mt
Class MT_JewelNewtonJulia

Object
  common:Generic
      common:Formula
          common:ConvergentFormula
              mt:MT_JewelNewtonJulia

class 
ConvergentFormula:MT_JewelNewtonJulia

Mark Townsend, May 2008

Ultra Fractal Source

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 class MT_JewelNewtonJulia(common.ulb:ConvergentFormula) {
 ;
 ; Mark Townsend, May 2008
 ;
 public:
   complex func Init(complex pz)
     ConvergentFormula.Init(pz)
     fH = 0.0001
     return pz
   endfunc
 
   complex func Iterate(complex pz)
     ConvergentFormula.Iterate(pz)
     complex zh = pz + fH
     complex fz = pz^@p_power + pz + @p_seed
     complex fzd =  1 / fH * ((zh^@p_power + zh + @p_seed) - fz)
     return pz - fz / fzd
   endfunc
 
 private:
   complex fH
 
 default:
   title = "Jewel Newton Julia"
   complex param p_seed
     caption = "Julia seed"
     default = (-1.3, 1.3)
   endparam
   complex param p_power
     caption = "Exponent"
     default = (5,0)
   endparam
   float param p_bailout
     caption = "Bailout"
     default = 1.0e-6
   endparam
 }
 

Constructor Summary

MT_JewelNewtonJulia()

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_JewelNewtonJulia

public MT_JewelNewtonJulia()

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