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Math Help - Would the following geometric construction be considered a fractal?

  1. #1
    Member mfetch22's Avatar
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    Would the following geometric construction be considered a fractal?

    I'm somewhat fimmilliar with what a fractal "looks" like, but I am not fimmiliar with the exact or precise mathematical definition of a fractal. Thats why I'm posting this question here to get some clarification. Would the following construction be considered a fractal?

    [1] Draw a pentagon of any size.

    [2] Inscribe a pentagram inside the pentagon such that its 5 vertices are shared by the pentagon's 5 vertices, i.e. they have the same set of vertices.

    [3] In addition, consider the intersection of edges within the pentagram to be considered as vertices.

    [4] This set of intersection vertices (and the edges that connect them) will create a new, smaller, "upside-down" pentagon within the original pentagon (formed by the pentagram of course).

    [5] Within this pentagon create an "upside-down" pentagram just as described as in steps 2 and 3 (except that its upside down).

    [6] Follow step 4 just as described, except take note that this newer pentagon will be "right-side-up".

    [7] Repeat steps 1-7 using this newly constructed pentagon

    I'm going to attach an image to this post of the geometrical construction I have described above. I'm not sure if it falls under the definition of a fractal, and thats why I'm asking here. Thanks in advance.
    Attached Thumbnails Attached Thumbnails Would the following geometric construction be considered a fractal?-06-30-2010-image001.jpg  
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  2. #2
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    Quote Originally Posted by mfetch22 View Post
    I'm somewhat fimmilliar with what a fractal "looks" like, but I am not fimmiliar with the exact or precise mathematical definition of a fractal. Thats why I'm posting this question here to get some clarification. Would the following construction be considered a fractal?

    [1] Draw a pentagon of any size.

    [2] Inscribe a pentagram inside the pentagon such that its 5 vertices are shared by the pentagon's 5 vertices, i.e. they have the same set of vertices.

    [3] In addition, consider the intersection of edges within the pentagram to be considered as vertices.

    [4] This set of intersection vertices (and the edges that connect them) will create a new, smaller, "upside-down" pentagon within the original pentagon (formed by the pentagram of course).

    [5] Within this pentagon create an "upside-down" pentagram just as described as in steps 2 and 3 (except that its upside down).

    [6] Follow step 4 just as described, except take note that this newer pentagon will be "right-side-up".

    [7] Repeat steps 1-7 using this newly constructed pentagon

    I'm going to attach an image to this post of the geometrical construction I have described above. I'm not sure if it falls under the definition of a fractal, and thats why I'm asking here. Thanks in advance.
    Based on this, my answer is no:

    "A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature."
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