Update README.md

README.md

@@ -1,3 +1,50 @@
 ---
 license: mit
----
+tags:
+- pytorch
+- neural-network
+- chaos-theory
+- logistic-map
+---
+# 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:
+
+![Prediction Results](./example_plot.png)
+
+##  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