Recursive wave: Difference between revisions

Revision as of 19:01, 30 January 2016

Revision as of 04:28, 2 February 2016

Line 2:

[[File:Recwave1.gif|thumbnail|A recursive wave of depth 1, 2 and 3.]]

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 ==

Line 12:

{{Equation box 1 |indent =: |title= |equation = <math>\psi_{n}(x) = \psi_{n-1}(x) + R(A(n)g_n(x),\ \psi_{n-1}'(x),\ f(n)x + \alpha(n))</math> |cellpadding= 6 |border |border colour = #0073CF |background colour=#F5FFFA}}

Wherewhere

{{Equation box 1 |indent =: |title= |equation = <math>g_n(x) = |\vec{w} \times |\psi_{n-1}'(x)||</math> |cellpadding= 6 |border |border colour = #0073CF |background colour=#F5FFFA}}

Andand

{{Equation box 1 |indent =: |title= |equation = <math>R(\vec{A}, \vec{B}, \theta) = e^{\vec{B}\theta /2}\vec{A}e^{-\vec{B}\theta /2}</math> |cellpadding= 6 |border |border colour = #0073CF |background colour=#F5FFFA}}