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Fractal Movie: Endless M
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About the Fractal Movie (Artistic):
This movie illustrates one of the fundamental characteristics of fractals: self similarity – the property that a suitably-selected portion of the image, when appropriately magnified, looks like the whole image. When played in a continuous loop, the 3-second movie gives the illusion of a never-ending succession of Mandelbrot fractals or “bugs” forming, growing, and disappearing off screen. In fact, there is a never-ending succession of bug fractals at higher and higher magnifications, but this movie just shows two of the fractals. I liked this animation sequence so much that I selected it as the default movie sequence that plays in the splash screens of the Fractal Viewer and Fractal Odyssey applications.
About the Fractal Movie (Technical):
This fractal movie shows an enlarged section of the stinger of the Mandelbrot fractal or “Mandelbrot bug”. The stinger, when magnified, is seen to be lumpy. When further magnified, these lumps are seen to be smaller versions of the Mandelbrot bug. I selected one of the lumps as the start of the movie rather than the original Mandelbrot bug so the stinger line would always run across the full width of the movie image (the stinger is only visible on the left of the bug at magnification = 1). With one of the lumps on the stinger sufficiently magnified as to clearly be the Mandelbrot bug (magnification = 83), the image is centered on a point to the left of the bug where the next lump will appear. As the magnification increases, the visible bug grows and shifts to the right. But before the visible bug disappears off screen, another lump on the stinger becomes visible at the center of the movie image. As magnification continues to increase, the newly formed bug continues to grow, itself shifting to the right. The clip ends with the new bug in the same position as the first bug (magnification = 4150). Thus, when played as a continuous loop, the movie gives the illusion of a never-ending succession of bugs.
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