Mathématiques
Visualisations interactives de concepts mathématiques
105 visualizations
Kuramoto Synchronization Model - Coupled Oscillator Phase Transitions
Interactive Kuramoto synchronization model simulation. Explore coupled oscillator phase transitions, order parameter dynamics, critical coupling strength, and collective synchronization phenomena with adjustable coupling strength, frequency spread, and oscillator count. Features circular phase display, real-time order parameter time series, frequency distribution histogram, and preset scenarios.
Hodgkin-Huxley Neuron Model - Action Potential Simulation
Interactive Hodgkin-Huxley neuron model simulation with RK4 ODE solver. Explore action potential generation, sodium/potassium ion channel gating dynamics (m, h, n variables), membrane potential time series, phase portrait (dV/dt vs V) showing limit cycles, conductance plots (g_Na, g_K), and spike frequency analysis with adjustable injected current, preset scenarios (resting, threshold, regular spiking, fast spiking, burst), full/reduced display modes, and multi-language support.
Turing Pattern - Gray-Scott Reaction-Diffusion Simulation
Interactive Turing pattern simulation using the Gray-Scott reaction-diffusion model. Explore self-organizing chemical patterns including spots, stripes, coral, mitosis, and turbulence with adjustable feed rate, kill rate, and diffusion parameters
Lotka-Volterra Predator-Prey Model - Interactive Population Dynamics
Interactive Lotka-Volterra predator-prey simulation with phase space trajectory, time series, RK4 ODE solver, classic/damped/explosive dynamics modes, and adjustable population parameters
Supply-Demand Shock Analyzer - Interactive Microeconomics Visualization
Interactive supply-demand model with curve shifting, tax incidence, price controls, welfare analysis (consumer/producer surplus, deadweight loss), elasticity effects, and preset economic shock scenarios
Bifurcation Diagram - Logistic Map Parameter Space Visualization
Interactive bifurcation diagram of the logistic map x_{n+1} = r x_n (1 - x_n) showing period-doubling cascades, Feigenbaum constants, chaos onset, and self-similar fractal structure through zoom
Benford's Law Visualization - 本福特定律可视化
Interactive visualization of Benford's Law (First Digit Law) exploring the leading digit distribution P(d)=log10(1+1/d). Features include preset data sources (world population, GDP, Fibonacci numbers, powers of 2, perfect squares, prime numbers, uniform random for comparison), custom data input (comma or newline separated), formula-based data generation (n^2, 2^n, n!, fib(n), prime(n)), real-time bar chart with Benford's theoretical curve overlay using Chart.js, deviation chart showing per-digit differences, chi-squared goodness-of-fit test with p-value calculation, adjustable dataset size slider to observe the law of large numbers effect, detailed statistics table with theoretical vs observed distribution, and comprehensive educational content covering Benford's Law theory (logarithmic scale uniformity), practical applications (election fraud detection, financial auditing, COVID-19 data verification, scientific integrity), and key insights about convergence behavior. Multi-language support (zh, en, de, es, fr, ru, pt).
Lattice Percolation: Phase Transitions - 格点渗流相变可视化
Interactive lattice percolation visualization demonstrating phase transitions and critical phenomena in statistical physics. Features include 2D square lattice with configurable grid size (16×16 to 64×64), adjustable occupation probability p with critical point p_c ≈ 0.593 highlighted, real-time cluster detection using union-find algorithm, automatic identification of percolating (spanning) clusters, color-coded display (regular clusters in blue, percolating cluster in green), step-by-step site addition for observing percolation process, automatic fill animation with speed control, random reset for exploring different configurations at same probability, comprehensive statistics (cluster count, maximum cluster size, max cluster ratio, percolation status), and real-time phase state indicator (subcritical p < p_c, critical p ≈ p_c, supercritical p > p_c). Educational content covers percolation theory (site occupation, cluster formation, connectivity emergence), phase transition concepts (subcritical fragmented phase, critical point with fractal clusters, supercritical connected phase), critical exponents and universality (β = 5/36, ν = 4/3, γ = 43/18), applications in epidemiology (disease outbreak thresholds, epidemic spreading), materials science (conductive composites, porous media), ecology (habitat fragmentation, species migration), network science (robustness, failure thresholds), and historical context (Broadbent and Hammersley 1957 gas mask research). Interactive features: click to add individual sites, auto-fill animation, grid size selection, color customization, cluster highlighting, responsive design. Perfect for statistical physics students, researchers in complex systems, epidemiology educators, and materials science instructors teaching phase transitions. Multi-language support (en, zh, es, fr, de, ru, pt).
