NAME
Math::PlanePath::MathImagePyramidReplicate -- replicating squares
SYNOPSIS
use Math::PlanePath::MathImagePyramidReplicate;
my $path = Math::PlanePath::MathImagePyramidReplicate->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION
This is a self-similar replicating pyramid shape made from 4 points each,
4
3
2
1
<- Y=0
-1
-2
-3
-4
^
-4 -3 -2 -1 X=0 1 2 3 4
The base shape is the initial N=0 to N=8 section,
+---+
| 2 |
+---+---+---+
| 3 | 0 | 1 |
+---+---+---+
It then repeats inverted to make a similar shape but upside-down,
+---+---+---+---+---+---+---+
| 5 4 7 | 2 |13 12 15 |
+---+ +---+ +---+ +---+
| 6 | 3 0 1 |14 |
+---+---+---+---+---+
| 9 8 11 |
+---+ +---+
|10 |
+---+
Level Ranges
A given replication extends to ...
Nlevel = 4^level - 1
- ... <= X <= ...
- ... <= Y <= ...
Complex Base
This pattern corresponds to expressing a complex integer X+i*Y in base b=...
X+Yi = a[n]*b^n + ... + a[2]*b^2 + a[1]*b + a[0]
using complex digits a[i] encoded in N in integer base 4 ...
a[i] digit N digit
---------- -------
0 0
1 1
i 2
-1 3
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::MathImagePyramidReplicate->new ()
-
Create and return a new path object.
($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.
SEE ALSO
Math::PlanePath, Math::PlanePath::CornerReplicate, Math::PlanePath::SquareReplicate, Math::PlanePath::LTiling, Math::PlanePath::GosperReplicate, Math::PlanePath::QuintetReplicate