Rossler Attractor Pattern using Python

 

import matplotlib.pyplot as plt

import numpy as np

from scipy.integrate import solve_ivp

def rossler(t,state,a=0.2,b=0.2,c=5.7):

    x,y,z=state

    dx=-y-z

    dy=x+a*y

    dz=b+z*(x-c)

    return[dx,dy,dz]

initial_state=[0.0,1.0,0.0]

t_span=(0,100)

t_eval=np.linspace(t_span[0],t_span[1],10000)

solution=solve_ivp(rossler,t_span,initial_state,t_eval=t_eval,rtol=1e-8)

x=solution.y[0]

y=solution.y[1]

z=solution.y[2]

fig=plt.figure(figsize=(6,6))

ax=fig.add_subplot(111,projection='3d')

ax.plot(x,y,z,lw=0.5,color='purple')

ax.set_title('Rossler Attractor')

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Required Libraries

import numpy as np

import matplotlib.pyplot as plt

from scipy.integrate import solve_ivp

numpy for numerical operations.

matplotlib.pyplot for plotting.

solve_ivp from SciPy to numerically solve differential equations.

2. Define the Rössler System Differential Equations

def rossler(t, state, a=0.2, b=0.2, c=5.7):

    x, y, z = state

    dx = -y - z

    dy = x + a * y

    dz = b + z * (x - c)

    return [dx, dy, dz]

Function rossler returns derivatives [dx/dt, dy/dt, dz/dt] for given state (x, y, z).

Parameters a, b, c control system behavior.

The Rössler system is a famous chaotic system.

3. Set Initial Conditions

initial_state = [0.0, 1.0, 0.0]

Starting point of the system in 3D space (x=0, y=1, z=0).

4. Define Time Interval and Evaluation Points

t_span = (0, 100)

t_eval = np.linspace(t_span[0], t_span[1], 10000)

t_span is time range from 0 to 100.

t_eval defines 10,000 evenly spaced points where the solution is calculated.

5. Numerically Solve the ODE System

solution = solve_ivp(rossler, t_span, initial_state, t_eval=t_eval, rtol=1e-8)

Uses solve_ivp to integrate the Rössler system over time.

High accuracy is requested with rtol=1e-8.

6. Extract Solutions

x = solution.y[0]

y = solution.y[1]

z = solution.y[2]

Extract arrays of x, y, z values from the solution at each time point. 

7. Create 3D Plot

fig = plt.figure(figsize=(10,7))

ax = fig.add_subplot(111, projection='3d')

Creates a new figure with size 10x7 inches.

Adds a 3D subplot for plotting. 

8. Plot the Rössler Trajectory

ax.plot(x, y, z, lw=0.5, color='purple')

Plots the 3D curve traced by (x, y, z) over time.

 Line width is thin (0.5), color purple.

9. Set Plot Titles and Axis Labels

ax.set_title('Rössler Attractor')

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

Sets the plot title and labels for the x, y, and z axes.

 10. Show the Plot

plt.show()

Displays the interactive 3D plot window with the attractor curve.