"A world that learns gravity — not one that knows it."

# Clone the repository
git clone https://github.com/aditisingh02/Infera.git
cd Infera

# Install dependencies
npm install

# Start the development server
npm run dev

# Open http://localhost:5173 in your browser

Infera is an interactive 3D physics sandbox where particles don't know physics — they learn it. Each object begins uncertain about fundamental constants like gravity, mass, and friction. Through Bayesian inference and Extended Kalman Filtering, particles continuously update their beliefs as they observe their own motion.

The result? A mesmerizing visualization of scientific discovery itself — watch uncertainty (purple glow) fade into certainty (white light) as the universe learns its own laws.

flowchart TD
    A[Initialize Particle] --> B[Set Prior Beliefs]
    B --> C["State: x = [pos, vel, g, m, f]ᵀ"]
    C --> D["Covariance: P (High Uncertainty)"]
    
    D --> E[Prediction Step]
    E --> F["x̂ₜ|ₜ₋₁ = f(x̂ₜ₋₁|ₜ₋₁)"]
    F --> G["Pₜ|ₜ₋₁ = FₜPₜ₋₁|ₜ₋₁Fₜᵀ + Qₜ"]
    
    G --> H[Observe Motion]
    H --> I["Measurement: zₜ"]
    
    I --> J[Compute Kalman Gain]
    J --> K["Kₜ = Pₜ|ₜ₋₁Hₜᵀ(HₜPₜ|ₜ₋₁Hₜᵀ + Rₜ)⁻¹"]
    
    K --> L[Update Beliefs]
    L --> M["x̂ₜ|ₜ = x̂ₜ|ₜ₋₁ + Kₜ(zₜ - Hₜx̂ₜ|ₜ₋₁)"]
    M --> N["Pₜ|ₜ = (I - KₜHₜ)Pₜ|ₜ₋₁"]
    
    N --> O{Uncertainty < Threshold?}
    O -->|No| P[Continue Learning]
    O -->|Yes| Q[Converged Beliefs]
    
    P --> R[Share with Global Prior]
    R --> S["P(θ|D) ∝ P(D|θ) × P(θ)"]
    S --> E
    
    Q --> T[Stable Physics Knowledge]
    T --> U[Visual: Purple → White]
    
    style A fill:#4d0de0
    style Q fill:#013436
    style T fill:#013436
    style U fill:#013436
    style M fill:#910459
    style N fill:#910459

State Vector: Each particle maintains beliefs about:

x_t = [position_x, position_y, velocity_x, velocity_y, gravity, mass, friction]ᵀ

Bayesian Update Rule:

P(θ|D) ∝ P(D|θ) × P(θ)
posterior = likelihood × prior

Extended Kalman Filter:

• Prediction: Forecast next motion based on current beliefs
• Update: Correct beliefs based on observed reality
• Convergence: Uncertainty shrinks as evidence accumulates

All particles contribute to a shared global consensus about universal constants, modeling how scientific communities form collective knowledge.

• Entropy Calculation: H = -Σ P(x) log P(x)
• Mutual Information: I(X;Y) between particle beliefs
• Convergence Analysis: Stability metrics and learning rates

The system attempts to rediscover physical laws (like F = ma) from learned data, demonstrating AI-driven scientific discovery.

Custom algorithms map probability distributions to visual effects:

glow_intensity = exp(-variance * decay_factor)
color = mix(purple, white, confidence_level)

• React 19 - Modern UI framework with hooks
• Three.js - WebGL 3D rendering and physics visualization
• @react-three/fiber - React renderer for Three.js
• Tailwind CSS - Utility-first styling with custom design system
• TypeScript - Type-safe development with advanced inference

• Custom Extended Kalman Filter - Nonlinear state estimation
• Bayesian Inference Engine - Posterior distribution updates
• Collision Detection System - Advanced particle interactions
• Information Theory Metrics - Entropy and mutual information

• WebGL Instanced Rendering - Efficient particle systems
• Frame-rate Monitoring - Real-time performance metrics
• Memory Management - Automatic cleanup and optimization

The Extended Kalman Filter handles nonlinear motion dynamics:

Prediction Step:

x̂_t|t-1 = f(x̂_t-1|t-1)  // Motion model
P_t|t-1 = F_t P_t-1|t-1 F_t^T + Q_t  // Covariance prediction

Update Step:

K_t = P_t|t-1 H_t^T (H_t P_t|t-1 H_t^T + R_t)^-1  // Kalman gain
x̂_t|t = x̂_t|t-1 + K_t(z_t - H_t x̂_t|t-1)  // State update  
P_t|t = (I - K_t H_t) P_t|t-1  // Covariance update

• Differential Entropy: H(X) = -∫ p(x) log p(x) dx
• Mutual Information: I(X;Y) = H(X) + H(Y) - H(X,Y)
• Kullback-Leibler Divergence: D_KL(P||Q) for belief comparison

• Kalman Filtering: R.E. Kalman (1960) - Optimal state estimation
• Bayesian Inference: Thomas Bayes (1763) - Probability theory foundations
• Information Theory: Claude Shannon (1948) - Mathematical communication theory
• Scientific Method: Visual representation of hypothesis testing and belief updating

Witness a universe discovering itself through probabilistic reasoning.