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import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
import cupy as cp
from tqdm import tqdm
import plotly.graph_objects as go
import streamlit as st
x = st.slider('Select a value')
st.write(x, 'squared is', x * x)
# Define the twelfth root of two
Q = 2 ** (1/12)
# Define the wave function of the universe with variants (using CuPy)
def wave_function_cupy(x, t, scale=1.0, phase_shift=0.0):
denominator = 2 * (t**2 + 1e-10) # Add a small value to avoid division by zero
return scale * Q * cp.exp(-x**2 / denominator) * cp.exp(-1j * (t + phase_shift))
# Simulation parameters
x = np.linspace(-10, 10, 100)
t = np.linspace(0, 10, 100)
X, T = np.meshgrid(x, t)
# Convert numpy arrays to CuPy arrays
X_cupy = cp.asarray(X)
T_cupy = cp.asarray(T)
# Variants parameters
scales = [0.5, 1.0, 1.5] # Different scaling factors
phase_shifts = [0, np.pi/4, np.pi/2] # Different phase shifts
# Initialize a 3D array to store results
wave_functions_3d = np.zeros((len(scales), len(phase_shifts), len(x), len(t)), dtype=complex)
# Simulate with variants and store results in the 3D array
for i, scale in enumerate(scales):
for j, phase_shift in enumerate(phase_shifts):
wave_functions_3d[i, j, :, :] = cp.asnumpy(wave_function_cupy(X_cupy, T_cupy, scale, phase_shift))
# --- Plotly Interactive Visualization ---
# Create the figure
fig = go.Figure(data=[
go.Surface(x=x, y=t, z=np.abs(wave_functions_3d[0, 0, :, :])**2)
])
fig.update_layout(
title="Wave Function of the Universe",
scene=dict(
xaxis_title="x",
yaxis_title="t",
zaxis_title="|ψ(x,t)|^2"
),
)
# Add Scale Slider
fig.update_layout(
sliders=[
dict(
active=True,
currentvalue=dict(
prefix="Scale: ",
font=dict(size=12)
),
steps=[
dict(
method="update",
args=[
{"z": [np.abs(wave_functions_3d[i, 0, :, :])**2]} # Update z data
],
label=f"Scale: {scales[i]:.2f}" # Label for step values
) for i in range(len(scales))
],
pad=dict(t=50),
len=0.9, # Length of the slider
x=0.1, # X position of the slider
y=0.1, # Y position of the slider
),
dict(
active=True,
currentvalue=dict(
prefix="Phase Shift: ",
font=dict(size=12)
),
steps=[
dict(
method="update",
args=[
{"z": [np.abs(wave_functions_3d[0, j, :, :])**2]} # Update z data
],
label=f"Phase Shift: {phase_shifts[j]:.2f}" # Label for step values
) for j in range(len(phase_shifts))
],
pad=dict(t=50),
len=0.9, # Length of the slider
x=0.1, # X position of the slider
y=0.3, # Y position of the slider
)
]
)
fig.show()
# --- End of Plotly ---
# --- Matplotlib Animation ---
# Animation
fig, ax = plt.subplots()
im = ax.imshow(np.abs(wave_functions_3d[0, 0, :, :]) ** 2, extent=[-10, 10, 0, 10], aspect='auto', cmap='viridis')
ax.set_xlabel('x')
ax.set_ylabel('t')
ax.set_title('Wave Function of the Universe')
cbar = fig.colorbar(im, ax=ax, label='|ψ(x,t)|^2')
def update(frame):
i, j = divmod(frame, len(phase_shifts)) # Get the index for the 3D array
im.set_array(np.abs(wave_functions_3d[i, j, :, :]) ** 2) # Update with the correct frame
ax.set_title(f'Wave Function at Scale: {scales[i]}, Phase Shift: {phase_shifts[j]:.2f}')
return im,
ani = FuncAnimation(fig, update, frames=len(scales) * len(phase_shifts), blit=True)
ani.save('wave_function_animation.gif', writer='pillow')
plt.show()
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