Standard Class Standard_LambdaMandelbrot

```Object
common:Generic
common:Formula
common:DivergentFormula
Standard:Standard_LambdaMandelbrot
```

`class DivergentFormula:Standard_LambdaMandelbrot`

Object version of LambdaMandelbrot in Standard.ufm Mandelbrot set corresponding to the classical Lambda Julia set. Use this fractal in Switch mode to find interesting Julia sets. Originally written by Damien M. Jones.

Ultra Fractal Source
``` class Standard_LambdaMandelbrot(common.ulb:DivergentFormula) {
;
; Object version of LambdaMandelbrot in Standard.ufm
;
; Mandelbrot set corresponding to the classical Lambda Julia
; set. Use this fractal in Switch mode to find interesting
; Julia sets.
;
; Originally written by Damien M. Jones.
;
public:
complex func Init(complex pz)
fPixel = pz
return @start
endfunc

complex func Iterate(complex pz)
return fPixel * pz * (1 - pz) ^ (@p_power - 1)
endfunc

private:
complex fPixel

default:
title = "Lambda (Mandelbrot)"
helpfile = "Uf*.chm"
helptopic = "Html/formulas/standard/lambda.html"
param start
caption = "Start Value"
default = (0.5, 0)
hint = "The starting value parameter can be used to distort the Mandelbrot \
set. Use (0.5, 0) for the standard Mandelbrot set."
endparam
param p_power ; Overrides p_power from Formula
caption = "Exponent"
default = (2, 0)
hint = "This parameter sets the exponent for the Lambda formula. \
Increasing the real part to 3, 4, and so on, will add discs to \
the fractal. Non-integer real values and non-zero imaginary values \
will create distorted Mandelbrot fractals. Use (2, 0) for the \
classic Lambda set."
endparam
param p_bailout ; Overrides p_bailout from DivergentFormula
caption = "Bailout"
default = 1.0e20
exponential = true
hint = "This parameter defines how soon an orbit bails out while \
iterating. Larger values give smoother outlines; values around 4 \
give more interesting shapes around the set. Values less than 4 \
will distort the fractal."
endparam
}
```

Constructor Summary
`Standard_LambdaMandelbrot()`

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:DivergentFormula
`GetUpperBailout, IsBailedOut`

Methods inherited from class common:Formula
`GetLowerBailout, GetPrimaryExponent`

Methods inherited from class common:Generic
`GetParent`

Methods inherited from class Object

Constructor Detail

Standard_LambdaMandelbrot

`public Standard_LambdaMandelbrot()`
Method Detail

Init

`public complex Init(complex pz)`
Description copied from class: `DivergentFormula`
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 `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)`
Description copied from class: `Formula`
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 `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