reb Class REB_TentMapJulia

Object common:Generic common:Formula common:DivergentFormula reb:REB_TentMapJulia

class
DivergentFormula:REB_TentMapJulia

Julia version of the Tent Map as described in Wikipedia and Mathworld.

This version of the tent map has somewhat different initializing conditions from those used by Kerry Mitchell. For this version: T(x) = s*x for x <= 0.5
T(x) = s*(1-x) for x > 0.5

An inverted form is available, along with several tent types and two flavors.

Ultra Fractal Source
class REB_TentMapJulia(common.ulb:DivergentFormula) {
; Julia version of the Tent Map as described in Wikipedia and Mathworld. <br>
; <p>
; This version of the tent map has somewhat different initializing conditions
; from those used by Kerry Mitchell. For this version:
;    T(x) = s*x for x <= 0.5  <br>
;    T(x) = s*(1-x) for x > 0.5 <br>
; <p> An inverted form is available, along with several tent types and two
; flavors.
public:
import "common.ulb"

; constructor
func REB_TentMapJulia(Generic pparent)
DivergentFormula.DivergentFormula(pparent)
endfunc

; initialize the formula
complex func Init(complex pz)
DivergentFormula.Init(pz)
m_c = pz
if @invert
pz = 1/(m_c+(0.000001,0.000001))
endif
if @flavor == "Flavor 1"
pz = @tentfn(pz)
endif
return pz
endfunc

; call for every iterated point
complex func Iterate(complex pz)
DivergentFormula.Iterate(pz)
if @flavor == "Flavor 2"
pz = @tentfn(pz)
endif
if @invert
if @type == "cabs"
if cabs(@tentfn2(pz)) <= @tent3
pz = @tent1*pz/(@seed+(0.000001,0.000001))
else
pz = @tent1*(@tent2-pz)/(@seed+(0.000001,0.000001))
endif
elseif @type == "real"
if real(@tentfn2(pz)) <= @tent3
pz = @tent1*pz/(@seed+(0.000001,0.000001))
else
pz = @tent1*(@tent2-pz)/(@seed+(0.000001,0.000001))
endif
elseif @type == "imag"
if imag(@tentfn2(pz)) <= @tent3
pz = @tent1*pz/(@seed+(0.000001,0.000001))
else
pz = @tent1*(@tent2-pz)/(@seed+(0.000001,0.000001))
endif
else
if imag(@tentfn2(pz)) > @tent3
pz = @tent1*(@tent2-pz)/(@seed+(0.000001,0.000001))
elseif real(@tentfn2(pz)) > @tent3
pz = @tent1*(@tent2-pz)/(@seed+(0.000001,0.000001))
else
pz = @tent1*pz/(@seed+(0.000001,0.000001))
endif
endif
else
if @type == "cabs"
if cabs(@tentfn2(pz)) <= @tent3
pz = @tent1*pz*@seed
else
pz = @tent1*(@tent2-pz)*@seed
endif
elseif @type == "real"
if real(@tentfn2(pz)) <= @tent3
pz = @tent1*pz*@seed
else
pz = @tent1*(@tent2-pz)*@seed
endif
elseif @type == "imag"
if imag(@tentfn2(pz)) <= @tent3
pz = @tent1*pz*@seed
else
pz = @tent1*(@tent2-pz)*@seed
endif
else
if imag(@tentfn2(pz)) > @tent3
pz = @tent1*(@tent2-pz)*@seed
elseif real(@tentfn2(pz)) > @tent3
pz = @tent1*(@tent2-pz)*@seed
else
pz = @tent1*pz*@seed
endif
endif
endif
return pz
endfunc

; Override the default function for bailout
bool func IsBailedOut(complex pz)
bool bail = false
if @test == 0
bail = (|pz| > @p_bailout)
elseif @test == 1
bail = (sqr(real(pz)) > @p_bailout)
elseif @test == 2
bail = (sqr(imag(pz)) > @p_bailout)
elseif @test == 3
bail = (sqr(real(pz)) > @p_bailout || sqr(imag(pz)) > @p_bailout)
elseif @test == 4
bail = (sqr(real(pz)) > @p_bailout && sqr(imag(pz)) > @p_bailout)
elseif @test == 5
bail = (sqr(abs(real(pz)) + abs(imag(pz))) > @p_bailout)
elseif @test == 6
bail = (sqr(real(pz) + imag(pz)) > @p_bailout)
endif
return bail
endfunc

protected:
complex m_c

default:
title = "Tent Map Julia"
int param v_tentmapjulia
caption = "Version (Tent Map Julia)"
default = 101
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_tentmapjulia < 101
endparam
text = "Based upon the Tent Map function:"
text = "   T(x) = s*x for x <= 0.5"
text = "   T(x) = s*(1-x) for x > 0.5"
text = "and the code for the Barnsley type fractals."
param type
caption = "Tent type"
default = 3
enum = "cabs" "real" "imag" "Pinsky"
endparam
param flavor
caption = "Flavor"
default = 0
enum = "Flavor 1" "Flavor 2"
endparam
bool param invert
caption = "Inversion"
default = false
endparam
param test
caption = "Bailout Test"
default = 0
enum = "mod" "real" "imag" "or" "and" "manh" "manr"
endparam
float param p_bailout
caption = "Bailout value"
default = 10000
min = 1
endparam
float param tent1
caption ="Tent param #1"
default = 1
endparam
float param tent2
caption ="Tent param #2"
default = 1
endparam
float param tent3
caption ="Tent param #3"
default = 0.5
endparam
func tentfn
caption = "Tent function"
default = ident()
endfunc
func tentfn2
caption = "Tent function #2"
default = ident()
endfunc
complex param seed
caption = "Julia seed"
default = (1.04375,0.35625)
hint = "Use this parameter to create many different Julia sets. A good \
way to set this parameter is with the Eyedropper or Explore features."
endparam
complex param p_power ; Overrides p_power from Formula
caption = "Power"
default = (2,0)
visible = false
endparam
}

Constructor Summary
REB_TentMapJulia()

REB_TentMapJulia(Generic pparent)
constructor

Method Summary
complex Init(complex pz)
initialize the formula
boolean IsBailedOut(complex pz)
Override the default function for bailout
complex Iterate(complex pz)
call for every iterated point

Methods inherited from class common:DivergentFormula
GetUpperBailout

Methods inherited from class common:Formula
GetLowerBailout, GetPrimaryExponent

Methods inherited from class common:Generic
GetParent

Methods inherited from class Object

Constructor Detail

REB_TentMapJulia

public REB_TentMapJulia(Generic pparent)
constructor

REB_TentMapJulia

public REB_TentMapJulia()
Method Detail

Init

public complex Init(complex pz)
initialize the formula

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)
call for every iterated point

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

IsBailedOut

public boolean IsBailedOut(complex pz)
Override the default function for bailout

Overrides:
IsBailedOut in class DivergentFormula
Parameters:
pz - last sequence value to test; this should be the value returned from the previous Iterate() call. Note that it is acceptable to ignore pz and use m_BailedOut, but any code calling IsBailedOut() should pass in the correct pz for Formula classes which do not use m_BailedOut.
Returns:
true if the sequence has bailed out (i.e. should be terminated)