Mathematik
Interaktive Visualisierungen mathematischer Konzepte
105 visualizations
IFS Iterated Function System (Barnsley Fern)
Interactive IFS visualization using affine transform families with probabilities. Adjust A_i, b_i, p_i, point count density, and color by transform, iteration time, or local density to observe self-similar fractal fern growth
Schumpeterian Business Cycles - Innovation-Driven Multi-Cycle Dynamics
Interactive visualization of Joseph Schumpeter's theory of innovation-driven business cycles. Explore the superposition of three cycles: Kitchin (3 years), Juglar (9 years), and Kondratieff (57 years). Understand creative destruction, innovation clusters, wave interference patterns, and historical examples from steam engines to AI technology
Kondratieff Wave - Long Economic Cycle Theory Visualization
Interactive visualization of the Kondratieff Wave (康波周期) economic cycle theory. Explore 50-60 year technological-financial-institutional supercycles with logarithmic linear model (lnYt = α + βt + ΣγiDi + εt), HP filtering (λ=10000), five historical waves from 1782-present, current position analysis for 2026 in Wave 5 Depression phase, and projections for Wave 6 driven by AI + New Energy + Life Sciences
Atomic Habits - Compound Effect & Habit Formation Visualization
Interactive visualization of James Clear's Atomic Habits theory. Explore compound effects (1.01^365 vs 0.99^365), growth curves with plateau breakthrough, identity voting model, four laws of behavior change, and the two-minute rule for task decomposition
Fermat's Principle - Light Path Optimization
Interactive visualization of Fermat's Principle demonstrating how light finds the path of least time. Explore Snell's Law derivation, path variations showing δL = 0, and time maps with adjustable refractive indices. Applications in optics, atmospheric refraction, and seismology
Fogg Behavior Model - B = M × A × P
Interactive exploration of BJ Fogg's Behavior Model from Stanford. Understand behavior change through the formula B = M × A × P (Behavior = Motivation × Ability × Prompt). Visualize how actions occur above the action line, explore three types of prompts (Spark, Facilitator, Signal), and discover applications in habit formation, product design, and behavioral science
Fractal Chaos Systems - Self-Similarity and Non-Integer Dimensions
Explore the fascinating world of fractals and chaotic systems with interactive visualizations including Mandelbrot set explorer, Julia sets with parameter controls, Barnsley fern (iterated function systems), fractal tree demonstrating self-similarity, and box-counting dimension calculation for estimating non-integer (Hausdorff) dimensions
Feigenbaum Constants Visualization - Universal Chaos Constants
Explore the Feigenbaum constants (δ ≈ 4.669201609) - universal constants discovered by Mitchell Feigenbaum in 1978 that describe the convergence rate of period-doubling bifurcations in chaotic systems, demonstrating universality across different maps (logistic, sine, tent)
Game Theory Simulator - Inadequate Equilibria
Explore core concepts from "Inadequate Equilibria" by Eliezer Yudkowsky through interactive game simulations. Play Prisoner's Dilemma, Stag Hunt coordination game, and watch population dynamics evolve. Discover why systems get stuck in suboptimal Nash equilibria, understand coordination problems, and learn when to defer to expertise vs. when to question systems. Features color-coded payoff matrices, Nash equilibrium highlighting, strategy evolution graphs, and real-world examples from the book
Tit-for-Tat Strategy Lab
Iterated Prisoner's Dilemma simulator focused on Tit-for-Tat, cooperation dynamics, and noise
Game Theory: Zero-Sum and Positive-Sum Games
Explore the fundamentals of game theory through interactive visualizations of zero-sum games (matching pennies) and positive-sum games (prisoner's dilemma), including Nash equilibrium, payoff matrices, and strategy evolution
Entropy and the Second Law of Thermodynamics
Interactive visualization of entropy, the second law of thermodynamics, particle diffusion, Maxwell's demon, and how energy injection maintains order in systems