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What is a Fractal?


My very first contact with fractals was in the Schiapol Airport in The Netherlands. Inside the terminal, there were three displays of a term I had never heard of before: fractals. One was a design made of tiles inlaid in the floor of the airport. Seemed to have no beginning and no end and the closer you looked, the more complex the design seemed. Another display was drawn on the ceiling of the terminal: the border between East and West Germany, a very intricate and complex tracing. The plaque that described it stated that as the scale grew larger, so did the length of the line dividing the two Germanies. The last display was a large fish tank, an aquarium. The plaque stated that the paths of the fish through the water was a form of a fractal. I didn't understand the term "fractal" yet, but I was interested. That interest is the reason for these pages.

The title of this creation is GEODE. It was taken from the web page published by the Physics Department of the University of Wisconsin.


Original, Physics Dept, Univ of Wisconsin
http://sprott.physics.wisc.edu/fractals/collect/
(288.3 KB)

This is a reduced image to speed loading (40% reduction). Click on the image to see the original, full-scale image, but it will be slow loading.


What is a fractal?

The dictionary definition of a fractal is: "Geom. an extremely irregular line or surface formed of an infinite number of similarly irregular sections: fractals have fractional dimension between one and two, or between two and three, dimensions" Clear? Not to me, it isn't. Here are reduced images, with the method used to reduce the image indicated. The first was reduced by "zooming" out.


¼ sized original


Sample Reduction(L) Scale Reduction(R)


Zoom Reduction
(26.5 KB)



Here is another, .JPG format this time, instead of .GIF:

Titled "Chain of Events" (195.8 KB)



And one more, first the 30% reduced original:

Titled "Blue" (in 24 colors) (249.4 KB)

And the same image reduced to two colors, with an 80% reduction in byte size -- notice how much faster it loads. But also notice the quality of the image.
Two Color Blue (39.9 KB)


This last image is the original Blue cropped and rotated but not reduced:

(32.8 KB)

Conclusion

Fractals with a dimension between one and two are objects (concepts?) between a line and a surface and fractals with a dimension between two and three are objects between a plane surface and a three-dimensional object. The above conceptual drawings attempt to show that. Slightly more clear than when you first came to this site? Hope so.

Would you like to see some more fractals? The remainder have also been reduced in size for faster loading. Come right along to Fractals (continued)



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