Activity Description Students work step-by-step through the generation of a different Hilbert-like Curve (a fractal made from deforming a line by bending it), allowing them to explore number patterns in sequences and geometric properties of fractals.

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Another Hilbert Curve Generator

Place in mathematics curriculum:

This activity can be used to:

• practice students' fraction manipulation skills
• practice students' pattern finding skills
• demonstrate the complexity of infinity
• motivate the ideas of self-similarity and recursion
• demonstrate fractal objects
• motivate the idea of a limit

This activity allows the user to step through the process of building a companion to the first Hilbert curve. This activity would work well in groups of two to four for about twenty to twenty-five minutes if you use the exploration questions and five minutes otherwise.

Preparations for this activity:

• give implicit directions on what they are to do. For example, "Today we are going to record data in the table on the worksheet and see if we can find a formula ... Then we will compare it to the original Hilbert curve..."
• answer the question "What does it mean by the n-th case?"
• discuss infinity, length, finding patterns in numbers, etc.