NAME

Math::PlanePath::MathImageQuintetCurve -- "plus" shaped curve

SYNOPSIS

use Math::PlanePath::MathImageQuintetCurve;
my $path = Math::PlanePath::MathImageQuintetCurve->new;
my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

In progress.

This path is a self-similar curve tracing out a "+" shape,

          ...                     93--92 
           |                       |   |             
     123-124                      94  91--90--89--88 
       |                           |               | 
     122-121-120 103-102          95  82--83  86--87 
               |   |   |           |   |   |   |     
     115-116 119 104 101-100--99  96  81  84--85     
       |   |   |   |           |   |   |                        
 113-114 117-118 105  32--33  98--97  80--79--78                
   |               |   |   |                   |                
 112-111-110-109 106  31  34--35--36--37  76--77                
               |   |   |               |   |                    
             108-107  30  43--42  39--38  75                    
                       |   |   |   |       |                    
              25--26  29  44  41--40  73--74                    
               |   |   |   |           |                        
          23--24  27--28  45--46--47  72--71--70--69--68        
           |                       |                   |        
          22--21--20--19--18  49--48  55--56--57  66--67        
                           |   |       |       |   |            
           5---6---7  16--17  50--51  54  59--58  65            
           |       |   |           |   |   |       |            
   0---1   4   9---8  15          52--53  60--61  64            
       |   |   |       |                       |   |            
       2---3  10--11  14                      62--63            
                   |   |                                        
                  12--13                                        
                                                                
                                                                
 ^
X=0 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 ...

The base figure is the initial N=0 to N=4.

        |
        |
0---1   4      base figure
    |   |
    |   |
    2---3

It corresponds to a traversal of a "+" shape,

     .....5
     .    |
     .   <|
     .    |
0----1....4.....
. v  |    |    .
.    |>   |>   .
.    |    |    .
.....2----3.....
     . v  .
     .    .
     .    .
     ......

The "v", ">" etc notches are side the figure is directed at the higher replication levels. The 0, 2 and 3 parts are the right hand side of the line which means a plain repetition of the base figure. The 1 and 4 parts are to the left which means a reversal. The first such reversal is seen above as N=5 to N=10.

5---6---7
        |    
        |       reversed figure
    9---8
    |
    |

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.

$path = Math::PlanePath::MathImageQuintetCurve->new ()

Create and return a new path object.

($x,$y) = $path->n_to_xy ($n)

Return the X,Y coordinates of point number $n on the path. Points begin at 0 and if $n < 0 then the return is an empty list.

Fractional positions give an X,Y position along a straight line between the integer positions.

$n = $path->n_start()

Return 0, the first N in the path.

SEE ALSO

Math::PlanePath, Math::PlanePath::Flowsnake