Instructions for Creating the Stair-Step Fractal

First Iteration: Follow steps 1-4 to create the first iteration of the Stair-step Fractal

  STEP 1: Take a piece of graph paper and fold it in half. (Hamburger fold)
STEP 2: With the folded edge facing towards you, measure 1/4 of the way in from the right edge of the paper and make a cut 1/2 way up the paper. Do the same thing from the left edge of the paper. You should now have a center flap.
STEP 3: Fold the center flap up to make a crease. Fold the center flap the other way to make a crease in the other direction.
STEP 4: Open the paper completely and lay flat on the table. Pull the center flap up. While pulling the center flap up, fold the paper in half (the same hamburger fold from step 1).
Second Iteration:
To complete the second iteration, fold the paper in half. The flap from the first iteration should be inside the hamburger fold.
Repeat STEPS 2-3 from the first iteration but this time you will measure 1/8 of the way in from the first cuts you made.
Repeat STEP 4 from the first iteration. When you unfold your paper you should see a total of 6 cuts and 6 crease marks which create three flaps. Pull the three flaps up. While pulling the flaps up, fold the paper in half.

Third Iteration: Repeat the process again for the third iteration.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.