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Fractal Movie: Lace
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About the Fractal Movie (Artistic):
When I was a small boy, my parents would take me to visit my great grandmother a couple of times a year. Her house was filled with lots of little things - like crystal paperweights, framed photographs, and porcelain figurines - the kinds of things that would instantly break if a small boy dared touch them. Although I was not too interested in these items, I was intrigued by what they were resting on. Under each was a small piece of lace hand-made by my great grandmother. Each piece of lace was similar, yet different - like snowflakes. The patterns in this movie look very much like my great grandmother's hand-made lace.
About the Fractal Movie (Technical):
The fractals in this movie are Julia-type fractals. Such fractals are more interesting for their overall shape than for their details at high magnification: thus, the screen images are at a magnification of only 3X.
The iteration threshold and image center are constant throughout the movie; motion is achieved by simply continuously varying the kernel – one of the three parameters that determine a fractal's basic shape (the only one of the three that can be varied in a movie).
Interestingly, there is virtually no interior or "solid" region to the fractals shown in the movie. The white in the fractals are the coordinates for which the fractal was almost - but not quite - solid (bounded). Mathematically, this is known as "Cantor dust".
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