A Shoshone camus root gathering basket (ISU museum). Note the beautiful twist of the vertical willow reeds. 

We can model the twisting vertical reeds in the camus basket as a three-dimensional spiral. Sprial symmetry is an important concept in many Native American knowledge systems.  A two-dimensional spiral can be modeled in polar coordinates: Here we set the distance from the center, radius r, equal to the angle (theta) of the radius: r = theta. As the angle sweeps around the plot, the radius moves farther from the center.
Now to make a three-dimensional spiral, or "helix." Here are some examples turning along a length measured in radians:

8 turns in 8Pi radians


2 turns in 8Pi radians


1 turn in 8Pi radians

Which one is closest to the helix we see in the basket above? 

Click here to download Maple file for helix

Imagine the vertical length is time, and the turns are turns of the seasons. What would the events in your life look like if you plotted them along a helix?

Now we can try our hand at simulating the basket. Go to the simulation window and experiment with the following parameters:  depth, width, twist, lines across width (n), lines across length (m).

The twist factor is the number of turns along the length of the basket.