15: Fractals
Fractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties.
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- 15.3: Fractal Dimension
- In addition to visual self-similarity, fractals exhibit other interesting properties. For example, notice that each step of the Sierpinski gasket iteration removes one quarter of the remaining area. If this process is continued indefinitely, we would end up essentially removing all the area, meaning we started with a 2-dimensional area, and somehow end up with something less than that, but seemingly more than just a 1-dimensional line.
Thumbnail: Zoom in of the Mandelbrot set (Public Domain; Simpsons contributor via Wikipedia )