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August 17, 2022 17:39
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| # by Matias I. Bofarull Oddo - 2022.08.16 | |
| # Pisano Cycle: https://oeis.org/A161553 | |
| # Pisano Period: https://oeis.org/A001175 | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| def pisano_cycle_and_period(modulus): | |
| cycle = [0, 1, 1] | |
| if modulus <= 1: | |
| return [0], 0 | |
| else: | |
| previous = cycle[1] | |
| current = cycle[2] % modulus | |
| while previous != 0 or current != 1: | |
| previous, current = current, (previous + current) % modulus | |
| cycle.append(current) | |
| return cycle[:-2], len(cycle[:-2]) | |
| def circle_XY(num_points): | |
| X = [] | |
| Y = [] | |
| for theta in np.linspace(0, np.pi * 2, num_points, endpoint=False): | |
| X.append(np.cos(theta - (np.pi / 2))) | |
| Y.append(np.sin(theta - (np.pi / 2))) | |
| return [X, Y] | |
| def ouroboros(circle_points): | |
| circle_points[0].append(circle_points[0][0]) | |
| circle_points[1].append(circle_points[1][0]) | |
| return circle_points | |
| for i in range(100): | |
| MODULO = i + 1 | |
| pisano_cycle, pisano_period = pisano_cycle_and_period(MODULO) | |
| print( | |
| "\nMod:", MODULO, "\n\nCycle:", pisano_cycle, "\n\nPeriod:", pisano_period, "\n" | |
| ) | |
| fig = plt.figure(figsize=(8, 8)) | |
| ax = fig.add_subplot(111) | |
| points = circle_XY(MODULO) | |
| ax.scatter(points[0], points[1], c="k") | |
| pisano_X = [] | |
| pisano_Y = [] | |
| for i in pisano_cycle: | |
| pisano_X.append(points[0][i]) | |
| pisano_Y.append(points[1][i]) | |
| ax.plot(pisano_X, pisano_Y, c="k") | |
| circle_frame = ouroboros(circle_XY(999)) | |
| ax.plot(circle_frame[0], circle_frame[1], c="gray", zorder=-1) | |
| ax.text(-0.88, +0.88, MODULO, weight="bold") | |
| plt.gca().set_position([0, 0, 1, 1]) | |
| plt.show() |
Author
dirediredock
commented
Aug 17, 2022
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