Complex Functions

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Complex Functions Support

ComplexFunctions is a FunctionSet of commonly used Fractal Science Kit fractal generator complex functions of 1 argument. Many of the built-in programs include ComplexFunctions in the properties section of the program instructions to define 1 or more Function Proxy Options.

ComplexFunctions is defined in the built-in macros as:

#define ComplexFunctions

functionSet ComplexFunctions {
  Ident
  ReflectAboutXAxis ReflectAboutYAxis
  ReflectAboutPositiveDiagonal ReflectAboutNegativeDiagonal
  ReflectAboutUnitCircle
  Rotate90 Rotate180 Rotate270
  Pow2 Pow3 Pow4 Pow5 Pow6
  Recip Recip2 Recip3 Recip4 Recip5 Recip6
  Sqrt Root3 Root4 Root5 Root6
  Exp Log Cis
  Sin Cos Tan Sec Csc Cot
  Sinh Cosh Tanh Sech Csch Coth
  Asin Acos Atan Asec Acsc Acot
  Asinh Acosh Atanh Asech Acsch Acoth
  Versin Covers Haversin Hacovers
  Versinh Coversh Haversinh Hacoversh
  Sinc Tanc Sinhc Tanhc
  Arsh Arch Arth
  Sigmoid Logit
  Expm1 Log1p
  Bifurcate Cardioid Convex Cayley Poisson
  Airfoil Airfoil2 Bipole Dipole
  Gudermannian AGudermannian
  CpxF1 CpxF2 CpxF3 CpxF4 CpxF5
  CpxF6 CpxF7 CpxF8 CpxF9 CpxF10
  CpxF11 CpxF12 CpxF13 CpxF14 CpxF15
  CpxF16 CpxF17 CpxF18 CpxF19 CpxF20
  CpxF21 CpxF22 CpxF23 CpxF24 CpxF25
  CpxF26 CpxF27 CpxF28 CpxF29 CpxF30
  CpxF31 CpxF32 CpxF33 CpxF34 CpxF35
  CpxF36 CpxF37 CpxF38 CpxF39 CpxF40
  CpxF41 CpxF42 CpxF43 CpxF44 CpxF45
  CpxF46 CpxF47 CpxF48 CpxF49 CpxF50
  CpxF51 CpxF52 CpxF53 CpxF54 CpxF55
  CpxF56 CpxF57 CpxF58 CpxF59 CpxF60
  CpxF61 CpxF62 CpxF63 CpxF64 CpxF65
  CpxF66 CpxF67 CpxF68 CpxF69 CpxF70
  CpxF71 CpxF72 CpxF73 CpxF74 CpxF75
  CpxF76 CpxF77 CpxF78 CpxF79 CpxF80
  ZTrans1 ZTrans2 ZTrans3 ZTrans4 ZTrans5
  ZTrans6 ZTrans7 ZTrans8 ZTrans9 ZTrans10
  ZTrans11 ZTrans12 ZTrans13 ZTrans14 ZTrans15
  ZTrans16 ZTrans17 ZTrans18 ZTrans19 ZTrans20
  ZTrans21 ZTrans22 ZTrans23 ZTrans24 ZTrans25
  ZTrans26 ZTrans27 ZTrans28 ZTrans29 ZTrans30
  ZTrans31 ZTrans32 ZTrans33 ZTrans34 ZTrans35
  ZTrans36 ZTrans37 ZTrans38 ZTrans39 ZTrans40
  ZTrans41 ZTrans42 ZTrans43 ZTrans44 ZTrans45
  ZTrans46 ZTrans47 ZTrans48 ZTrans49 ZTrans50
}
#end

The following is an example that uses ComplexFunctions to define a function proxy F:

properties:
 
  #include ComplexFunctions
 
  option F {
    type = ComplexFunctions
    caption = "f(z)"
    default = Ident
  }

This results in the function proxy F as shown below:

ComplexFunctions Example

 

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