I generated the function with the Python script:

#!/usr/bin/python
from random import *

k = 0
for i in xrange(1000000):
    k += gauss(0, 1)
    print i, k

I redirected the output to a file, then I plotted it with gnuplot with:

set term png size 6000,4500
set out 'out.png'
pl [][-600:700] 'randfunc.txt' w p ps 3 pt 7

ps 3 pt 7 gives circular dots of 17 pixels in diameter. The high number of samples caused them to overlap, forming a continuous line. (Actually, in the places where the function happened to change very quickly, there were gaps between them, but in the downscaled version they are not evident.)