Six views on Monte Carlo estimation, in pure Python [OC] Visualization

What This Visualization Shows

This data visualization displays "Six views on Monte Carlo estimation, in pure Python [OC]" and provides a clear visual representation of the underlying data patterns and trends. The visualization focuses on Hi everyone,

Sharing a visualization of Monte Carlo methods I put together. All six panels are generated from a single pure-Python module I wrote (no NumPy, no SciPy, no compiled extensions), so every number you see comes from actual code running the algorithms, not hand-plotted data.

What's in each panel:

* **1 - pi via unit square.** 2,000 random points; the fraction inside the quarter circle times 4 converges to pi. * **2 - convergence.** Running estimate vs sample count (log-x), with a +-1 sigma band. It tightens the way you'd expect from the central limit theorem. * **3 - Buffon's needle.** Dropping needles on parallel lines, the crossing probability gives pi via 2L / (D . P). Slower convergence than the unit square, but a nice independent estimator. * **4 - error decay.** |estimate - pi| on log-log. The dashed line is the O(1/sqrt N) theoretical rate, and the observed error tracks it closely. * **5 - MC integration.** Integral of sin(x) over \[0, pi\] by uniform random sampling. True value is 2; the MC estimate sits right on it. * **6 - 2D random walk.** Six independent diffusion trajectories, 500 steps each, showing the spread you get from symmetric random motion.

The point of doing it in pure Python isn't speed, it's readability: every estimator above is a short function you can open and read top to bottom, which is what made it easy to visualize each one honestly.

Tools: Python + matplotlib. Repo with the actual implementations: [https://github.com/Furox88/cognitive-discovery-system](https://github.com/Furox88/cognitive-discovery-system)

Happy to dig into how any of the panels were computed. Which estimator surprised you, or which would you want to see at higher sample counts?, which allows us to understand complex relationships and insights within the data through visual storytelling.

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