re/Im ratio
z-direction Re/Im ratio
Elliptical spheres are neither spheres nor elliptic. Elliptical spheres are complex vectors
r={x,y,z}
such that
r.r=1
and
x
,
y
,
z
are elliptic functions. A possible parametrization of these vectors is given through Neville theta functions as
r
α,m
(z)=
1
1-m
ϑ
n
(αm)
ϑ
n
(zm)

1-m
m
ϑ
s
(αm)
ϑ
s
(zm),
m
ϑ
c
(αm)
ϑ
c
(zm),
ϑ
d
(αm)
ϑ
d
(zm)
,
z∈
,
α∈
,
m∈
.
In this Demonstration,
z
runs over part of the complex plane and
α
and
m
are complex parameters. The graphic displays variable relative fractions of the real and imaginary parts of
x
,
y
, and
z
.