Trace text with Langton ant

langton_text.py

execfile('viridis.py')

from matplotlib.colors import ListedColormap
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline
from PIL import Image

def image2array(filename):
    im = Image.open('logo.jpg')
    return np.array(im.convert('L')) > 100

def getEdgePoints(array):
    n = array.shape[0]
    rows = np.array(np.repeat(np.matrix(np.arange(1, n + 1)).T, n, axis = 1))
    cols = np.array(np.repeat(np.matrix(np.arange(1, n + 1)), n, axis = 0))
    horizontaledges = np.hstack([array[:,:-1] - array[:,1:], np.zeros((n,1))]) != 0
    verticaledges = np.hstack([(array.T[:,:-1] - array.T[:,1:]), np.zeros((n,1))]).T != 0
    edges = horizontaledges | verticaledges
    rowi = rows[edges].flatten().tolist()
    coli = cols[edges].flatten().tolist()
    return zip(rowi, coli)

def updatePosition(position, direction):
    movement = [(1,0), (0,1), (-1, 0), (0, -1)] # up, down, right, left, like a clock
    return tuple(np.array(position) + np.array(movement[direction]))
    
# Model -> Model
def update(model): 
    newPosition = updatePosition(model['position'], model['direction'])
    model['path'][newPosition] += 1
    x,y = newPosition
    n = model['grid'].shape[0]
    model['position'] = (x % (n - 1), y % (n - 1))
    currentValue = model['grid'][newPosition]
    if currentValue == 0:
        model['direction'] = (model['direction'] + 1) % 4
        model['grid'][newPosition] = 1
    else:
        model['direction'] = (model['direction'] - 1) % 4
        model['grid'][newPosition] = 0
    return model  
    
def sample(x, nSamples):
    n = len(x)
    return map(lambda x: x[1], sorted(zip(np.random.random(n), x), key = lambda x: x[0]))[:nSamples]    
    
n = 1000
offset = int(n / 2.0)
iters = int(3e4) #int(3e7) # Took 8 min. to compute
im = image2array('logo.jpg')
rand = np.random.random((n, n)) > 0.1
mat = im & rand
nPoints = 1000
startingPoints = sample(getEdgePoints(im), nPoints) #(np.random.random((nPoints, 2)) * 1000).astype(int).tolist()

paths = []

for point in startingPoints:
    initialModel = {
        "grid": mat.copy(),
        "position": point,
        "direction": 0,
        "path": np.zeros((n, n))
    } 
    for i in xrange(iters): 
        initialModel = update(initialModel)
    
    paths.append(initialModel['path'])
    
plt.figure(figsize = (50,50)) # High resolution (takes a while)
plt.imshow(
  sum(paths) - im * 10,
  cmap = 'Greys_r',
  interpolation = 'nearest',
  vmax = 500)
plt.axis("off")