Cut-out sets, fractal voids and cosmic structure

Details Cut-out sets, fractal voids and cosmic structure Cut-out sets, fractal voids and cosmic structure

2006-03-21

arxiv.org/abs/astro-ph/0603572v1

PhysicaD223:248-255,2006

Astronomy and Astrophysics

Astrophysics

16 pages

Scientific paper

10.1016/j.physd.2006.09.021

"Cut-out sets" are fractals that can be obtained by removing a sequence of disjoint regions from an initial region of d-dimensional euclidean space. Conversely, a description of some fractals in terms of their void complementary set is possible. The essential property of a sequence of fractal voids is that their sizes decrease as a power law, that is, they follow Zipf's law. We prove the relation between the box dimension of the fractal set (in d <= 3) and the exponent of the Zipf law for convex voids; namely, if the Zipf law exponent e is such that 1 < e < d/(d-1) and, in addition, we forbid the appearance of degenerate void shapes, we prove that the corresponding cut-out set has box dimension d/e (d-1 < d/e < d). We explore the application of this result to the large scale distribution of matter in cosmology, in connection with ``cosmic foam'' models.

Affiliated with

Also associated with

No associations

Rating

Cut-out sets, fractal voids and cosmic structure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cut-out sets, fractal voids and cosmic structure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cut-out sets, fractal voids and cosmic structure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-301656