Fractalize your Mind
May 15th 2006 04:42
What are Fractals?
Fractals are way cool. A fractal (from the Latin fractus, meaning broken, or fractured) is a shape that is recursively constructed. What does that mean? Well, it means that no matter how many times you magnify or shrink it, it will appear similar at all scales. If you think about that, it may occur to you that this means that fractals are infinitely complex (if it doesn't, don't worry, I'm an intellectual imposter).
Approximate fractals occur in natural systems over an extended, but finite scale. They exist in clouds, snowflakes, river networks, and blood vessels! Trees and ferns are fractals that exist in nature, and through modelling the branch of a fern using a recursive algorithm, we create a miniature replica of the whole (not identical, but similar).
The mathematics of fractals also have applications in art, music, medicine, seismology, cosmology, computer game design, and much more. Oh yeh, and they also show up in crop circles.
I'm not sure I know enough about all this (in fact I'm sure I don't), but it's interesting to see these patterns existing in nature, and throughout so many parts of our lives and ourselves. Kind of reminds me of the excrutiatingly beautiful nature of mathematics. It feel like we are moving towards God. But then that's nothing new.
'mandelbrot set'- a famous fractal(wikipedia)
Fractals are way cool. A fractal (from the Latin fractus, meaning broken, or fractured) is a shape that is recursively constructed. What does that mean? Well, it means that no matter how many times you magnify or shrink it, it will appear similar at all scales. If you think about that, it may occur to you that this means that fractals are infinitely complex (if it doesn't, don't worry, I'm an intellectual imposter).
Approximate fractals occur in natural systems over an extended, but finite scale. They exist in clouds, snowflakes, river networks, and blood vessels! Trees and ferns are fractals that exist in nature, and through modelling the branch of a fern using a recursive algorithm, we create a miniature replica of the whole (not identical, but similar).
the 'Julia set' (wikipedia)
I'm not sure I know enough about all this (in fact I'm sure I don't), but it's interesting to see these patterns existing in nature, and throughout so many parts of our lives and ourselves. Kind of reminds me of the excrutiatingly beautiful nature of mathematics. It feel like we are moving towards God. But then that's nothing new.
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Someone discovered, mathematically, that the most efficient antenna was one that was shaped fractally... so in the back of your cellphone, there may be a metal fractal acting as an antenna!