How to move the mouse in a realistic way using Python?

How to make the mouse move automatically, realistically, using Python?

I was able to find and change a code that produces a "V" -shaped movement on the screen. However, I would like to move the mouse using non-linear movements.

I found some interesting ideas:

I'm having a hard time incorporating the mathematical part of the nonlinearity of the movement into my code.

Code:

import sys
import time
import win32api

if (len(sys.argv) < 4):
    print "Como utilizar: python mousemove.py dx dy speed"
    sys.exit()

current = win32api.GetCursorPos()
cx = sx = current[0]
cy = sy = current[1]

mx = int(sys.argv[1])
my = int(sys.argv[2])
vx = vy = int(sys.argv[3])

print "Movendo", mx, my, "com", vx, "pixels por segundo"
print "Pressione 'q' para sair"

last = time.time()

while(True):
    if win32api.GetAsyncKeyState(ord('Q')):
        sys.exit()

    current = time.time()
    tick = current - last
    last = current

    if mx > 0:
        cx += vx * tick;
        if cx > mx + sx or cx < sx:
            vx = -vx;
            cx = max( sx, min( mx + sx, cx ) )
    if( my > 0 ):
        cy += vy * tick;
        if cy > my + sy or cy < sy:
            vy = -vy;
            cy = max( sy, min( my + sy, cy ) )

    win32api.SetCursorPos((int(cx),int(cy)))
    time.sleep(0.001)

Mathematical excerpt that draws a V:

if mx > 0:
    cx += vx * tick;
    if cx > mx + sx or cx < sx:
        vx = -vx;
        cx = max( sx, min( mx + sx, cx ) )
if( my > 0 ):
    cy += vy * tick;
    if cy > my + sy or cy < sy:
        vy = -vy;
        cy = max( sy, min( my + sy, cy ) )

Question:

How do I set the conditions to incorporate a certain randomness (non-linearity) in the movement of the mouse cursor?