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
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)
Editor: Scott S Albert
Critical Thinking in Mathematics Education
Now an example with the form: