Curve Stitching

In this project, you will create a mathematical art design and explore its variations. (Click the picture to see an animation.)
Curve stitching design being drawn line by line in each quadrant

This design uses straight lines to make shapes that look curved and is sometimes sewn with thread or drawn on paper. Here are some examples of and variations on this design made with string, computers, pencils on paper, and even pencils glued together:

Talk with Your Partner

  1. With your partner discuss how to make this design. Develop an algorithm that will generate the first quadrant of the design and then use abstraction to extend the design to the other quadrants.

  1. Write a Snap! program to generate the design.

    Click for a hint about setting up the design.

    Below is a partial table of coordinates for the first quadrant of the design, showing which points on the y-axis are joined to which points on the x-axis.
    axes with first quadrant of design

    31b8e172-b470-440e-83d8-e6b185028602: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:31b8e172-b470-440e-83d8-e6b185028602

    Click for a suggestion about how to start in Snap!

    There are many possible approaches to this problem. One approach could use the for block:
    for (i)=(0) to (15)

If There Is Time…

  1. Using the same principles, create a surrounding frame for your design.
    Curve stitching design with its perimeter frame

    Both the original curve and the frame are made of four quarter-pictures.

Take It Further…

  1. Add another copy of the design slanted at 45° as shown below.
    8 spiked curve stitching design

    Want a mathematical hint?

    You could use the Pythagorean Theorem:
    First quadrant triangle with hypotenuse 1 in a unit circle Application of Pythagorean Theorem to triangle with hypotenuse 1 using algebra to show that other sides are each square root(2)/2

  1. Here are some more variations that employ color and more complex geometric arrangements. Create these and your own variations in Snap!.
    Colored 12 spike curve stitching design Multi-colored 8 spike curve stitching design in a perimeter frame Constellation of curve stitching design

  1. Use what you know about creating animations in Snap! to produce an animation based on this design. To allow for dynamic movements such as rotations, you will need to devise a completely different way of creating your design than using fixed coordinates.

    Want to see an example?

    This animation explores the artistic concept of “negative space” by using a grid of rotating copies of the design. How would you revise your program to generate animations like this?
    A 6 by 4 grid of curve stitching designs rotating to reveal the negative space of the underlying background