ruff-0.4: relatively useful fractal functions

Copyright(c) Claude Heiland-Allen 2011,2015
LicenseBSD3
Maintainerclaude@mathr.co.uk
Stabilityunstable
Portabilityportable
Safe HaskellNone
LanguageHaskell98

Fractal.RUFF.Mandelbrot.Nucleus

Description

Mu-atom period, nucleus and bond point finding.

Synopsis

Documentation

findPeriod Source

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.

findNucleus Source

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.

findBond Source

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.

findInternal Source

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].