Abstract
It is possible to visualize the Cosmic Web as an inter-connected network of one dimensional filaments, two dimensional sheets and three dimensional volume filling structures, which we refer to as clusters. We have considered the Local Dimension D, as a tool to locally quantify the shape in the neigbourhood of different galaxies along the Cosmic Web. We expect D ~ 1, 2 and 3 for a galaxy located in a filament, sheet and cluster respectively. We have analysed the Cosmic Web using Local Dimension in a LCDM N-body simulations and to a three dimensional volume limited galaxy sample from the Sloan Digital Sky Survey (SDSS). We now want to test for luminosity, colour and morphology dependence of the galaxy structures (filaments, sheets and clusters) in three dimensional volume of SDSS data.
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