The TI-83 has a sort of stairstep program built in. This material is from page 17-8 of the TI-83 Plus Guidebook (English version), where stairstep diagrams are called "Cobweb Attractors."

1. Press [MODE]. Select Seq and the default mode settings. Press [2nd][FORMAT]. Select Web format and the default format settings.

2. Press [Y=]. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y=K X (1-X):

   
   u(n)=Ku(n-1)(1-u(n-1))
   u(nMin)=.01
   
   

   (Remark: The book uses K for our variable rho. The lower-case u is the [2nd] function on the [7] key.)

3. Press [2nd][QUIT] to return to the home screen, and then store 2.9 to K.

4. Press [WINDOW]. Set the window variables.

   nMin=0	Xmin=0	Ymin=-.26
   nMax=10	Xmax=1	Ymax=1.1
   PlotStart=1	Xscl=1	Yscl=1
   PlotStep=1

5. Press [TRACE] to display the graph, and then press [RightArrow] to trace the cobweb.

Remark: Here's what the screen looked like after I followed all these directions and then pressed the right-arrow key about 25 times.