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 bokeh.plotting import figure, show

# Holmes map parameters (adjusted for stability)
a = -0.5
b = -0.2

# Number of iterations and initial conditions
num_points = 10000
x0, y0 = 0.5, 0.5

# Generate points for the Holmes map
x, y = [x0], [y0]
for _ in range(num_points - 1):
    x_new = y[-1]
    y_new = -a * x[-1] - b * y[-1] + x[-1]**2

    # Limit the maximum values to prevent overflow
    if abs(x_new) > 100 or abs(y_new) > 100:
        break

    x.append(x_new)
    y.append(y_new)

# 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 = ["#FEE8C8", "#FDBB84", "#FC8D59", "#EF6548", "#D7301F", "#B30000", "#7F0000"]

# Create the Bokeh figure
p = figure(title="Holmes Map Visualization (Corrected)",
           background_fill_color="#f9f9f9",
           x_axis_label="X",
           y_axis_label="Y",
           match_aspect=True)

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

# Show the plot
show(p)