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Thread: Loci vs. Fractal

  1. #1
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    Loci vs. Fractal

    Is there a connection between loci​ [in math] to fractal (patterns) [in physics]?!
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    Re: Loci vs. Fractal

    "Loci" (plural of "locus") simply means sets of points that satisfy some condition. A "locus" can be as simple as a line or a circle. A set is "fractal" if it has fractional "generalized dimension" such as the "box counting dimension" or "information dimension".
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    An example of mine

    Can be a connection between loci to Snowflake shape?!
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    Re: An example of mine

    Quote Originally Posted by policer View Post
    Can be a connection between loci to Snowflake shape?!
    Not, perhaps, in the sense that you seem to be getting at. I'm sure you could find a fractal that has the appearance of a snowflake. But a fractal does not cover an area, nor does it contain straight lines. There is always a "texture" to the fractal: a straight line would break down into an infinitely detailed collection of "dots."

    -Dan
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    Re: An example of mine

    Quote Originally Posted by topsquark View Post
    Not, perhaps, in the sense that you seem to be getting at. I'm sure you could find a fractal that has the appearance of a snowflake. But a fractal does not cover an area, nor does it contain straight lines. There is always a "texture" to the fractal: a straight line would break down into an infinitely detailed collection of "dots."

    -Dan
    I'm not sure I agree with this. I'm pretty sure the perimeter of a Koch snowflake is continuous.
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    Forum Admin topsquark's Avatar
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    Re: An example of mine

    Quote Originally Posted by romsek View Post
    I'm not sure I agree with this. I'm pretty sure the perimeter of a Koch snowflake is continuous.
    Really? My bad then. Thanks for the catch.

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