## Standard Class Standard_Newton

```Object
common:Generic
common:Formula
common:ConvergentFormula
Standard:Standard_Newton
```

`class ConvergentFormula:Standard_Newton`

Object version of Newton in Standard.ufm. Standard Newton fractal.

Ultra Fractal Source
``` class Standard_Newton(common.ulb:ConvergentFormula) {
;
; Object version of Newton in Standard.ufm.
; Standard Newton fractal.
;
public:
complex func Init(complex pz)
ConvergentFormula.Init(pz)
return pz
endfunc

complex func Iterate(complex pz)
ConvergentFormula.Iterate(pz)
return ((@p_power - 1) * pz^@p_power + @r) / (@p_power * pz ^ (@p_power - 1))
endfunc

default:
title = "Newton"
helpfile = "Uf*.chm"
helptopic = "Html/formulas/standard/newton.html"
rating = recommended
param p_power ; Overrides p_power from Formula
caption = "Exponent"
default = (3,0)
hint = "Specifies the exponent of the equation that is solved by \
Newton's method. Use real numbers (set the imaginary part \
to zero) to obtain classic Newton fractals."
endparam
param r
caption = "Root"
default = (1,0)
hint = "Specifies the root of the equation that is solved. Use larger \
numbers for slower convergence."
endparam
param p_bailout ; Overrides p_bailout from ConvergentFormula
caption = "Bailout value"
default = 0.00001
min = 0
exponential = true
hint = "This parameter defines how soon a convergent orbit bails out while \
iterating. Smaller values give more precise results but usually \
require more iterations."
endparam
}
```

Constructor Summary
`Standard_Newton()`

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

### Standard_Newton

`public Standard_Newton()`
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