Generating graphs that look like stock charts

"It turns out it's pretty easy to generate graphs that look like stock prices graphs. Just generate a bunch of random values from 0-1, then take the integral of that (each integrated value is the sum of all the previous original value)".

Functions to generate normally distributed variates exist in many languages. Why not use them instead of using uniform variates? For even greater realism, generate Student-t variates with say 5 degrees of freedom to account for fat tails in the return distribution.