Celestial Mechanics & Astrodynamics🪐 L1-L5 Points
RK4 numerical integrator in corotating frame with Hill equipotential surfaces and Halo orbits
$$\ddot{x} - 2\dot{y} = \frac{\partial U_{\text{eff}}}{\partial x}, \quad \ddot{y} + 2\dot{x} = \frac{\partial U_{\text{eff}}}{\partial y}$$
Interactive orbital simulator of the Circular Restricted Three-Body Problem (CR3BP). Solves the five equilibrium Lagrange points (L1-L5), renders Hill effective potential contours, computes the Jacobi constant in real time, and tests space missions like JWST (L2), SOHO (L1), and Trojans (L4).
#RK4#Mecánica Celeste#Jacobi#Coriolis#Halo Orbits
Reinforcement Learning & Optimization⚡ Bellman GridWorld
Sequential optimization, optimality principle, and fixed-point operator convergence
$$V^*(s) = \max_a \left[ \mathcal{R}(s, a) + \gamma \sum_{s'} \mathcal{P}(s'|s,a) V^*(s') \right]$$
Visual laboratory for Markov Decision Processes (MDP) and dynamic programming. Adjust discount factor gamma, compute value iterations step by step with the Bellman operator, and visualize optimal policy convergence.
#MDP#Reinforcement Learning#Value Iteration#Dynamic Programming
Deep Learning Architecture & NLP🔥 QKV Attention
Scaled dot-product attention matrices (Softmax), multi-head attention, and contextual representations
$$\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$$
Analytical visualizer of the algorithmic core powering modern Large Language Models (LLMs). Explore how Query, Key, and Value vector matrices interact, computing contextual attention weights token by token.
#Transformers#Self-Attention#NLP#LLMs#Softmax
Information Theory & Probability📊 Shannon Entropy
Uncertainty, optimal compression, Kullback-Leibler divergence, and channel capacity
$$H(X) = -\sum_{i=1}^n P(x_i) \log_2 P(x_i)$$
Interactive simulator of discrete and continuous probability distributions. Manipulate Bernoulli and multinomial distributions to compute entropy in bits, informational redundancy, and lossless compression bounds.
#Entropy#Information Theory#Probability#KL Divergence
Topology & Network Architectures🧠 Neural Zoo
Complete taxonomy: Perceptrons, CNNs, RNNs, Transformers, Autoencoders, and Diffusion
Interactive catalog featuring tensor flow diagrams of the primary neural topologies throughout AI history, from multilayer perceptrons and ResNets to diffusion models and Graph Neural Networks.
#Architectures#CNN#RNN#Autoencoders#Diffusion
Mathematical Physics & Universal Laws📐 17 Equations
From the Pythagorean Theorem to Black-Scholes and Navier-Stokes with rigorous mathematics
$$\rho \left(\frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u}\right) = -\nabla p + \mu \nabla^2 \mathbf{u} + \mathbf{f}$$
Interactive compendium of the seventeen mathematical equations that changed physics, astronomy, engineering, and finance, with operator breakdown, historical context, and modern applications.
#Physics#Calculus#Navier-Stokes#Maxwell#Schrödinger
Software Engineering & ML Frameworks⚖️ PyTorch vs TF
Dynamic computation graphs (eager) vs optimized static graphs (XLA) and production pipelines
$$\nabla_{\theta} \mathcal{L}(\theta) = \frac{\partial \mathcal{L}}{\partial \hat{y}} \frac{\partial \hat{y}}{\partial \theta}$$
Detailed architectural and syntactical analysis comparing the two dominant deep learning frameworks. Automatic differentiation, distributed parallelism, ONNX portability, and hardware compilation.
#PyTorch#TensorFlow#Autograd#CUDA#Engineering
Pure Mathematics & Foundational Conjectures🏆 Millennium Problems
The greatest unsolved mathematical conjectures: P vs NP, Riemann, Yang-Mills, Navier-Stokes
$$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} = 0 \implies \text{Re}(s) = \frac{1}{2}$$
Rigorous survey of the seven mathematical challenges formulated in 2000 by CMI. Precise statements, computational and physical ramifications, and current status of resolution attempts.
#Clay Institute#Riemann#P vs NP#Navier-Stokes#Poincaré
Recreational Arithmetic & Didactics🐫 35 Camels
Fractional arithmetic, unit closure, and deductive elegance in «The Man Who Counted»
$$\frac{1}{2} + \frac{1}{3} + \frac{1}{9} = \frac{17}{18} < 1$$
Analytical resolution of the classic inheritance dilemma presented by Beremiz Samir. Discover why fractional sums of 1/2, 1/3, and 1/9 fall short of 1, and how an extra 36th camel resolves the distribution with surplus for all.
#Malba Tahan#Beremiz Samir#Number Theory#Didactics