⚡ 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 40 MATH & STATISTICS

🌌 The 3D Word Embedding Galaxy

Cosine similarity geometry and semantic vector arithmetic (King - Man + Woman = Queen).

\cos(\mathbf{u}, \mathbf{v}) = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\| \|\mathbf{v}\|}, \quad \vec{v}_{\text{queen}} \approx \vec{v}_{\text{king}} - \vec{v}_{\text{man}} + \vec{v}_{\text{woman}}
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TOOL 41 MATH & STATISTICS

🎯 The Monte Carlo Pi Dartboard

Approximating mathematical constants using pseudo-random uniform dart sampling.

\pi \approx 4 \times \frac{N_{\text{inside}}}{N_{\text{total}}}
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TOOL 42 MATH & STATISTICS

🪙 The Central Limit Theorem Coin Flipper

Sampling distributions of the mean converging to normality irrespective of parent distribution.

Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}} \xrightarrow{d} \mathcal{N}(0,1)
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TOOL 43 MATH & STATISTICS

📐 The Matrix Transformation Grid Elastic

Linear algebra determinant shearing, eigenbasis stretching, and rotation matrices.

\begin{bmatrix} x_2 \\ y_2 \end{bmatrix} = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x_1 \\ y_1 \end{bmatrix}, \quad \det(A) = ad - bc
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TOOL 44 MATH & STATISTICS

🌀 The Prime Number Spiral Sieve

Ulam & Sacks polar spirals revealing mysterious quadratic prime diagonal bands.

r = \sqrt{n}, \quad \theta = \sqrt{n} \cdot 2\pi
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TOOL 45 MATH & STATISTICS

🌻 The Fibonacci Golden Ratio Spiral

Phyllotaxis seed dispersion through the golden angle $\Phi = 137.508^\circ$.

\phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887, \quad \theta = 2\pi(1 - 1/\phi)
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TOOL 46 MATH & STATISTICS

🧪 The Bayes' Theorem Diagnostic Filter

Prior probability, likelihood ratios, and posterior belief updating.

P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)}
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TOOL 47 MATH & STATISTICS

🖼️ The Fourier Image Compression Sliders

2D Discrete Cosine Transform (DCT) frequency quantization (JPEG pipeline).

F(u,v) = \frac{1}{4} C(u) C(v) \sum_{x=0}^{7} \sum_{y=0}^{7} f(x,y) \cos\frac{(2x+1)u\pi}{16} \cos\frac{(2y+1)v\pi}{16}
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TOOL 48 MATH & STATISTICS

🧭 The Vector Field Particle Flow

Divergence, curl, and gradient flow lines in 2D vector calculus.

\nabla \cdot \mathbf{F} = \frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y}, \quad \nabla \times \mathbf{F} = \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}
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Showing 1 to 9 of 12 interactive simulations in Advanced Math & Statistical Engines