Documentation of objfractal

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Function Synopsis

ObjVal = objfractal(Chrom, P1, P2)

Help text

 OBJective function Fractal Mandelbrot

 This function implements a fractal function and its discretization.
 The Fractal function is highly multimodal and emulates noisy 
 real-world objective functions.

 The objective function is obtained by an approximation of the 
 simplified real part C(x) of the Weierstrass-Mandelbrot function.
 C(x) is continuous but has no derivative at any point. With the
 box-dimension BoxDim (1 < BoxDim < 2) of this function the ruggedness
 of the surface can be controlled. Higher values for BoxDim increase
 the complexity of this objective function and vice versa.

 The Weierstrass-Mandelbrot function is described in:
    Mandelbrot, B.B. The fractal geometry of nature. 
       New York: Freeman, 1983.

 Syntax: ObjVal = objfractal(Chrom, P1, P2)

 Input parameters:
    Chrom     - Matrix containing the chromosomes of the current
                population. Each row corresponds to one individual's
                string representation.
                If Chrom == [NaN xxx]  or 
                   Chrom == [NaN xxx yyy], 
               then special values will be returned, see Output parameters
                   xxx == 1 (or []) return boundaries
                   xxx == 2 return title 
                      yyy == 0 return title of continuous variant
                      yyy == 1 return title of discrete variant
                   xxx == 3 return value of global minimum
    P1        - (Optional) Number indicating which variant is used,
                if Chrom is not NaN or []. 
                   P1 = 1  use discrete version
                   P1 = 0  use continuous version
                If P1 is omitted or P1 = [] the continuos version 
                   is used (P1 = 0).
    P2        - (Optional) Scalar containing the box dimension BoxDim 
                (1 < BoxDim < 2) of this objective function.
                 If P2 is omitted, empty or out of range, then the
                    default value BoxDim = 1.85 is used.
       
 Output parameters:
    ObjVal    - Column vector containing the objective values of the
                individuals in the current population.
                if called with 
                   Chrom == [NaN xxx] or Chrom == [NaN xxx yyy], 
                then ObjVal contains
                   xxx == 1 (or []), matrix with the boundaries of 
                                     the varaibles
                   xxx == 2, text with the title of the function
                      yyy omitted: title of continuous variant
                      yyy = 0      title of continuous variant
                      yyy = 1      title of discrete variant
                   xxx == 3, value of global minimum

 Examples:

  % continuous variant of the Fractal function with default box
  % dimension BoxDim = 1.85
  >> objfractal(Chrom)

  % discrete variant of the Fractal function with default box
  % dimension BoxDim = 1.85
  >> objfractal(Chrom, 1)

  % discrete variant of the Fractal function with box dimension
  % BoxDim = 1.4.
  >> objfractal(Chrom, 0, 1.4)