Recursive wave

Note: This article was proposed for deletion on Wikipedia.

A recursive wave is a self-similar curve in three-dimensional space that is constructed by iteratively adding a helix around the previous curve.

Construction

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 w⃗ is chosen to be the fixed "rag" vector.

R is a function that rotates a vector A⃗ around an axis defined by a vector B⃗ by θ degrees. In this case it is expressed with quaternions.