2024-heraklion-testing-debugging/material/logistic_map_plots.ipynb

In [13]:

%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

def plot_style(figsize=(12, 6), labelsize=20, titlesize=24, ticklabelsize=14, **kwargs):
    basic_style = {
       'figure.figsize': figsize,
       'axes.labelsize': labelsize,
       'axes.titlesize': titlesize,
       'xtick.labelsize': ticklabelsize,
       'ytick.labelsize': ticklabelsize,
    }
    basic_style.update(kwargs)
    return plt.rc_context(rc=basic_style)

In [20]:

def logistic_map(x, r):
    return r * x * (1 - x)

def iterate_map(x0, r, n):
    xs = [x0]
    for _ in range(n):
        x_np1 = logistic_map(xs[-1], r)
        xs.append(x_np1)
    return xs

In [43]:

x = np.linspace(0, 1, 100)
r = 1.5
f_x = logistic_map(x, r)

In [44]:

with plot_style(figsize=(5, 5), titlesize=20):
    plt.plot(x, f_x)
    plt.plot([0, 1], [0, 1], 'r--', lw=1)
    plt.xlim(0, 1)
    plt.ylim(0, 1)
    plt.xlabel('x')
    plt.ylabel('f(x)')
    plt.title(f'r = {r}')

In [84]:

r = 1.5
xs_01 = iterate_map(x0=0.1, r=r, n=20)
xs_03 = iterate_map(x0=0.3, r=r, n=20)
xs_05 = iterate_map(x0=0.4, r=r, n=20)
with plot_style(figsize=(5, 5), titlesize=20):
    plt.plot(xs_01, lw=3, label=0.1)
    plt.plot(xs_03, lw=3, label=0.3)
    plt.plot(xs_05, lw=3, label=0.5)
    plt.ylim(0, 1)
    plt.xticks([0, 5, 10, 15, 20])
    plt.xlabel('iteration')
    plt.ylabel('x')
    plt.title(f'r = {r}')
    plt.legend(title='$x_0$ value', fontsize=14, title_fontsize=16, frameon=False)

In [85]:

r = 3.2
xs_01 = iterate_map(x0=0.1, r=r, n=20)
xs_03 = iterate_map(x0=0.3, r=r, n=20)
xs_05 = iterate_map(x0=0.4, r=r, n=20)
with plot_style(figsize=(5, 5), titlesize=20):
    plt.plot(xs_01, lw=3, label=0.1)
    plt.plot(xs_03, lw=3, label=0.3)
    plt.plot(xs_05, lw=3, label=0.5)
    plt.ylim(0, 1)
    plt.xticks([0, 5, 10, 15, 20])
    plt.xlabel('iteration')
    plt.ylabel('x')
    plt.title(f'r = {r}')
    plt.legend(title='$x_0$ value', fontsize=14, title_fontsize=16, frameon=False)

In [86]:

r = 3.9
xs_01 = iterate_map(x0=0.1, r=r, n=20)
xs_03 = iterate_map(x0=0.3, r=r, n=20)
xs_05 = iterate_map(x0=0.4, r=r, n=20)
with plot_style(figsize=(5, 5), titlesize=20):
    plt.plot(xs_01, lw=3, label=0.1)
    plt.plot(xs_03, lw=3, label=0.3)
    plt.plot(xs_05, lw=3, label=0.5)
    plt.ylim(0, 1)
    plt.xticks([0, 5, 10, 15, 20])
    plt.xlabel('iteration')
    plt.ylabel('x')
    plt.title(f'r = {r}')
    plt.legend(title='$x_0$ value', fontsize=14, title_fontsize=16, frameon=False)

In [ ]: