https://github.com/louis-finegan/lorenz-attractors-pygame-python3
Chaos Equations (Lorenz Attractors) in python3 using the pygame, scipy and numpy libaries.
https://github.com/louis-finegan/lorenz-attractors-pygame-python3
chaos-equations lorenz-attractor numpy pygame python python3 scipy
Last synced: about 2 months ago
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Chaos Equations (Lorenz Attractors) in python3 using the pygame, scipy and numpy libaries.
- Host: GitHub
- URL: https://github.com/louis-finegan/lorenz-attractors-pygame-python3
- Owner: Louis-Finegan
- License: mit
- Created: 2023-01-20T22:45:11.000Z (over 2 years ago)
- Default Branch: master
- Last Pushed: 2023-04-12T16:14:56.000Z (about 2 years ago)
- Last Synced: 2025-02-01T18:36:35.180Z (4 months ago)
- Topics: chaos-equations, lorenz-attractor, numpy, pygame, python, python3, scipy
- Language: Python
- Homepage:
- Size: 2.17 MB
- Stars: 3
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Lorenz Attractors
## Lorenz Attractors
The Lorenz Attractors are governed by the following System of Ordinary Differential Equations:
$$\frac{dx}{dt}=\sigma(y-x)$$
$$\frac{dy}{dt}=x(\rho-z)-y$$
$$\frac{dz}{dt}=xy-\beta z$$
For more information Click [here](https://en.wikipedia.org/wiki/Lorenz_system).
## Purpose
Demonstrate the chaotic nature of the Lorenz Attractors with slight variation in the initial conditions.
## Libaries Used:
1. `numpy`
2. `scipy` using the `integrate` module
3. `pygame`
## Approach
3 instances of the `lorenz` class were created with slight variation in their initial conditions. these conditions were random using numpy's uniform random number generator:
[np.random.uniform(0.99, 1.01),np.random.uniform(0.99, 1.01),np.random.uniform(0.99, 1.01)]
The initial condition was centered around `[1, 1, 1]`. This is to stop the points in the solution from displaying off the pygame display.
NOTE: Initial conditions will be printed in the terminal.
The System of Ordinary Differential Equation were solved by using, `solve_ivp` function, Then the `plot.game` method is called which generates the interactive pygame display with the 3 solutions: white red and/or blue, appearing point by point at *30 fps*.
## How to use
Run the python file `main.py`.
1. Press `s` to start then select one of the following options:
* press `a` to generate all 3 solution on the display at the same time.
* press `w` to generate the white solution.
* press `g` to generate the green solution.
* press `b` to generate the green solution.
2. Press `q` or close the window to quit.
3. Press `r` to reset the display.
4. follow on from step 1 to generate a new plot.
## Conclusion
It is clear, by observing all 3 solutions after a sufficent amount of time, there nature is hugely different. Then it can be said with a slight change in the Lorenz Attractors initial conditions, these models will have different solutions after a long period of time.