Thanks to comments, it should be a plane but why does it look a bit like a fractal? Does my code overlook something or some err in plotting tool? I used Python and GNUplot.
Apparently an animated illusion.
And generated the points with Python and generated graph with GnuPlot like:
$ python copyPasteTheCodeToFile.py > .data $ gnuplot -e "set terminal png; set grid; splot '.data'"
import itertools def main(): density = 100.0 mySet= [x/density for x in range(int(density))] points="" for (x,y,z) in [(x,y,z) for x,y,z in itertools.product(mySet, repeat=3) if x+y+z==1]: points = points + "%s\t%s\t%s\n"%(str(x),str(y),str(z)) print points main()
can you spot an err? I cannot hence I thought A) mathematical err, B) algoritmic err or C) outside-party/program-err, cannot really say which one.
It is a floating point error! The error is the conditional
x+y+z==1. Since computers don't evaluate floats like 1.0 + 1.0 to 2.0 but something slightly different, the conditional fails with some right points. The fix is:
$abs(x+y+z-1) < \epsilon$
where the epsilon $\epsilon$ is some very small number like
1e-10. It is still open why there are just the holes in the grid. Why not other points? And why is it vertically symmetric? Is it so with every computer? Does the pattern vary between computers? Anyway I am still investigating why there this specific pattern with this conditional. We know now why there are the patters but we don't know why these patterns. I am running the commands with bulk i86 comp.