Math

Technology in Mathematics Education

Fall 2003, Volume 4, Issue 1

As part of the **Science and Its Applications Lecture Series**, **Erich Hauenstein** gave an excellent presentation on fractals. This edition explores that topic.

SELF-SQUARED FRACTAL CURVES

Self squared curves are curves in the complex plane which remain invariant under quadratic transformation. We examine the problem of iterates of the functions
, or
.
The following examples are computed by direct inverse iteration.

First define a function that allows a random choice between two possible inverses for a quadratic function.

returns +1 or -1.

Calculate based on this function:

Now pick a value for m. (Change the value of m to see other curves.)

(detail of curve is directly proportional to number of iterations)

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Editor: Scott S Albert

Meditating Mathematicians

M^{2}

Critical Thinking in Mathematics Education

Now an example with the form: