s_l2.py

import numpy as np
from numpy.linalg import matrix_power
from matplotlib import pyplot as plt
import seaborn as sns

SIZE = 100
M = np.zeros((SIZE, SIZE))

# encoding rolls of die
for y in xrange(SIZE):
    if y <= (SIZE - 6 - 1):
        M[y, np.arange(y+1, y+7)] = 1
    elif y == SIZE - 1:  # end, absorbing state
        pass
    else:
        # this should be checked more carefully. This is the "bounce-off" behaviour.
        M[y, (y+1):] = 1
        M[y, (SIZE-(6 - (SIZE-y-2))):SIZE-1] += 1


def slip_effect(M, start_node, end_node):
    """
    Ex: if am in position 1, and then roll a 2, I should temporarily be on position 3 before slipping to position 13. Thus everywhere that _should_ have landed me on position 3 should instead be moved to position 13, and all position 3s should be erased. 
    """
    ix, = np.where(M[:, start_node])
    M[ix, end_node] += 1
    M[:, start_node] = 0
    return M


# encoding of snakes

M = slip_effect(M, 16, 6)
M = slip_effect(M, 86, 23)
M = slip_effect(M, 98, 77)
M = slip_effect(M, 63, 59)
M = slip_effect(M, 61, 18)
M = slip_effect(M, 94, 74)
M = slip_effect(M, 92, 72)
M = slip_effect(M, 53, 33)

# encoding of ladders

M = slip_effect(M, 3, 13)
M = slip_effect(M, 8, 30)
M = slip_effect(M, 19, 37)
M = slip_effect(M, 27, 83)
M = slip_effect(M, 39, 59)
M = slip_effect(M, 50, 66)
M = slip_effect(M, 62, 80)
M = slip_effect(M, 70, 90)

M = M/6.0



def reshape_vector(v):
    M10 = v.reshape(10, 10)
    M10[1::2, :] = M10[1::2, ::-1]
    return np.flip(M10, 0)

def plot(M, label):
    plt.figure()
    labels = reshape_vector(np.arange(1, 101))
    ax = sns.heatmap(M, linewidths=.5,  vmin=0, square=True, annot=labels, fmt='d', cbar=False)
    ax.set_xticklabels("")
    ax.set_yticklabels("")
    ax.set_title("Move %s" % label)
    plt.savefig("/Users/camerondavidson-pilon/code/s_l/images/%s.png" % label, dpi=)


for i in xrange(1, 100):
    m = reshape_vector(matrix_power(M, i)[0,:])
    plot(m, i)
    print i