Fractals and Recursions

Discussion in 'Off-Topic' started by silver 2039, Oct 21, 2006.

  1. silver 2039

    silver 2039 Deity

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    What the hell are fractals and recursions? I can't figure out these definations. Damn wikipeida. I need to know in terms of math.

     
  2. Erik Mesoy

    Erik Mesoy Core Tester / Intern

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    A fractal is an infinitely complex shape usually generated by means of (infinite) recursion. Recursion is the repetition of something (usually pattern-generating).

    Take a look at the Koch Snowflake.

    Recursion is, in this example, the process of putting a triangle on the middle third of each line, then putting a triangle on the middle third of each line, then putting a triangle on the middle third of each line, then...

    A fractal is the result of this process.

    Not all recursions lead to fractals and not all fractals are recursively generated, but most are.
     
  3. silver 2039

    silver 2039 Deity

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    So something like the Sierpinsiki's traingle?
     
  4. Erik Mesoy

    Erik Mesoy Core Tester / Intern

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    Yes, except that it removes instead of adding.

    An infinitely detailed Koch snowflake has a finite area (it's bounded inside a sphere) but an infinitely long border.

    An infinitely detailed Sierpinski triangle has zero area, an outside border equal to the normal triangle, and infinite total border length.
    (Math: The limit of (3/4)^n as n approaches infinity is zero.)
     
  5. Syterion

    Syterion Voodoo Economist

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    Recursion is when an instance of something causes another instance of it to be called, like a function in programming that calls itself. A fractal is a shape made by repeating shapes in a pattern, often recursively.
     
  6. CruddyLeper

    CruddyLeper Unworshipped Deity

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    Fractal = shape with fractional dimensions.

    You can think of something with 2 dimensions like a square. Or 3 dimensions like a cube.

    Now try to imagine what happens when a shape has 2.3 dimensions.

    "To iterate is human. To recurse is divine".

    Imagine a simple program that takes a number, doubles it, and outputs the answer. Then it runs again with the result from the last cycle.

    This cycling or "looping" is a crucial feature of recursion. Iteration is doing the same thing over and over - recursion is similar but can take it's data from the output of the last cycle.

    Best book I have yet come across on the subject is "Fractals Everywhere" by Dr Michael Barnesley. Although that's more about iterated systems than recursion.
     
  7. pboily

    pboily fingerlickinmathematickin

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