# brownian.motion()

## Demonstration of Brownian Motion

### Yihui Xie & Lijia Yu / 2017-04-04

Brownian motion, or random walk, can be regarded as the trace of some cumulative normal random numbers.

The location of the next step is `current location + random Gaussian numbers`

, i.e.,

`$$x_{k+1} = x_{k} + rnorm(1)$$`

`$$y_{k + 1} = y_{k} + rnorm(1)$$`

where `\((x, y)\)`

stands for the location of a point.

```
library(animation)
ani.options(interval = 0.05, nmax = 150)
brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow",
main = "Demonstration of Brownian Motion")
```

plot of chunk demo-a