01.3D_Wave_Visualization_and_Interactive_Learning.py

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import plotly.graph_objs as go
from ipywidgets import interactive, FloatSlider, HTML

# Generate pulse data
x = np.linspace(0, 10, 500)
pulse = np.exp(-0.2 * (x - 3) ** 2) * np.sin(4 * np.pi * x)

# Create pulse animation using Matplotlib
fig, ax = plt.subplots()
line, = ax.plot(x, pulse)

def animate(t):
    line.set_ydata(np.roll(pulse, int(t * 20)))
    return line,

ani = animation.FuncAnimation(fig, animate, frames=np.linspace(0, 10, 200), interval=50, blit=True)
plt.close()  # Close the initial figure

def sinusoidal_wave(x, t, A, k, omega, phi):
    return A * np.sin(k * x - omega * t + phi)

x_values = np.linspace(0, 10, 500)
t_values = np.linspace(0, 2, 200)
A = 1.0
k = 2 * np.pi / 5
omega = 2 * np.pi / 2
phi = 0.0

# Calculate wave data
wave_data = np.array([[sinusoidal_wave(x, t, A, k, omega, phi) for x in x_values] for t in t_values])

# Create an interactive HTML element for displaying information
info_text = HTML()
info_text.value = "<b>Select different parameters to visualize the wave behavior.</b>"

def plot_wave(amplitude, wave_number, angular_frequency, initial_phase):
    fig = go.Figure()

    for t in t_values:
        y_values = sinusoidal_wave(x_values, t, amplitude, wave_number, angular_frequency, initial_phase)
        fig.add_trace(go.Scatter(x=x_values, y=y_values, mode='lines', name=f't = {t:.2f}'))

    fig.update_layout(title='Interactive Sinusoidal Wave',
                      xaxis_title='x', yaxis_title='y',
                      xaxis_range=[0, 10], yaxis_range=[-1.5, 1.5],
                      annotations=[dict(text="Wavelength (λ)", x=4.5, y=-1.7, font_size=12, showarrow=False),
                                   dict(text="Amplitude (A)", x=7.5, y=1.2, font_size=12, showarrow=False)])
    fig.update_xaxes(title_text="x (Distance)")
    fig.update_yaxes(title_text="y (Amplitude)")

    info_text.value = (
        f"<b>Wave Characteristics:</b><br>"
        f"Amplitude (A): {amplitude}<br>"
        f"Wave Number (k): {wave_number:.2f}<br>"
        f"Angular Frequency (ω): {angular_frequency:.2f}<br>"
        f"Initial Phase (ϕ): {initial_phase:.2f}"
    )

    fig.show()

# Create interactive sliders for user input
interactive_plot = interactive(plot_wave,
                                amplitude=FloatSlider(min=0.1, max=2, step=0.1, value=A),
                                wave_number=FloatSlider(min=0.5, max=5, step=0.5, value=k),
                                angular_frequency=FloatSlider(min=0.5, max=5, step=0.5, value=omega),
                                initial_phase=FloatSlider(min=0, max=2 * np.pi, step=0.1, value=phi))

# Arrange layout for interactive plot and information
output = interactive_plot.children[-1]
output.layout.height = '350px'
layout = go.Layout(
    title="Wave Visualization and Interactive Learning",
    grid={"rows": 1, "columns": 2},
    annotations=[
        dict(text="Amplitude (A)", x=0.2, y=0.7, font_size=16, showarrow=False),
        dict(text="Wavelength (λ)", x=0.9, y=0.7, font_size=16, showarrow=False)
    ]
)

# Display the complete layout with interactive plot and information
final_layout = go.FigureWidget(layout=layout)
for t in t_values:
    y_values = sinusoidal_wave(x_values, t, A, k, omega, phi)
    trace = go.Scatter(x=x_values, y=y_values, mode='lines', name=f't = {t:.2f}')
    final_layout.add_trace(trace)

final_layout.update_layout({'updatemenus': None})
final_layout.layout.update(updatemenus=[
    {
        'type': 'buttons',
        'showactive': False,
        'buttons': [
            {
                'label': 'Wave Visualization',
                'method': 'animate',
                'args': [None, {'frame': {'duration': 50, 'redraw': True}, 'fromcurrent': True}],
            }
        ]
    },
    {
        'type': 'buttons',
        'showactive': False,
        'buttons': [
            {
                'label': 'Pause',
                'method': 'animate',
                'args': [[None], {'frame': {'duration': 0, 'redraw': False}, 'mode': 'immediate',
                                 'transition': {'duration': 0}}],
            }
        ]
    },
    {
        'type': 'buttons',
        'showactive': False,
        'buttons': [
            {
                'label': 'Wave Characteristics',
                'method': 'relayout',
                'args': [{'annotations': [{'text': info_text.value, 'x': 0.5, 'y': 1.2, 'showarrow': False,
                                          'font': {'size': 12}}]}]
            }
        ]
    }
])

final_layout.show()