High Quality Content by WIKIPEDIA articles! In mathematics,
effective dimension is a modification of Hausdorff dimension and
other fractal dimensions which places it in a computability theory
setting. There are several variations (various notions of effective
dimension) of which the most common is effective Hausdorff
dimension. Dimension, in mathematics, is a particular way of
describing the size of an object (contrasting with measure and
other, different, notions of size). Hausdorff dimension generalizes
the well-known integer dimensions assigned to points, lines,
planes, etc. by allowing one to distinguish between objects of
intermediate size between these integer-dimensional objects. For
example, fractal subsets of the plane may have intermediate
dimension between 1 and 2, as they are "larger" than lines or
curves, and yet "smaller" than filled circles or rectangles.
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