⚡ Interactive Computational Laboratory

60 Real-Time AI, Physics & Mathematical Simulators

100% client-side algorithmic simulations. Manipulate neural nodes, quantum attractors, particle fields, and tokenization vectors directly in your browser with zero latency.

60 Live Engines
5 Disciplines
0 ms Server Load
60 FPS Audio & Motion
🌐 All Simulators (60) 📊 AI & DATA (13) 👁️ VISION & ROBOTICS (13) 🌀 PHYSICS & CHAOS (13) 🧮 MATH & STATISTICS (12) 🔏 LLM & CRYPTOGRAPHY (9)
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TOOL 01 AI & DATA

⚡ The Neural Network Node Fire & Feedforward Ticker

Forward propagation potential waves with activation threshold firing.

z^{[l]} = W^{[l]} a^{[l-1]} + b^{[l]}, \quad a^{[l]} = \sigma(z^{[l]})
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TOOL 02 AI & DATA

🌿 The Decision Tree Labyrinth

Recursive binary partition splits navigating entropy threshold boundaries.

H(S) = - \sum_{i=1}^{c} p_i \log_2(p_i)
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TOOL 03 AI & DATA

🏔️ The Gradient Descent Topographical Optimization Trace

Ball rolling through non-convex loss manifolds with momentum vectors.

\theta_{t+1} = \theta_t - \alpha \nabla_\theta J(\theta_t) + \beta v_{t-1}
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TOOL 04 AI & DATA

🎯 The K-Means Cluster Sandbox

Centroid convergence and Voronoi partition dynamics on live point clouds.

J = \sum_{i=1}^{k} \sum_{x \in S_i} \|x - \mu_i\|^2
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TOOL 05 AI & DATA

🧩 The Transformer Attention Matrix Grid

Multi-head Query-Key-Value dot product heatmaps and softmax routing.

\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V
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TOOL 06 AI & DATA

🧬 The Genetic Algorithm Creature Race

Darwinian mutation, crossover vectors, and generational fitness selection.

P(i) = \frac{f_i}{\sum_{j=1}^{N} f_j}
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TOOL 07 AI & DATA

📐 The PCA Dimension Crusher

Eigenvector projection reducing high-dimensional variance into 2D manifolds.

\Sigma v = \lambda v, \quad \max_{w} w^T \Sigma w
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TOOL 08 AI & DATA

⚔️ The Support Vector Machine Hyperplane Knife

Maximum-margin separating hyperplanes with linear & RBF kernel projections.

\min_{w,b} \frac{1}{2} \|w\|^2 \quad \text{s.t.} \quad y_i(w \cdot x_i + b) \ge 1
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TOOL 09 AI & DATA

🎭 The Latent Space Face Morpher

Continuous geodesic interpolation through generative manifold coordinates.

z_{\text{interp}} = (1 - t)z_1 + t z_2
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Showing 1 to 9 of 60 interactive simulations