(a) Random Walker

run.py

# Random Walker ThP4 14.Mai 2020
# Quentin Wach
import matplotlib.pyplot as plt
import matplotlib
import matplotlib.ticker as ticker
from matplotlib import rc
rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
rc('text', usetex=True)
import numpy as np
import math
np.random.seed(14520)

# Figure Setup
matplotlib.style.use('ggplot')
fig, ax = plt.subplots(1, figsize=(6,2.7), dpi=300)

# Parameter
P = 0.3               # Schritt nach Links
Q = 1 - P             # Schritt nach Rechts
T = (10,100,1000)     # Schritte
V = 10000              # Versuche pro Experiment

# Experimente
for t in T:

    # Endpunkte [Schritte]
    X = []
    for v in range(V):
        x = 0       # Startpunkt
        for i in range(t):
            if np.random.random_sample() <= P:
                x -= 1
            else:
                x += 1
        X.append(x)
    X = sorted(X)
    
    # Wahrscheinlichkeiten
    Y = []
    for x in X:
        Y.append(X.count(x)/len(X))

    # Historgramm
    ax.fill_between(X, Y, facecolor='black', step="mid", zorder=30)

    # entferne Überflüssige Daten (besser wäre, sie zu mitteln)
    new_X = []; new_Y = []
    for x in X:
        if x not in new_X:
            new_X.append(x)
            new_Y.append(Y[X.index(x)])

    # Shannon-Information
    I = 0
    for y in new_Y:
        I += y * math.log(y, np.e)
    print(I)


# Axes & Grid
ax.set_ylim(0,0.28)
ax.xaxis.set_major_locator(ticker.MultipleLocator(50))
ax.xaxis.set_minor_locator(ticker.MultipleLocator(10))
ax.grid(b=True, color='white', linestyle="--", linewidth=0.5, zorder=0)

# Label & Text
plt.ylabel("Wahrscheinlichkeit", size=9)
plt.xlabel(r"Schritte $x$", size=9)
plt.text(15, 0.25, r"$P_1[x(t=10)]$")
plt.text(35, 0.10, r"$P_2[x(t=100)]$")
plt.text(395, 0.045, r"$P_3[x(t=1000)]$")

# Render
plt.tight_layout()
plt.savefig("Abb_1.png", bbox_inches="tight")