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Chaos and Fractals

Chaos and Fractals. Seth Drebitko, and Michael Runyon. Iteration. The action or process of repeating such as a procedure in which repetition of a sequence of operations yields results successively closer to a desired outcome. A Natural iteration. The Perfect Fern Leaf.

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Chaos and Fractals

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  1. Chaos and Fractals Seth Drebitko, and Michael Runyon

  2. Iteration The action or process of repeating such as a procedure in which repetition of a sequence of operations yields results successively closer to a desired outcome

  3. A Natural iteration The Perfect Fern Leaf

  4. Iterations in computing Program using numerical iterations in the search for new Mersenne Prime Numbers.

  5. Mathematical iterations The MengerSpounge

  6. Fractals A curve or geometric figure, each part of which has the same statistical character as the whole.

  7. A Natural Fractal Uniquely Predictable Snowflakes

  8. Fractals in Design Useful in modeling structures in which similar patterns recur at progressively smaller scales.

  9. Mathematical Fractals Koch Snowflake

  10. Mandelbrot set Both a specific fractal and class of fractal. A Mandelbrot set marks the points on a complex plane.

  11. Mandelbrot’s in Nature RomanescoCalibrese (Cauliflower)

  12. Mandelbrot’s in math • Colors in Mandelbrot sets are used to highlight specific regions. • The colors show the number of iterations until a given point falls within the set. • You may also want to highlight particularly unique areas generated.

  13. Mandelbrot’s in Computing Nearly all forms of computer languages are capable of computing and rendering a Mandelbrot set despite being one of the most complex shapes in mathematics.

  14. Julia set A set of complex numbers that do not converge to any limit when a given mapping is repeatedly applied to them. In some cases the result is a connected fractal set.

  15. Julia’s in Nature Crop Circles Created in a field.

  16. Julia’s in math

  17. Julia Sets in Design Julia sets are often used in the creation of computer generated artwork.

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