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lorenz_map.py
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lorenz_map.py
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"""Map of Lorenz attractor."""
# MIT License
#
# Copyright (c) 2024 Pavel Tišnovský
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# coding: utf-8
# # Mapa Lorenzova atraktoru
# import všech potřebných knihoven - Numpy a Matplotlibu
import matplotlib.pyplot as plt
import numpy as np
def lorenz(x, y, z, s=10, r=28, b=2.667):
"""Výpočet dalšího bodu Lorenzova atraktoru."""
x_dot = s * (y - x)
y_dot = r * x - y - x * z
z_dot = x * y - b * z
return x_dot, y_dot, z_dot
# krok (změna času)
dt = 0.005
# celkový počet vypočtených bodů na Lorenzově atraktoru
n = 20000
# prozatím prázdné pole připravené pro výpočet
x = np.zeros((n,))
y = np.zeros((n,))
z = np.zeros((n,))
# počáteční hodnoty
x[0], y[0], z[0] = (0.0, 0.5, 1.05)
# vlastní výpočet atraktoru
for i in range(n - 1):
x_dot, y_dot, z_dot = lorenz(x[i], y[i], z[i])
x[i + 1] = x[i] + x_dot * dt
y[i + 1] = y[i] + y_dot * dt
z[i + 1] = z[i] + z_dot * dt
WIDTH = 256
HEIGHT = 256
raster = np.zeros(shape=(HEIGHT, WIDTH, 3), dtype=np.uint8)
ax = 255.0 / (max(x) - min(x))
ox = min(x)
ay = 255.0 / (max(y) - min(y))
oy = min(y)
az = 255.0 / (max(z) - min(z))
oz = min(z)
# vytvoření mapy
for yi in range(HEIGHT):
# počáteční hodnoty
x[0], y[0], z[0] = (1.0, 0.5, 1.05)
# vlastní výpočet atraktoru
c = 2.0 + yi / 80.0
for i in range(n - 1):
x_dot, y_dot, z_dot = lorenz(x[i], y[i], z[i], 10, 28, c)
x[i + 1] = x[i] + x_dot * dt
y[i + 1] = y[i] + y_dot * dt
z[i + 1] = z[i] + z_dot * dt
for xi in range(WIDTH):
raster[yi][xi][0] = (x[xi * 50] - ox) * ax
raster[yi][xi][1] = (y[xi * 50] - oy) * ay
raster[yi][xi][2] = (z[xi * 50] - oz) * az
plt.figure(1, figsize=(8, 6), dpi=100)
plt.imshow(raster)
# uložení grafu
plt.savefig("lorenz_map.png")
plt.show()