Numpy

#
# Good god my code is shite
# Kind Regards

import numpy as np
import math
import Image

def dofilter(array1):
    xsize, ysize = array1.shape
    a0 = np.zeros(size)
    diffx = np.diff(array1)
    diffy = np.diff(array1,axis=0)
    a0[:,:xsize-1] += diffx
    a0[:,1:] -= diffx
    a0[:ysize-1] += diffy
    a0[1:] -= diffy
    return a0*0.5

def step_forward(a1,a1v,n=1,action=None):
    for bx in xrange(n):
        if action:
            a1 = action(a1)
        a1v += dofilter(a1)*k_const
        a1 += a1v
    return a1, a1v

def action_1(x):
    x[ox-1:ox+1,oy-1:oy+1] = 0.9
    return x


size = (200,200)
k_const = 0.25
speed = 3
a1 = np.zeros(size)
a1v = np.zeros(size)


for imnum in xrange(400):
    ox = int(100 + (math.sin(imnum*0.2)*20))
    oy = int(100 - (math.cos(imnum*0.2)*20))

    if imnum < 75:
        a1, a1v = step_forward(a1,a1v,n=speed,action=action_1)
    else:
        a1, a1v = step_forward(a1,a1v,n=speed)

    im = Image.fromarray(np.uint8((a1+1)*128))
    im.save("output_k_" + format(imnum,"03d") + ".png")