The Jurassic Park Fractal

In this assignment we will learn how to make the Jurassic Park fractal. This fractal got this name because various stages of it it were drawn in the book Jurassic Park, by Michael Crichton. It is also called the dragon curve or dragon fractal.

The fractal can be produced in the following way. Start by drawing a vertical line segment. Make a note of the starting (e.g., top) and ending point of the segment. Next, rotate it 90 degrees (counterclockwise) about the end point, and draw together the original image and the rotated image. To continue, mark the ending point of the rotated image. Rotate the entire image 90 degrees about that point, and combine the original with the rotated image. This process can be repeated as many times as desired. To help you perform the process, note that the ending point of the original image gets matched with the starting point of the rotated image.

Here are pictures of the first 15 steps. In each picture the original is drawn in blue and the rotated image in red. Each successive image was shrunk to make it fit inside the same size square. However, the thickness of the lines is always the same; that is why it appears that the picture is being filled in. The picture at the top of the page was made by performing the process until the 15th step.

Building the fractal in Geometer's Sketchpad: Follow the following steps.

  1. Draw a vertical line segment and label the top point.
  2. Double click on the bottom point to select it as the rotation center, highlight the entire drawing, and rotate it 90 degrees.
  3. Hide the rotation point, select the non-labelled end point as the rotation center, highlight the entire drawing, and rotate 90 degrees.

You can repeat the final step as many times as you wish.

Problem 1. Perform 15 iterations of the process above to get a good dragon fractal. You may wish to shrink your original line segment as you get further along in the process.

Problem 2. Make a table giving how many line segments are in the drawing at each stage. For example, at the first stage there is 1 segment and at the second state there are 2 segments.

An alternative method to build the fractal is to use paper folding. This method is fairly easy to use for the first few steps, but it soon becomes impossible to continue. See http://math.rice.edu/~lanius/frac/jurra.html for a description of how to do the folding.