Standard Class Standard_Triangle

Object common:Generic common:Coloring common:GradientColoring Standard:Standard_Triangle

class

Object version of Triangle in Standard.ucl. Variation on the Triangle Inequality Average coloring method from Kerry Mitchell. The smoothing used here is based on the Smooth formula, which only works for z^n+c and derivates. Originally written by Damien M. Jones

Ultra Fractal Source
;
; Object version of Triangle in Standard.ucl.
;
; Variation on the Triangle Inequality Average coloring method from Kerry
; Mitchell. The smoothing used here is based on the Smooth formula, which only
; works for z^n+c and derivates.
;
; Originally written by Damien M. Jones
;
public:
func Init(complex pz, complex ppixel)
fSum = 0
fSum2 = 0
fAC = cabs(ppixel)
endfunc

func Iterate(complex pz)
fSum2 = fSum
if m_Iterations > 1
float az2 = cabs(pz - GetPixel())
float lowbound = abs(az2 - fAC)
fSum = fSum + ((cabs(pz) - lowbound) / (az2 + fAC - lowbound))
endif
endfunc

float func ResultIndex(complex pz)
fSum = fSum / m_Iterations
fSum2 = fSum2 / (m_Iterations - 1)
float il = 1 / log(@power)
float lp = log(log(@bailout) / 2)
float f = il * lp - il*log(log(cabs(pz)))
return fSum2 + (fSum - fSum2) * (f + 1)
endfunc

private:
float fAC
float fSum
float fSum2

default:
title = "Triangle Inequality Average"
helpfile = "Uf*.chm"
helptopic = "Html/coloring/standard/triangleinequalityaverage.html"
rating = recommended
param power
caption = "Exponent"
default = 2.0
hint = "This should be set to match the exponent of the \
formula you are using. For Mandelbrot, this is usually 2."
endparam
param bailout
caption = "Bailout"
default = 1e20
min = 1
exponential = true
hint = "This should be set to match the bail-out value in \
the Formula tab. Use a very high value for good results."
endparam
}

Constructor Summary
Standard_Triangle()

Method Summary
void Init(complex pz, complex ppixel)
Set up for a sequence of values
void Iterate(complex pz)
Process the next value in the sequence
float ResultIndex(complex pz)
Produce a resulting color index after a sequence is finished

Methods inherited from class common:Coloring
GetPixel

Methods inherited from class common:Generic
GetParent

Methods inherited from class Object

Constructor Detail

Standard_Triangle

public Standard_Triangle()
Method Detail

Init

public void Init(complex pz,
complex ppixel)
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:
Parameters:
pz - first value for the sequence; for a normal coloring formula, this will be #z
ppixel - seed value for the sequence; for a normal coloring formula, this will be #pixel

Iterate

public void Iterate(complex pz)
Process 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. Note that such processing generally will not know in advance precisely how long the sequence is, and should be prepared to deal with sequences of arbitrary length.

Your coloring may determine at some point that a solid color should be used rather than an index value.

Overrides:
Parameters:
pz - next value in the sequence; corresponds to #z in a coloring formula

ResultIndex

public float ResultIndex(complex pz)