## jlb Class JLB_NewtonUtilityTransform

```Object
common:Generic
common:Transform
common:UtilityTransform
jlb:JLB_NewtonUtilityTransform
```

`class UtilityTransform:JLB_NewtonUtilityTransform`

The Newton formula as a Transform.

Ultra Fractal Source
``` class JLB_NewtonUtilityTransform(common.ulb:UtilityTransform) {
; The Newton formula as a Transform.
public:

; @param pz
; @return the new pz
complex func Iterate(complex pz)
if (@p_std)
return (2*sqr(pz)*pz+1)/(3*sqr(pz))
else
return pz*(1-@relax) + \
@relax * ((@p_power - 1) * pz^@p_power + @r) / \
(@p_power * pz ^ (@p_power - 1))
endif
endfunc

default:
title = "Newton"
int param v_NewtonUtilityTransform
caption = "Version (Newton_UtilityTransform)"
default = 100
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_NewtonUtilityTransform < 100
endparam
bool param p_std
caption = "Standard"
default = true
endparam

complex param p_power
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."
visible = !@p_std
endparam
param r
caption = "Root"
default = (1,0)
hint = "Specifies the root of the equation that is solved. Use larger \
numbers for slower convergence."
visible = !@p_std
endparam
param relax
caption = "Relaxation"
default = (1,0)
hint = "This can be used to alter the convergence of \
the formula."
visible = !@p_std
endparam
}
```

Constructor Summary
`JLB_NewtonUtilityTransform()`

Method Summary
` complex` `Iterate(complex pz)`
Transform a single point within a sequence

Methods inherited from class common:Transform
`Init, IsSolid, IterateSilent`

Methods inherited from class common:Generic
`GetParent`

Methods inherited from class Object

Constructor Detail

### JLB_NewtonUtilityTransform

`public JLB_NewtonUtilityTransform()`
Method Detail

### Iterate

`public complex Iterate(complex pz)`
Description copied from class: `Transform`
Transform a single point within a sequence

After a sequence has been set up with Init(), this function will be called once for each value in the sequence. Note that all values in the sequence must be processed in order (they cannot be processed out of order). If the sequence contains only one value, Init() will still be called and then Iterate() will be called just once.

Overrides:
`Iterate` in class `Transform`
Parameters:
`pz` -
Returns:
the new pz