#! /bin/sh

# plot y**a mod N, should be periodic

export GDFONTPATH="/usr/share/fonts/open-sans"
export GNUPLOT_DEFAULT_GDFONT="OpenSans-Semibold"

N=33
y=5

title="z = $y**a mod $N"
xlabel="a"
ylabel="z"

labels="set title \"$title\"\nset xlabel \"$xlabel\"\nset ylabel \"$ylabel\""

export GDFONTPATH="/usr/share/fonts/liberation"
export GNUPLOT_DEFAULT_GDFONT="LiberationSans-Regular"

awk 'BEGIN {
 N = '$N'; y = '$y'; z = 1; for( a = 0; a < N; ++a) { print a, z; z = y*z % N; }
}' |
 (printf "set term gif\nset output\n $labels\n plot '-' notitle with linespoints\n"; cat) |
 gnuplot > period.gif