NAME
Math::NumSeq::GolayRudinShapiro  parity of adjacent 11 bit pairs
SYNOPSIS
use Math::NumSeq::GolayRudinShapiro;
my $seq = Math::NumSeq::GolayRudinShapiro>new;
my ($i, $value) = $seq>next;
DESCRIPTION
This is the Golay/Rudin/Shapiro sequence of +1 or 1 according to there being an even or odd number of adjacent 11 bit pairs in i.
GRS(i) = (1) ^ (count 11 bit pairs)
starting from i=0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
The first 1 is at i=3 which is binary 11 with a single 11 bit pair, then i=6 binary 110 likewise 1. Or later for example i=14 is binary 1110 which has two adjacent 11 pairs (overlaps count), so value=1.
The value is also the parity of the number of evenlength runs of 1 bits in i. An even length run has an odd number of 11 pairs, so each of them is a 1 in the product. An oddlength run of 1 bits is an even number of 11 pairs and so is +1 and has no effect on the result.
Such a parity of evenlength 1bit runs and hence the GRS sequence arises as the "dX,dY" change for each segment of the alternate paper folding curve. See "dX,dY" in Math::PlanePath::AlternatePaper.
Values Type
Parameter values_type => '0,1'
gives values 0 and 1, being the count of adjacent 11s taken modulo 2, ie. 0 if even, 1 if odd.
values_type => '0,1'
0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, ...
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::GolayRudinShapiro>new ()
$seq = Math::NumSeq::GolayRudinShapiro>new (values_type => $str)

Create and return a new sequence object.
Random Access
$value = $seq>ith($i)

Return the
$i
'th value from the sequence, being +1 or 1 according to the number of adjacent 11 bit pairs in$i
. $bool = $seq>pred($value)

Return true if
$value
occurs in the sequence, which simply means$value == 1
or$value == 1
. Or ifvalues_type=>'0,1'
then 0 or 1.
SEE ALSO
Math::NumSeq, Math::NumSeq::GolayRudinShapiroCumulative, Math::NumSeq::BaumSweet, Math::NumSeq::Fibbinary
Math::PlanePath::AlternatePaper
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2010, 2011, 2012 Kevin Ryde
MathNumSeq 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.
MathNumSeq 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 MathNumSeq. If not, see <http://www.gnu.org/licenses/>.