from bokeh.plotting import figure, output_file, show
from bokeh.io import output_notebook
from bokeh.models import ColumnDataSource

# Set Bokeh output to notebook
output_notebook()

import numpy as np
from scipy.integrate import odeint
from bokeh.plotting import figure, show

# Van der Pol oscillator parameter
mu = 2.0  # Controls the nonlinearity and damping

# Van der Pol system function
def van_der_pol(state, t):
    x, y = state
    x_dot = y
    y_dot = mu * (1 - x**2) * y - x
    return [x_dot, y_dot]

# Initial conditions and time steps
initial = [2, 0]
t = np.linspace(0, 100, 10000)

# Solve Van der Pol equations
solution = odeint(van_der_pol, initial, t)
x = solution[:, 0]
y = solution[:, 1]

# Split data into segments for multi-line
num_segments = 7
xs = np.array_split(x, num_segments)
ys = np.array_split(y, num_segments)

# Define a color palette
colors = ["#FFE5D9", "#FFB3B3", "#FF9999", "#FF6666", "#FF3333", "#CC0000", "#990000"]

# Create the Bokeh figure
p = figure(title="Van der Pol Oscillator Visualization",
           background_fill_color="#f9f9f9",
           x_axis_label="X",
           y_axis_label="Y")

# Add the multi_line glyph
p.multi_line(xs, ys, line_color=colors, line_alpha=0.8, line_width=1.5)

# Show the plot
show(p)

from IPython.display import Image, display

# Display the image
display(Image(url="https://snipboard.io/HfrZtc.jpg"))