상미분 방정식: 로렌츠 방정식(Lorenz Equations)

import numpy as np

from scipy.integrate import odeint

import matplotlib.pyplot as plt

from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg

import tkinter as tk

# 로렌츠 방정식 정의

def lorenz(X, t, sigma, beta, rho):

    x, y, z = X

    dx_dt = sigma * (y - x)

    dy_dt = x * (rho - z) - y

    dz_dt = x * y - beta * z

    return [dx_dt, dy_dt, dz_dt]

# 그래프 그리기 함수

def plot_lorenz(sigma, beta, rho, x0, y0, z0):

    t = np.linspace(0, 50, 10000)

    initial_state = [x0, y0, z0]

    solution = odeint(lorenz, initial_state, t, args=(sigma, beta, rho))

    fig, ax = plt.subplots(subplot_kw={"projection": "3d"})

    ax.plot(solution[:, 0], solution[:, 1], solution[:, 2], lw=0.5)

    ax.set_title("Lorenz Attractor")

    ax.set_xlabel("X Axis")

    ax.set_ylabel("Y Axis")

    ax.set_zlabel("Z Axis")

    canvas = FigureCanvasTkAgg(fig, master=window)

    canvas.draw()

    canvas.get_tk_widget().pack()

# 버튼 클릭 이벤트

def on_submit():

    try:

        sigma = float(entry_sigma.get())

        beta = float(entry_beta.get())

        rho = float(entry_rho.get())

        x0 = float(entry_x0.get())

        y0 = float(entry_y0.get())

        z0 = float(entry_z0.get())

        plot_lorenz(sigma, beta, rho, x0, y0, z0)

    except ValueError:

        tk.messagebox.showerror("입력 오류", "올바른 숫자를 입력해주세요.")

# GUI 설정

window = tk.Tk()

window.title("Lorenz Equations Solver")

tk.Label(window, text="Sigma (σ):").pack()

entry_sigma = tk.Entry(window)

entry_sigma.pack()

tk.Label(window, text="Beta (β):").pack()

entry_beta = tk.Entry(window)

entry_beta.pack()

tk.Label(window, text="Rho (ρ):").pack()

entry_rho = tk.Entry(window)

entry_rho.pack()

tk.Label(window, text="Initial x:").pack()

entry_x0 = tk.Entry(window)

entry_x0.pack()

tk.Label(window, text="Initial y:").pack()

entry_y0 = tk.Entry(window)

entry_y0.pack()

tk.Label(window, text="Initial z:").pack()

entry_z0 = tk.Entry(window)

entry_z0.pack()

submit_button = tk.Button(window, text="Plot Lorenz Attractor", command=on_submit)

submit_button.pack()

window.mainloop()

 

 

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