## 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
``` 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
text = "This an Ikenaga Julia that includes the Fractint bailout options."
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)