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
M2
Critical Thinking in Mathematics Education
Now an example with the form: