ruff-0.3.2: relatively useful fractal functions

Portabilityportable
Stabilityunstable
Maintainerclaudiusmaximus@goto10.org
Safe HaskellNone

Fractal.RUFF.Mandelbrot.Nucleus

Description

Mu-atom period, nucleus and bond point finding.

Synopsis

Documentation

findPeriodSource

Arguments

:: (Floating r, Ord r) 
=> Integer

maximum period

-> r

radius

-> Complex r

center

-> Maybe Integer 

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.

findNucleusSource

Arguments

:: (Floating r, Fractional r) 
=> Integer

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.

findBondSource

Arguments

:: (Floating r, Fractional r) 
=> Integer

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.

findInternalSource

Arguments

:: (Floating r, Fractional r) 
=> Integer

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].