The random walk is a way to create a path based on random decisions at junctions. If you’ve played a **procedurally generated video game**, including major examples like ** Minecraft** and

*Stardew Valley*as well as cult favorites like

*Spelunky*and

*Dwarf Fortress*, you’ve encountered a random walk in the form of a dungeon or terrain made this way in the programming. More @

**Popular Mechanics**

2D Random Walk math helps game programmers to plot interesting pathways in games like Minecraft Dungeons. (above)

# Plot a 2D Random Walk

There are 4 choices:

UP, DOWN, LEFT, RIGHT

Note: This 2D random walk is limited to a 1-unit step length and right angles turns.

Set the Random Number Spinner **here** to 4 and generate 8 random moves of 1 unit and plot the moves on the worksheet(below).

1 up

2 down

3 right

4 left

Printable Worksheet:** 2D Random Walk Worksheet**

**Here are 5 X 8 step 2D Random Walks.**

**These 2D Random Walks do not look like the path taken by a drunk mathematician.**

# Drunken Mathematician

**This looks like a drunken mathematician and the 2D Random Walk for a drunk mathematician would look like pathways shown below with variable step lengths and turns from 0-360°.**

All Random Walks can be mathematically modeled. eg. Go to MIT **here**. This math can be quite complicated (See** here**.) But all we want to do is plot the 2D Random Walk to see random numbers in action.