Angular projections of fractal sets

Author: Durrer R.   Eckmann J.-P.   Sylos Labini F.   Montuori M.   Pietronero L.  

Publisher: Edp Sciences

E-ISSN: 1286-4854|40|5|491-496

ISSN: 0295-5075

Source: EPL (EUROPHYSICS LETTERS), Vol.40, Iss.5, 2010-03, pp. : 491-496

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Abstract

We discuss various questions which arise when one considers thecentral projection of three-dimensional fractal sets (galaxy catalogs)onto the celestial globe.The issues are related to how fractal such projections look.First we show that the lacunarity in the projection can be arbitrarilysmall. Further characteristics of the projected set —in particular scaling— dependsensitively on how the apparent sizes of galaxies are taken intoaccount. Finally, we discuss the influence of the opacity of galaxies.Combining these ideas, seemingly contradictory statements aboutlacunarity and apparent projections canbe reconciled.