First of all, isn't that just the most adorable critter?

When the caterpillar is done feeding it will usually change color a bit, turning a reddish brown, especially along the back.

Under natural conditions, imperial caterpillars pupate several inches to a foot or more deep in the soil.  As caterpillars are not built for burrowing, it takes them quite along time to get down to where they want to go.  It is relatively easy to provide them with a container of soil, any loose soil will do, but it should not be very moist.  If you give them only 6-8 inches to work with that will be fine.  The container and soil should be left undisturbed for a full two weeks.  After that, I recommend carefully sifting through the soil to locate the pupa.  I have found that leaving the pupa in place in the soil leads to survival problems because it is hard to keep the soil in a natural condition when in an artificial container.  It ends up being too dry or too wet, and the pupa may perish.  Another option that works every bit as well is to put the caterpillar into a small plastic container with only 1/2 inch of soil, close it with a ventilated lid, and put it someplace dark and quiet.  In a short time the caterpillar will give up trying to dig deeply and simply transform into a pupa on the surface of the soil.  For what to do once you have a pupa, please email me directly at <personal data hidden> and I'll get into the lengthy description of the process via regular email.