from pylab import *
from IPython.core.display import Image 
def fig(x): return Image(filename="Figures/"+x+".png") 
from pylab import *
def figs(*args):
    for i,f in enumerate(args):
        subplot(1,len(args),i+1)
        axis("off")
        fig = imshow(imread("Figures/"+f+".png"))
        
from scipy import linalg

# McCulloch-Pitts Neuron
figs("mp-concrete","mp-neuron-abstract")

def H(x): return 1.0*(x>=0.0)

fig("gates-1")

fig("gates-2")

# example output from Rule 110
fig("r110-example")

# interacting "particles" in Rule 110
fig("r110-interactions")

fig("rule110-construction")

# Rule 110 Zoom
# http://uncomp.uwe.ac.uk/genaro/rule110/ctsRule110.html
figs("rule110-zoom")

N = 100
niter = 100
vstart = 1.0 * (rand(N)>0.5)

# counting the number of bits
Mall = linalg.circulant(1*(roll(arange(N)<3,-1)))
imshow(Mall,interpolation='none',cmap=cm.gray)
print 1*(dot(Mall,vstart)>=3)

Mlo = linalg.circulant(-1*(arange(N)<2))

# Rule 110, two steps
v = vstart.copy()
result = []
for i in range(niter):
    result.append(v)
    v111 = (dot(Mall,v)>=3)
    vx00 = (dot(Mlo,v)>=0)
    on = (-1*v111-1*vx00>=0)
    v = 1*on

imshow(array(result),interpolation='nearest',cmap=cm.gray)

Z = zeros((N,N))
v = concatenate([vstart,zeros(2*N)])
M = array(bmat([[Z,-1*eye(N),-1*eye(N)],[Mall,Z,Z],[Mlo,Z,Z]]))
b = concatenate([zeros(N),3*ones(N),zeros(N)])


imshow(M)

result = []
for i in range(2*niter):
    result.append(v)
    v = H(dot(M,v)-b)

result = array(result)
imshow(result,interpolation='nearest',cmap=cm.gray)

imshow(result[::2,:N],interpolation='nearest',cmap=cm.gray)