Poincaré Section: Dimension Reduction - 庞加莱截面降维可视化
Interactive Poincaré section visualization for understanding dimension reduction through sampling in continuous dynamical systems. Features include multiple driven systems (driven damped pendulum, driven Duffing oscillator, rotating pendulum), real-time numerical integration using RK4 method, automatic Poincaré point collection at section plane crossings (φ = φ₀), configurable section phase, transient skip period, and maximum point count, continuous trajectory visualization alongside discrete Poincaré points, automatic dynamics analysis (period-1 fixed points, period-n orbits, quasiperiodic invariant circles, chaotic strange attractors), statistical analysis (mean, standard deviation of θ and ω), fractal dimension estimation via box-counting, and comprehensive educational content covering Poincaré section theory (stroboscopic sampling, dimension reduction from 3D to 2D), interpretation of Poincaré map patterns (single point = period-1, n points = period-n, closed loop = quasiperiodic, fractal cloud = chaos), applications in physics (particle accelerators, plasma confinement, celestial mechanics), biology (cardiac rhythms, neural oscillations, circadian rhythms), engineering (mechanical vibrations, electrical circuits, control systems), and mathematics (bifurcation theory, chaos theory, ergodic theory), and historical context (Henri Poincaré's 19th century work on the three-body problem). Interactive features: start/stop simulation, reset with new initial conditions, adjustable point size and visualization options, real-time statistics display, automatic pattern recognition, and responsive design. Perfect for chaos theory students, nonlinear dynamics researchers, physics educators, and mathematics instructors teaching dynamical systems. Multi-language support (en, zh, es, fr, de, ru, pt).
Phase Space: Vector Fields & Flow - 相空间向量场可视化
Interactive phase space visualization for exploring dynamical systems ẋ = f(x) through vector fields and flow trajectories. Features include multiple classic systems (linear system, Van der Pol oscillator, Duffing oscillator, Lotka-Volterra predator-prey, damped pendulum), real-time RK4 numerical integration, interactive trajectory initiation by clicking anywhere in phase space, vector field visualization with adjustable grid density and arrow scaling, pan and zoom capabilities, parameter sliders for dynamic system exploration, equilibrium point detection and display, stability analysis with real-time feedback, multiple simultaneous trajectory tracking with distinct colors, and comprehensive educational content covering phase space theory, equilibrium point classification (source, sink, saddle, center, spiral), stable and unstable manifolds, applications in physics (classical mechanics, celestial mechanics), biology (population dynamics, neural networks), engineering (control systems, circuit analysis), and economics (market dynamics), and historical context (Henri Poincaré's 19th century foundational work). Interactive features: pause/resume simulation, clear trajectories, customizable vector field display, real-time state information display, multi-system comparison, and responsive design. Perfect for dynamics students, physics/engineering researchers, mathematics educators, and nonlinear dynamics enthusiasts. Multi-language support (en, zh, es, fr, de, ru, pt).
Sankey Diagram Generator
Interactive Sankey diagram generator for visualizing flow, energy transfers, and data relationships with customizable nodes and links. Features include drag-and-drop data input, preset templates (energy flow, budget allocation, user journey, supply chain), real-time D3.js rendering with d3-sankey layout algorithm, node dragging for layout customization, hover highlighting with flow values, multiple color schemes (by category, gradient flow, single color), responsive SVG visualization, and comprehensive educational content covering history (Matthew Sankey's 1898 invention for steam engine efficiency), applications (energy auditing, material flow analysis, financial flows, website analytics, supply chain, epidemiology), and the conservation principle. Interactive features: add/remove/edit links dynamically, color scheme switching, metrics dashboard (total nodes, links, flow), tabular data view with percentages, and tooltip information display. Perfect for data analysts, economists, researchers, and operations managers working with flow data, conversion funnels, budget allocation, and resource optimization. Multi-language support (zh, en, es, fr, de, ru, pt).
Option Greeks Visualizer
Interactive Black-Scholes option pricing visualizer with 3D option price surface, Delta/Gamma/Theta/Vega/Rho heatmaps, live parameter controls, and educational interpretation for finance students, traders, and quants.