/ 
math-image-72
River stage zero No dependents
/ Math::PlanePath::MathImageQuintetReplicate

NAME

Math::PlanePath::MathImageQuintetReplicate -- self-similar "+" tiling

SYNOPSIS

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

DESCRIPTION

In progress.

This is a self-similar tiling of the plane with "+" shapes. It's the same kind of tiling as the QuintetCurve (and QuintetCentres), but with the middle square of the "+" centred on the origin.

        12                         3

    13  10  11       7             2

        14   2   8   5   6         1

    17   3   0   1   9         <- Y=0

18  15  16   4  22                -1

    19      23  20  21            -2

                24                -3

             ^
-4 -3 -2 -1 X=0  1  2  3  4

Complex Base

This tiling corresponds to expressing a complex integer X+i*Y in base b=i+2

X+Yi = a[n]*b^n + ... + a[2]*b^2 + a[1]*b + a[0]

with each digit a[i] = 0, 1, i, -1, or -i. Those digits are then represented in integer N by 0,1,2,3,4.

The base b=i+2 is at an angle atan(1/2) = 26.56 degrees and successive powers b^2, b^3, b^4 etc rotate around by that much each time.

FUNCTIONS

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

$path = Math::PlanePath::MathImageQuintetReplicate->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::KochCurve, Math::PlanePath::HilbertCurve, Math::PlanePath::PeanoCurve, Math::PlanePath::ZOrderCurve

HOME PAGE

http://user42.tuxfamily.org/math-image/index.html

LICENSE

Copyright 2011 Kevin Ryde

Math-Image is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-Image is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-Image. If not, see <http://www.gnu.org/licenses/>.