#!/usr/bin/env python

# -*- coding: utf-8 -*-

'''

Reaction Diffusion : Gray-Scott model

References:

----------

Complex Patterns in a Simple System

John E. Pearson, Science 261, 5118, 189-192, 1993.

Encode movie

------------

ffmpeg -r 30 -i "tmp-%03d.png" -c:v libx264 -crf 23 -pix_fmt yuv420p bacteria.mp4

'''

import numpy as np

import matplotlib.pyplot as plt

n,k = 100, 4

Z = np.zeros((n+2,2*n+2))

dt = 0.05

plt.ion()

size = 3*np.array(Z.shape)

dpi = 72.0

figsize= size[1]/float(dpi),size[0]/float(dpi)

fig = plt.figure(figsize=figsize, dpi=dpi, facecolor="white")

fig.add_axes([0.0, 0.0, 1.0, 1.0], frameon=False)

im = plt.imshow(Z, interpolation='bicubic', cmap=plt.cm.hot)

plt.xticks([]), plt.yticks([])

for i in xrange(50000):

L = ( Z[0:-2,1:-1] +

Z[1:-1,0:-2] - 4*Z[1:-1,1:-1] + Z[1:-1,2:] +

Z[2: ,1:-1] )

Z[1:-1,1:-1] += k*L*dt

Z[ n/2-20:n/2+20, n-5:n-1] = 1

Z[ n/2-20:n/2+20, n+1:n+5] = -1

if i % 30 == 0:

im.set_data(Z)

im.set_clim(vmin=Z.min(), vmax=Z.max())

plt.draw()

# To make movie

# plt.savefig("./tmp/tmp-%03d.png" % (i/10) ,dpi=dpi)

plt.ioff()

# plt.savefig("../figures/zebra.png",dpi=dpi)

# plt.savefig("../figures/bacteria.png",dpi=dpi)

plt.savefig("../figures/diffusion.png",dpi=dpi)

plt.show()