mt
Class MT_BofNewtonII

Object
  common:Generic
      common:Formula
          common:ConvergentFormula
              mt:MT_BofNewtonII

class 
ConvergentFormula:MT_BofNewtonII

Mark Townsend, May 2008

Ultra Fractal Source

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 class MT_BofNewtonII(common.ulb:ConvergentFormula) {
 ;
 ; Mark Townsend, May 2008
 ;
 public:
   complex func Init(complex pz)
     ConvergentFormula.Init(pz)
     fPixel = pz
     fH = 0.0001
     return @p_start
   endfunc
 
   complex func Iterate(complex pz)
     ConvergentFormula.Iterate(pz)
     complex zh = pz + fH
     complex fz = (pz - 1) * (pz^2 + pz + fPixel)
     complex fzd = 1 / fH * ((zh - 1) * (zh^2 + zh + fPixel) - fz)
     return pz - fz / fzd
   endfunc
 
 private:
   complex fPixel
   complex fH
 
 default:
   title = "Bof Newton II"
   complex param @p_start
     caption = "Starting point"
     default = (0, 0)
   endparam
   complex param p_power
     visible = false
   endparam
   float param p_bailout
     caption = "Bailout"
     default = 1.0e-6
   endparam
 }
 

Constructor Summary

MT_BofNewtonII()

Method Summary

complex	Init(complex pz) Set up for a sequence of values
complex	Iterate(complex pz) Produce the next value in the sequence

Methods inherited from class common:ConvergentFormula

GetLowerBailout, IsBailedOut

Methods inherited from class common:Formula

GetPrimaryExponent, GetUpperBailout

Methods inherited from class common:Generic

GetParent

Methods inherited from class Object

Constructor Detail

MT_BofNewtonII

public MT_BofNewtonII()

Method Detail

Init

public complex Init(complex pz)

Description copied from class: ConvergentFormula

Set up for a sequence of values

This function will be called at the beginning of each sequence of values (e.g. at the beginning of each fractal orbit).

Overrides:

Init in class ConvergentFormula

Parameters:

pz - seed value for the sequence; for a normal fractal formula, this will be #pixel

Returns:

first value in the sequence; this corresponds to #z in a fractal formula

Iterate

public complex Iterate(complex pz)

Description copied from class: ConvergentFormula

Produce the next value in the sequence

As long as the sequence has not bailed out, this function will be continually called to produce sequence values.

Overrides:

Iterate in class ConvergentFormula

Parameters:

pz - previous value in the sequence; corresponds to #z in a fractal formula. Note that you should always use this value for computing the next iteration, rather than a saved value, as the calling code may modify the returned value before passing it back to the next Iterate() call.

Returns:

the next value in the sequence