| | | | | | | | | | | | | | | | | | | | | | | | | | S | u | b | j | e | c | t | : | | W | h | a | t | | i | s | | a | | f | r | a | c | t | a | l | ? | | | | | | | | | | | | | | | | | | | | | | | | | | |
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| | Q2: | What is a fractal? What are some examples of fractals? |
| | A2: | A fractal is a rough or fragmented geometric shape that can be |
| subdivided in parts, each of which is (at least approximately) a reduced-size |
| copy of the whole. Fractals are generally self-similar and independent of |
| scale. |
| There are many mathematical structures that are fractals; e.g. Sierpinski |
| triangle, Koch snowflake, Peano curve, Mandelbrot set, and Lorenz attractor. |
| Fractals also describe many real-world objects, such as clouds, mountains, |
| turbulence, coastlines, roots, branches of trees, blood vesels, and lungs of |
| animals, that do not correspond to simple geometric shapes. |
| Benoit B. Mandelbrot gives a mathematical definition of a fractal as a set |
| of which the Hausdorff Besicovich dimension strictly exceeds the topological |
| dimension. However, he is not satisfied with this definition as it excludes |
| sets one would consider fractals. |
| According to Mandelbrot, who invented the word: "I coined fractal from the |
| Latin adjective fractus. The corresponding Latin verb frangere means "to |
| break:" to create irregular fragments. It is therefore sensible - and how |
| appropriate for our needs! - that, in addition to "fragmented" (as in fraction |
| or refraction), fractus should also mean "irregular," both meanings being |
| preserved in fragment." (The Fractal Geometry of Nature, page 4.) |
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