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

# Parameters for the Cat Map
a = 1
b = 1
m = 100  # Size of the grid

# Number of iterations and initial conditions
num_points = 10000
x0, y0 = 10, 20  # Initial position

# Generate points for Arnold's Cat Map
x, y = [x0], [y0]
for _ in range(num_points - 1):
    x_new = (x[-1] + y[-1]) % m
    y_new = (x[-1] + a * y[-1]) % m
    x.append(x_new)
    y.append(y_new)

# Scale the values for visualization
x = np.array(x) / m
y = np.array(y) / m

# 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 = ["#FFFFCC", "#A1DAB4", "#41B6C4", "#2C7FB8", "#253494", "#1D91C0", "#225EA8"]

# Create the Bokeh figure
p = figure(title="Arnold's Cat Map Visualization",
           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)

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()

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()

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()

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()

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()

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()

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()

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

import pandas as pd

# Set Bokeh output to notebook
output_notebook()

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()