Hawai'i Space Grant Consortium, Hawai'i Institute of Geophysics and Planetology, University of Hawai'i, 1996

Running Water and Random Numbers
idea by A. Colleen Yows

To model the development of drainage basins by using random rolls of a number cube.

Key Words







oxbow lake

alluvial fan


flood plain

stream piracy

drainage basin



graph paper

number cube (one per group)


colored pencils

Streams and rivers have significantly altered the surfaces of Earth and Mars with channels and valleys as well as sedimentary deposits. Streams continuously change shape and orienation in response to the amount of water and sediment being carried in the channel. This activity investigates how streams may evolve on a planetary surface by simulating the development of streams and drainage basins using random rolls of a number cube.


Each group will need one piece of graph paper and one number cube.

Label the top of the paper "highlands" and the bottom of the paper "lowlands".

Place 20 pencil dots, randomly, on any intersections within the top five rows of the graph paper. Each dot represents a source of running water (for example, raindrops, spring water, melting snow, etc.)

Make a note somewhere that the:

1 & 2 on the cube means Right,

3 & 4 on the cube means Straight,

5 & 6 on the cube means Left.

Select one of the highest dots to begin. Then use the cube to determine randomly the flow direction, as described in these three examples:
  • If you throw a 1 or 2, then draw a line from the dot diagonally down to the right to the next intersection of lines.
  • If you throw a 3 or 4, then draw a line from the dot straight down to the next intersection of lines.
  • If you throw a 5 or 6, then draw a line from the dot diagonally down to the left to the next intersection of lines.

After you have drawn a line from the first dot, choose another dot at the highest level. Then throw the number cube and repeat step 5.

Repeat for all the dots. Always choose a dot at the highest level. This will help to keep the flow relatively even, at least at the beginning. In every case, you must choose the dot (water source) before tossing the cube to insure the randomness of the experiment.

After you have moved all of the dots at least once, go back to the highest line and continue rolling the cube and extending the lines in the proper directions.

Whenever one stream merges with another, the streams combine and travel as a single but larger system. Continue the stream with 2 or more lines, side-by-side, depending on how many lines have merged. Also, you now move this multiple-line stream a distance equivalent to the number of lines making up this system in the direction determined by the number cube. To keep this activity simple, when two separate streams merge, end that turn.

Example: A 3-line-wide stream merges with a 5-line-wide stream. End that turn at that point. On that line's next turn, you roll a 2. You would then draw an 8-line-wide stream diagonally down to the right 8 squares.

Continue choosing lines, rolling the cube, and extending lines until you come to the bottom of the paper. If time permits, tape another piece of graph paper onto the bottom and continue!

When you have finished drawing the drainage systems, label any features that you recognize such as: divides, meanders, tributaries, etc.

How many drainage basins did this activity produce?

Shade in each basin lightly with colored pencils and make up names for the principal rivers for easy referral.

Using a scale of 1 cm = 1 km,. determine the approximate area of each drainage basin and label your diagram with these values.

Compare your diagram with your classmates' diagrams. Did each diagram produce one kind of pattern from the original random points?

Locate any positions on your diagram where stream piracy might occur in the future as a result of flooding or some other erosional event.

Is it possible for this diagram to show meanders? Explain.

Is it possible for oxbow lakes to show up in this activity? Explain.

What new knowledge have you and your partner gained from this exercise?

Go to Running Water and Random Numbers Teacher pages.

Return to Gradation Activity Index.

Return to Hands-On Activities home page.