File:Logistic iterates, together, r=3.56994567.svg
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[edit]DescriptionLogistic iterates, together, r=3.56994567.svg |
English: Logistic map iterates plotted together, when r=3.56994567.
```python import numpy as np import matplotlib.pyplot as plt def logistic_map(x, r): return r * x * (1 - x) def function_iter(f, n, x, **kwargs): for _ in range(n): x = f(x, **kwargs) return x r_min, r_max = 3.56994567, 4 delta = 4.6692 frames_per_delta = 1 total_deltas = 1 frames = frames_per_delta * total_deltas scaling_factor = delta**(1/frames_per_delta) rs = r_max + (r_min - r_max) / (scaling_factor ** np.array(range(frames)))
for r in rs: highest_exponent = 8 fig, ax = plt.subplots(figsize=(30, 6)) x_values = np.linspace(0, 1, 100000) y_values = x_values last_n_iter = 0 for n in range(highest_exponent): n_iter = 2**n y_values = function_iter(logistic_map, n_iter - last_n_iter, y_values, r=r) last_n_iter = n_iter ax.plot(x_values, y_values, label=f'iteration = {2**n}', alpha=0.2, color='blue') ax.hlines(0.5, 0, 1, linewidth=0.3, alpha=0.8, linestyle='--', color='black') fig.suptitle(f'Up to {2**(highest_exponent-1)} iterates of the Logistic map with r = {r}',y=1.0) plt.tight_layout() plt.savefig(f'logistic_iterates_together_{r}.svg') plt.show()``` |
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Source | Own work |
Author | Cosmia Nebula |
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current | 23:55, 6 April 2024 | 2,700 × 540 (1.3 MB) | Cosmia Nebula (talk | contribs) | Uploaded while editing "Feigenbaum function" on en.wikipedia.org |
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