Bottom Classification - BioSonics, Inc

APPENDIX: FRACTALS
http://library.thinkquest.org/12740/
Classic geometry
• We live in 3-dimensional space (width, length, and depth).
• Plane (length and width) is 2-dimensional.
• Line (length) is 1-dimensional.
• Point is 0-dimensional.
• We can visualize an object in each of those dimensions.
Theoretical world of mathematicians
• Mathematicians created 4 and more dimensional space, which is difficult to visualize.
• Our universe can be presented as 4-dimensional space (3 geometrical dimensions & time).
• If we can have n- dimensions (integers), why not fractals?
Meaning of fractals
• A defining property of fractals is self-similarity, or the repetition of patterns at all scales.
• Another property that commonly exists in fractals is infinite complexity and detail.
• The formal definition of fractals involves fractional dimension, which itself is somewhat complex.
Example: Koch curve
• Start with line.
• Put a "kink" in the line segment, sort of making it more complex.
• Put a "kink" in each line segment.
• Continue this to get the Koch curve.
• Kinks cause the line segment to grow towards becoming a plane, since it is expanding "height-wise".
• However, this curve is not 2-dimensional.
• It's only FD = 1.2618.
• It is more than 1-dimensional, but not quite 2-dimensional.
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