Upload logistic_map_approximator.pth

# Logistic Map Approximator (Neural Network)

This model approximates the **logistic map equation**:

> xₙ₊₁ = r × xₙ × (1 − xₙ)

It is trained using a simple feedforward neural network to learn chaotic dynamics across different values of `r` ∈ [2.5, 4.0].

## Model Details

- **Framework:** PyTorch
- **Input:**
- `x` ∈ [0, 1]
- `r` ∈ [2.5, 4.0]
- **Output:** `x_next` (approximation of the next value in sequence)
- **Loss Function:** Mean Squared Error (MSE)
- **Architecture:** 2 hidden layers (ReLU), trained for 100 epochs

## Performance

The model closely approximates `x_next` for a wide range of `r` values, including the chaotic regime.

Visualization:


## Files

- `logistic_map_approximator.pth`: Trained PyTorch model weights
- `mandelbrot.py`: Full training and evaluation code
- `README.md`: You're reading it
- `example_plot.png`: Comparison of true vs predicted outputs

## Applications

- Chaos theory visualizations
- Educational tools on non-linear dynamics
- Function approximation benchmarking

## License

MIT License

logistic_map_approximator.pth

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