Recursive wave explained

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

Clarification

Each wave at non-zero depth

n is described by an amplitude A(n) , frequency f(n) and phase offset \alpha(n) .g _{n(x)} represents a unit vector that is perpendicular to the previous curve at x . An arbitrary vector \vec{w} is chosen to be the fixed "rag" vector.R is a function that rotates a vector \vec{A} around an axis defined by a vector \vec{B} by \theta degrees. In this case it is expressed with quaternions.

See also

• Solenoid (DNA)