Gnuplot example: Math Invaders - Remember Space Invaders and Galaxian?

This is a parameter animation (plotted upside down) for the modified Thomae function:

gnuplot script:

d = 0.001
m = 250
f(n,k,x) = k > m ? 3.2 : ( abs(k*x - int(k*x)) < d ? \
3.2-(1+0.1*n*n)/(k*k-abs(k*x)) : f(n,k+1,x) )
set xrange [-1.6:1.6]
set yrange [0:3.2]
set size ratio -1
set samples 10000
unset key
unset xtics
unset ytics
unset border
set bmargin 0
set lmargin 0
set rmargin 0
set tmargin 0
set term gif size 400, 400 animate background rgb "black"
set output "C:\math_invaders.gif"
set pointsize 0.5
do for [i=0:150]{
  plot f(i,1,sin(x)) with points pt 11 lc rgb "white"
}
set output


Note that we set less samples(10000). By incresing samples to 200000,
we can obtain a more accurate (but less fun) picture.

( Mathematical software used: gnuplot )


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• Gnuplot example: plotting functions defined on rational numbers