A recursive wave is a self-similar curve in three-dimensional space that is constructed by iteratively adding a helix around the previous curve.
A recursive wave of depth
n
can be constructed as following:
where
and
Each wave at non-zero depth
n
is described by an amplitude
A
(
n
)
, frequency
f
(
n
)
and phase offset
α
(
n
)
.
g
n
(
x
)
represents a unit vector that is perpendicular to the previous curve at
x
. An arbitrary vector
w
→
is chosen to be the fixed "rag" vector.
R
is a function that rotates a vector
A
→
around an axis defined by a vector
B
→
by
θ
degrees. In this case it is expressed with quaternions.
