Simulating Stochastic Systems — Course Visualizations

Supplemental visualizations for Theodore Pavlic's Simulating Stochastic Systems at Arizona State University.

Lectures and other helpful short video tutorials can be found at TedPavlic's YouTube channel.

© 2026 Theodore P. Pavlic · MIT License

Monte Carlo Methods

Monte Carlo Explorer — interactive explainer

Estimate π by dartboard sampling and by dropping Buffon’s needles, measure a floor area from the crossings of a robot’s own trails, then integrate a function by averaging random draws, running repeated experiments to watch 95% confidence intervals accumulate around the true value.

Pseudorandom Number Generation

Pseudorandom Number Explorer — interactive explainer

Why do simulations use deterministic “random” numbers, and how are they made? Step through LCGs, combined generators, and the MRG32k3a inside production simulation tools, testing every stream for uniformity and independence – including the special angle that exposes RANDU's planes. Four further tabs turn that determinism into watermarks: parameter fingerprints, keyed re-seeding, and the tournament sampling behind Google's SynthID for LLM text, ending with a tiny in-page language model whose marked prose a keyed detector picks out of a twenty-one-key lineup.

Input Modeling

Input Analyzer — fit a distribution to sample data

Paste your own data and fit fourteen candidate distributions by maximum likelihood, ranked by AIC and BIC beside the histogram square-error criterion Arena uses, so you can watch the two disagree as you drag the bin slider. Chi-square, Kolmogorov–Smirnov, and Anderson–Darling tests come with bootstrap p-values that stay valid when the parameters were estimated from the same data, and the export panel writes the fit out as an Arena, Simio, AnyLogic, R, MATLAB, or SciPy expression.

Output Analysis

Power Explorer — statistical power by simulation and by formula

How many replications does it take to detect a difference? Pick a test — t, z, two-sample t, variance, proportion, chi-square, ANOVA, or regression slope — and watch the null and alternative sampling distributions separate as n grows, with α, β, and the tabled critical values labeled on the plot. A Monte Carlo engine estimates power by brute-force rejection counting and converges onto the exact noncentral-distribution answer, both directions of the analysis (power from n, minimum n for a target) work by formula and by search, and a live OC chart, a paired-comparison panel connecting correlation to common random numbers, and verified MATLAB/R/Python export round it out.

More from Ted Pavlic

Bio-Inspired AI & Optimization — Course Visualizations
Supplemental visualizations for a separate ASU graduate course on optimization and multi-agent control inspired by biological and physical systems: genetic algorithms, evolution strategies, swarm intelligence, and neural computation.
Topic Visualizers — Interactive Explainers
Interactive web demonstrations across science, mathematics, statistics, and engineering.
Notes, Documents, & Guides
Markdown-formatted notes and instructional guides on a variety of fundamental and applied science and engineering topics.
Lectures and short video tutorials on YouTube
Including the Office Hours playlist.