reb
Class REB_IkenagaJulia

Object
  common:Generic
      common:Formula
          common:DivergentFormula
              reb:REB_IkenagaJulia

class 
DivergentFormula:REB_IkenagaJulia

Based upon the Ikenaga fractal

The function was discovered by Bruce Ikenaga who passed it on to A.K. Dewdney which appeared in his book "The Armchair Universe". I first used this formula in Fractint, about 1993 - Ron Barnett. The formula uses Fractint style bailouts.

Ultra Fractal Source

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 class REB_IkenagaJulia(common.ulb:DivergentFormula) {
 ; Based upon the Ikenaga fractal <br>
 ; <p>
 ; The function was discovered by Bruce Ikenaga who passed it on to A.K. Dewdney
 ; which appeared in his book "The Armchair Universe". I first used this formula
 ; in Fractint, about 1993 - Ron Barnett. The formula uses Fractint style bailouts.
 public:
   import "common.ulb"
 
   ; constructor
   func REB_IkenagaJulia(Generic pparent)
      DivergentFormula.DivergentFormula(pparent)
    endfunc
 
   ; initialize the formula
   complex func Init(complex pz)
     DivergentFormula.Init(pz)
     return pz
   endfunc
 
   ; call for every iterated point
   complex func Iterate(complex pz)
     DivergentFormula.Iterate(pz)
     return pz^3 + (@seed-1)*pz - @seed
   endfunc
 
   ; Override the default function for bailout
   bool func IsBailedOut(complex pz)
     bool bail = false
     if @test == 0
       bail = (|pz| > @p_bailout)
     elseif @test == 1
       bail = (sqr(real(pz)) > @p_bailout)
     elseif @test == 2
       bail = (sqr(imag(pz)) > @p_bailout)
     elseif @test == 3
       bail = (sqr(real(pz)) > @p_bailout || sqr(imag(pz)) > @p_bailout)  
     elseif @test == 4
       bail = (sqr(real(pz)) > @p_bailout && sqr(imag(pz)) > @p_bailout)  
     elseif @test == 5
       bail = (sqr(abs(real(pz)) + abs(imag(pz))) > @p_bailout)
     elseif @test == 6
       bail = (sqr(real(pz) + imag(pz)) > @p_bailout)
     endif
     return bail
   endfunc
 
 default:
   title = "Ikenaga Julia"
   int param v_ikenagajulia
     caption = "Version (Ikenaga Julia)"
     default = 101
     hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
     visible = @v_ikenagajulia < 101
   endparam
   heading
     text = "This an Ikenaga Julia that includes the Fractint bailout options."
   endheading
   param test
     caption = "Bailout Test"
     default = 0
     enum = "mod" "real" "imag" "or" "and" "manh" "manr"
     hint = "mod is the standard bailout. The remaining bailout methods are \
             from Fractint."
   endparam
   float param p_bailout ; Overrides p_bailout from DivergentFormula
     caption = "Bailout value"
     default = 10000.0
     min = 1.0
     hint = "Use a value of 4 if the bailout test is other than mod."
   endparam
   complex param seed
     caption = "Julia seed"
     default = (0.0,-0.1625)
     hint = "Use this parameter to create many different Julia sets. A good \
             way to set this parameter is with the Eyedropper or Explore features."
   endparam
   complex param p_power ; Overrides p_power from Formula
     caption = "Power"
     default = (2,0)
     visible = false
   endparam
 }
 

Constructor Summary

REB_IkenagaJulia()

REB_IkenagaJulia(Generic pparent)
constructor

Method Summary

complex	Init(complex pz) initialize the formula
boolean	IsBailedOut(complex pz) Override the default function for bailout
complex	Iterate(complex pz) call for every iterated point

Methods inherited from class common:DivergentFormula

GetUpperBailout

Methods inherited from class common:Formula

GetLowerBailout, GetPrimaryExponent

Methods inherited from class common:Generic

GetParent

Methods inherited from class Object

Constructor Detail

REB_IkenagaJulia

public REB_IkenagaJulia(Generic pparent)

constructor

REB_IkenagaJulia

public REB_IkenagaJulia()

Method Detail

Init

public complex Init(complex pz)

initialize the formula

Overrides:

Init in class DivergentFormula

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)

call for every iterated point

Overrides:

Iterate in class Formula

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

IsBailedOut

public boolean IsBailedOut(complex pz)

Override the default function for bailout

Overrides:

IsBailedOut in class DivergentFormula

Parameters:

pz - last sequence value to test; this should be the value returned from the previous Iterate() call. Note that it is acceptable to ignore pz and use m_BailedOut, but any code calling IsBailedOut() should pass in the correct pz for Formula classes which do not use m_BailedOut.

Returns:

true if the sequence has bailed out (i.e. should be terminated)