AIPS NRAO AIPS HELP file for MANDL in 31DEC21



As of Fri Dec 3 2:35:44 2021


MANDL: Create a sub-section of the MANDLEBROT Set

INPUTS

OBJECT                             Source name
IMSIZE                             Output image size (cells)
CELLSIZE                           Cellsize (0=Fill X-Y Range)
OUTNAME                            Output image name (name)
OUTCLASS                           Output image name (class)
OUTSEQ           -1.0     9999.0   Output image name (seq. #)
OUTDISK           0.0        9.0   Output image disk unit #.
CPARM                              Set Region selection,
                                   1:XMin;2:YMin;3:XMax;4:YMax
                                   5:Max Value for Set (0=> 256)

HELP SECTION

MANDL
Task:  Mandelbrot set capability for AIPS.  Can make an image as
       large as is desired, but is limited by the dynamic range
       of floating point numbers.
Note:  Setting all numeric parameters to zero causes the whole
       set to be calculated.
       Glen Langstion, MPIfR and MIT, October 1987
Adverbs:
  OBJECT.....Object name.
  IMSIZE.....Desired image size in cells.
  CELLSIZE...Desired cell spacing, currently assumes sec.
             The mandelbrot set is only interesting in the -2
             to 1 range in x and -1 to 1 in y, so for a 256x256
             image, 0.012 gives the whole region.  For
             CELLSIZE=0, the X and Y min and max are used to
             calculate the CELLSIZE.
  OUTNAME....Output image name (name).     Standard behavior
             with default = 'MANDELBRO'.
  OUTCLASS...Output image name (class).    Standard defaults.
  OUTSEQ.....Output image name (seq. #).   0 => highest unique.
  OUTDISK....Disk drive # of output image. 0 => highest number
             with sufficient space.
  CPARM......1:XMin, 2:YMin, 3:XMax, 4:YMax
             Used in combination with cells to calculate the map
             center and scale

EXPLAIN SECTION

MANDL:  Task which creates and fills an AIPS catalogue image
        file with a section of the Mandelbrot Set.
DOCUMENTOR: Glen Langston, MPIfR and MIT

                          PURPOSE

     MANDL is designed as a thought provoking display of a very
simple mathmatical function.  The algorthym is a very simple
recursive calculation, using the initial coordinate of the
point at each set of the calculation.

     The algorithm is as follows:
       For each point, (x,y), in the desired section of the
       plane, calculate the complex square of this point.
         If the magnitude is greater than 2, stop at this
         iteration.
         If it is not, add the inital x,y coordinate and
         repeat until tired. (Here 256)

      In Coded Form:
         z1 = 0
         z2 = 0
         FOR I = 1 to 256
           z1 = z1 + x
           z2 = z2 + y
           znext1 = z1*z1 - z2*z2
           z2 = 2*z1*z2
           z1 = znext1
           zmag = sqrt(z1*z1+z2*z2)
           if (zmag .gt. 2) return i
         ENDDO
         return i

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