initial commit with 2024 materials

testing_project/plot_logistic.py

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+"""Usage:
+```
+plot_trajectory(100, 3.6, 0.1)
+plot_bifurcation(2.5, 4.2, 0.001)
+```
+"""
+import numpy as np
+from matplotlib import pyplot as plt
+
+from logistic import iterate_f
+
+
+def plot_trajectory(n, r, x0, fname="single_trajectory.png"):
+    """
+    Saves a plot of a single trajectory of the logistic function
+
+    inputs
+        n: int (number of iterations)
+        r: float (r value for the logistic function)
+        x0: float (between 0 and 1, starting point for the iteration)
+        fname: str (filename to which to save the image)
+
+    returns
+        fig, ax (matplotlib objects)
+    """
+    xs = iterate_f(n, x0, r)
+    fig, ax = plt.subplots(figsize=(10, 5))
+    ax.plot(list(range(n)), xs)
+    fig.suptitle('Logistic Function')
+
+    fig.savefig(fname)
+    return fig, ax
+
+
+def plot_bifurcation(start, end, step, fname="bifurcation.png", it=100000,
+                     last=300):
+    """
+    Saves a plot of the bifurcation diagram of the logistic function. The
+    `start`, `end`, and `step` parameters define for which r values to
+    calculate the logistic function. If you space them too closely, it might
+    take a very long time, if you dont plot enough, your bifurcation diagram
+    won't be informative. Choose wisely!
+
+    inputs
+        start, end, step:  float (which r values to calculate the logistic
+                                  function for)
+        fname: str (filename to which to save the image)
+        it: int (how many iterations to run for each r value)
+        last: int (how many of the last iterates to plot)
+
+
+    returns
+        fig, ax (matplotlib objects)
+    """
+    r_range = np.arange(start, end, step)
+    x = []
+    y = []
+
+    for r in r_range:
+        xs = iterate_f(it, 0.1, r)
+        all_xs = xs[len(xs) - last::].copy()
+        unique_xs = np.unique(all_xs)
+        y.extend(unique_xs)
+        x.extend(np.ones(len(unique_xs)) * r)
+
+    fig, ax = plt.subplots(figsize=(20, 10))
+    ax.scatter(x, y, s=0.1, color='k')
+    ax.set_xlabel("r")
+    fig.savefig(fname)
+    return fig, ax