⚡ 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 52 LLM & CRYPTOGRAPHY

✂️ The Tokenization Cutting Board

Byte-Pair Encoding (BPE) iterative subword merge frequency slicing.

\text{Merge}(t_a, t_b) \to t_{ab} \quad \text{where } \text{freq}(t_a t_b) = \max
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TOOL 53 LLM & CRYPTOGRAPHY

🌡️ The Temperature Vector Sampler

Logit scaling, top-k truncation, and nucleus (top-p) cumulative probability sampling.

P(w_i) = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)}, \quad \sum_{i \in V^{(p)}} P(w_i) \ge p
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TOOL 54 LLM & CRYPTOGRAPHY

📽️ The NeRF Camera Raycast Volumizer

Neural Radiance Fields volumetric raymarching through continuous 5D coordinates.

C(\mathbf{r}) = \int_{t_n}^{t_f} T(t) \sigma(\mathbf{r}(t)) \mathbf{c}(\mathbf{r}(t), \mathbf{d}) dt
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TOOL 55 LLM & CRYPTOGRAPHY

🌫️ The Diffusion Model Denoising Timeline

Forward stochastic degradation versus reverse score-based Langevin denoising.

x_{t-1} = \frac{1}{\sqrt{\alpha_t}} \left(x_t - \frac{1 - \alpha_t}{\sqrt{1 - \bar{\alpha}_t}} \epsilon_\theta(x_t, t)\right) + \sigma_t z
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TOOL 56 LLM & CRYPTOGRAPHY

📝 The OCR Bounding Box Stringer

Connectionist Temporal Classification (CTC) sequence decoding on text lines.

p(\pi \mid x) = \prod_{t=1}^{T} y_{\pi_t}^t, \quad \mathcal{B}(\pi) = l
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TOOL 57 LLM & CRYPTOGRAPHY

🏎️ The Visual Odometry Horizon Tracker

Essential matrix 5-point algorithm recovering camera 6DoF translation vectors.

\mathbf{x}_2^T \mathbf{E} \mathbf{x}_1 = 0, \quad \mathbf{E} = [\mathbf{t}]_\times \mathbf{R}
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TOOL 58 LLM & CRYPTOGRAPHY

🔐 The RSA Asymmetric Key Locksmith

Euler's totient function and modular multiplicative inverse key generation.

ed \equiv 1 \pmod{\phi(n)}, \quad c = m^e \pmod{n}, \quad m = c^d \pmod{n}
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TOOL 59 LLM & CRYPTOGRAPHY

🗝️ The Zero-Knowledge Proof Secret Cave

Quisquater-Guillou interactive proof verifying knowledge without revealing the secret.

P(\text{Cheater passes } k \text{ rounds}) = \left(\frac{1}{2}\right)^k
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TOOL 60 LLM & CRYPTOGRAPHY

🎨 The Diffie-Hellman Color Mixing Protocol

Discrete logarithm one-way trapdoor function visual color exchange.

A = g^a \pmod{p}, \quad B = g^b \pmod{p}, \quad K = B^a \equiv A^b \equiv g^{ab} \pmod{p}
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Showing 1 to 9 of 9 interactive simulations in Advanced LLM, CV & Cryptographic Nodes