Teaching Materials/Pop-Up Fractals

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Title Making a Pop-Up Fractal
Description The original instructions for constructing a pop-up fractal were retrieved from FractalFoundation. This resource simply acts as a jumpstart for our further exploration.
Concept Although it seems difficult, the process of making a pop-up fractal is actually quite simple.
Goals
Required Materials – Rectangular piece of paper

– Ruler

– Pencil

– Scissors

Procedure .

Steps to Construct the Fractal

Preparing the Paper: Starting with a rectangular piece of paper, fold the paper vertically.

Step 1: Use a ruler to find the midpoint of the folded paper.

Step 2: Draw a straight line from the middle of the folded edge to the midpoint. Cut on the line.

Step 3: Fold the top flap over. Then take the flap and invert it so that it is folded inside itself. The paper should now look like a series of steps. If you open the entire piece of paper like a book, the flap that was folded over and inverted should appear to be popping out.

For Future Iterations: Repeat this process starting from Step 1, for as many iterations as you like. Find the midpoint of the section, and continue the steps. Remember to treat the new sections as individual pieces of paper! This is a fractal, so this process repeats itself for further iterations, just on a different scale.

For visual reference, see the image to the right.

PopUpSteps.gif


PopUpStep2.png PopUpStep3.png PopUpStep4.png
PopUpStep5.png PopUpStep6.png PopUpStep7.png


The image to the right shows the first 3 iterations of the pop-up fractal. Notice that the steps are perfectly reiterated, as they should be in a fractal. The process is carried out at increasingly smaller scales, creating smaller "steps" in the side of the paper. Iterations.gif
Other Notes

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