Standard
Class Standard_PhoenixMandel

Object
  common:Generic
      common:Formula
          common:DivergentFormula
              Standard:Standard_PhoenixMandel

class 
DivergentFormula:Standard_PhoenixMandel

Object version of PhoenixMandel in Standard.ufm. Mandelbrot variant of the Phoenix fractal type discovered by Shigehiro Ushiki. The general equation is of the form z(n+1) = z(n)^a + c*z(n)^b + p*z(n-1) If a=2 and b=0 (classic Phoenix) then this type will work with the Smooth and Triangle Inequality coloring algorithms. Originally written by Damien M. Jones

Ultra Fractal Source

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 class Standard_PhoenixMandel(common.ulb:DivergentFormula) {
 ;
 ; Object version of PhoenixMandel in Standard.ufm.
 ;
 ; Mandelbrot variant of the Phoenix fractal type discovered by
 ; Shigehiro Ushiki. The general equation is of the form
 ;
 ;     z(n+1) = z(n)^a + c*z(n)^b + p*z(n-1)
 ;
 ; If a=2 and b=0 (classic Phoenix) then this type will
 ; work with the Smooth and Triangle Inequality coloring
 ; algorithms.
 ;
 ; Originally written by Damien M. Jones
 ;
 public:
   complex func Init(complex pz)
     fY = (0, 0)
     fPixel = pz
     if (@start == (0,0)); bug in beta 5
       return pz
     else
       return @start
     endif
   endfunc
 
   complex func Iterate(complex pz)
     complex newz = pz^@p_power + pz^@power2 * fPixel + @induct * fY
     fY = pz
     return newz
   endfunc
 
 private:
   complex fPixel
   complex fY
 
 default:
   title = "Phoenix (Mandelbrot)"
   helpfile = "Uf*.chm"
   helptopic = "Html/formulas/standard/phoenix.html"
   rating = recommended
   param start
     caption = "Start Value"
     default = (0,0)
     hint = "Starting value for each point. You can use this to \
             'perturb' the fractal."
   endparam
   param p_power ; Overrides p_power from Formula
     caption = "Exponent 1"
     default = (2,0)
     hint = "Defines the primary exponent for the fractal. The classic \
             Phoenix curve uses exponent (2, 0)."
   endparam
   param power2
     caption = "Exponent 2"
     default = (0,0)
     hint = "Defines the secondary exponent for the fractal.  The classic \
             Phoenix curve uses exponent (0, 0)."
   endparam
   param induct
     caption = "Distortion"
     default = (0.5,0)
     hint = "Sets how 'strong' the previous iteration's effect should be \
             on the fractal."
   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 will give smoother outlines."
   endparam
 }
 

Constructor Summary

Standard_PhoenixMandel()

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_PhoenixMandel

public Standard_PhoenixMandel()

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