O/⚪ᕤᕦ⚪ИN⚪ꖴ⚪ᙏ⚪ᗩ⚪ᴥ⚪ᕤᕦ⚪Ⓞ⚪ᴥ⚪ߦ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ߦ⚪ᴥ⚪Ⓞ⚪ᕤᕦ⚪ᴥ⚪ᗩ⚪ᙏ⚪ꖴ⚪ИN⚪ᕤᕦ⚪/⚪ИN⚪Ⓞ⚪옷⚪✤⚪人⚪ߦ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ߦ⚪人⚪✤⚪옷⚪Ⓞ⚪ИN⚪/⚪ᴥ⚪ᗱᗴ⚪✤⚪人⚪ߦ⚪ᑎ⚪ᒍᒐ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᒍᒐ⚪ᑎ⚪ߦ⚪人⚪✤⚪ᗱᗴ⚪ᴥ⚪/YP.⚪ᴥ⚪ᗱᗴ⚪✤⚪Ⓞ⚪ᙁ⚪ߦ⚪◯⚪ᗱᗴ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᑐᑕ⚪ᑎ⚪ꗳ⚪◯⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ᗝ⚪ᗱᗴ⚪ꖴ⚪ꗳ⚪ꖴ⚪ᑐᑕ⚪ᗱᗴ⚪ߦ⚪ᔓᔕ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᔓᔕ⚪ߦ⚪ᗱᗴ⚪ᑐᑕ⚪ꖴ⚪ꗳ⚪ꖴ⚪ᗱᗴ⚪ᗝ⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪◯⚪ꗳ⚪ᑎ⚪ᑐᑕ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗱᗴ⚪◯⚪ߦ⚪ᙁ⚪Ⓞ⚪✤⚪ᗱᗴ⚪ᴥ⚪.PY

import numpy as np
from ipywidgets import interact
import plotly.graph_objects as go
from math import *

def kappa(formula, x):
    return eval(formula, {'acos': acos, 'exp': exp, 'cos': cos, 'sin': sin, 'pi': pi, 'x': x})

def plot(formula='(1 + cos(((4)/2)*x))/2', RANGE_FROM=0, RANGE_TO=4*pi, N=10):
    num_points = 1+2**N

    # Generate x values with the specified number of points
    x_vals = np.linspace(RANGE_FROM, RANGE_TO, num_points)

    # Compute kappa values
    kappa_vals = np.array([kappa(formula, x_val) for x_val in x_vals])

    theta_vals = np.cumsum(kappa_vals) * (x_vals[1]-x_vals[0]) if num_points > 1 else np.array([0])
    x_coords_ = np.cumsum(np.cos(theta_vals)) * (x_vals[1] - x_vals[0]) if num_points > 1 else np.array([0])
    y_coords_ = np.cumsum(np.sin(theta_vals)) * (x_vals[1] - x_vals[0]) if num_points > 1 else np.array([0])

    # Check if the first point is zero, if not, add it manually
    if x_coords_[0] != 0 or y_coords_[0] != 0:
        x_coords = np.insert(x_coords_, 0, 0)
        y_coords = np.insert(y_coords_, 0, 0)
    else:
        x_coords = x_coords_
        y_coords = y_coords_

    fig = go.Figure()

    fig.add_trace(go.Scatter(x=x_coords, y=y_coords, mode='lines', name='Curve'))

    fig.update_layout(autosize=True, xaxis=dict(scaleanchor='y', scaleratio=1))
    fig.show()

# Create the interactive plot
interact(plot, formula='(1 + cos(((4)/2)*x))/2', RANGE_FROM=(0, 4*pi, pi/4), RANGE_TO=(0, 4*pi, pi/4), N=(1,16));