Activity Description Step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, and explore number patterns in sequences and geometric properties of fractals.

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Hilbert Curve Generator

Place in mathematics curriculum:

• 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 Hilbert curve. This activity would work well in groups of two to four for about twenty 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 ..."
• answer the question "What does it mean by the n-th case?"
• discuss infinity, length, finding patterns in numbers, ect.