def setup():
    size(1000, 500)

def draw():
    # clear canvas to white background color
    background(255)
    # transform to scene coordinates, as pixel coordinates are annoying
    translate(0, 0.5+height/2.0)
    scale(width/10.0, -height/5.0)
    strokeWeight(0.02)
    # the number of frames per "scene"
    sceneframes = 500
    # the animation will cycle through 4 different "scenes"
    iscene = (frameCount/sceneframes)%4
    # frame number within this scene
    isceneframe = frameCount%sceneframes
    # amplitude of first wave is always +1.0
    A1 = 1.0
    # amplitude of second wave varies scene by scene
    A2 = [1.0, -1.0, 0.5, -0.5][iscene]
    # cook up a "time" that loops from tmin to tmax within each scene
    tmin = -1.0; tmax = +11.0; dt = (tmax-tmin)/sceneframes
    t = tmin + isceneframe*dt
    # speed of wave propagation
    vwave = 1.0
    # width of gaussian wave packet
    sigma = 0.2
    # positions of the two wave packets' centers
    x1 = vwave*t
    x2 = vwave*(10-t)
    # loop over x axis positions to draw the wave function psi(x)
    xmin = 0.0; xmax = 10.0; dx = (xmax-xmin)/width
    xlast = 0.0; psilast = 0.0
    for ix in range(width):
        x = xmin + ix*dx
        # calculate the two wave functions psi1(x) and psi2(x)
        psi1 = A1 * exp(-0.5*((x-x1)/sigma)**2)
        psi2 = A2 * exp(-0.5*((x-x2)/sigma)**2)
        psi = psi1 + psi2
        # draw line segment from previous point to this point
        line(xlast, psilast, x, psi)
        # this point becomes "previous" point for next iteration
        xlast, psilast = x, psi