Variance is Fractal

[TomCowley]

Let's see.. a few definitions for fractal:

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A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale.

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A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.

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A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry.

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Ok, so you are talking about a concept as though it's a geometric shape. Marijooana is good, mmmm-kay?

Let's list common properties of fractals:

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A fractal often has the following features:

It has a fine structure at arbitrarily small scales.

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Fail, poker actions are discrete.

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It is too irregular to be easily described in traditional Euclidean geometric language.

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Fail, even if I give you the benefit of the doubt translating to a graph, since sample variance is hardly irregular.

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It is self-similar (at least approximately or stochastically).

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Fail, sample variance curves aren't self-similar.

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It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

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Fail, obviously.

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It has a simple and recursive definition.

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Fail, obviously.

So I ask again, what the hell are you talking about when you say variance is fractal?