ruff-0.4.0.1: relatively useful fractal functions

Copyright (c) Claude Heiland-Allen 20112015 BSD3 claude@mathr.co.uk unstable portable None Haskell98

Fractal.RUFF.Mandelbrot.Nucleus

Description

Mu-atom period, nucleus and bond point finding.

Synopsis

# Documentation

Arguments

 :: (Floating r, Ord r) => Int maximum period -> r radius -> Complex r center -> Maybe Int

Find the period of the lowest period nucleus inside a square.

The algorithm is based on Robert Munafo's page, Finding the Period of a mu-Atom http://mrob.com/pub/muency/period.html.

Arguments

 :: (Floating r, Fractional r) => Int period -> Complex r estimate -> [Complex r]

Given the period and approximate location, successively refine this estimate to a nucleus.

The algorithm is based on Robert Munafo's page Newton-Raphson method http://mrob.com/pub/muency/newtonraphsonmethod.html.

Arguments

 :: (Floating r, Fractional r) => Int period -> Complex r nucleus -> r angle -> [Complex r]

Given the period and nucleus, find succesive refinements to the bond point at a given internal angle.

The algorithm is based on ideas from http://mrob.com/pub/muency/derivative.html.

Arguments

 :: (Floating r, Fractional r) => Int period -> Complex r nucleus -> r radius -> r angle -> [Complex r]

Given the period and nucleus, find an interior point at a given internal angle and radius in (0,1].