# Brownian motion. From random steps to stock prices.

Twelve paced conversations build a stock-price model one idea at a time. Begin with a fair coin and discover how independent movements create a spread that scales with the square root of time.

Explore fixed sampled paths, normal distribution slices, drift and volatility. Compare additive dollar moves with geometric Brownian motion, then examine log returns, mean versus median and consistent time units.

These are educational model illustrations, not live market data or forecasts. This premium lesson has its own access setting covering the interactive and all twelve conversations.

Canonical page: https://21ifm.com/quant/brownian-motion

## Explore

- [Continue to Itô’s extra term](https://21ifm.com/quant/curvature-lift)
- [Gaussian foundations](https://21ifm.com/ai/gaussian)