Online material

Appendix A: Supercluster data

In Table A.1 we present data on superclusters.

Appendix B: Minkowski functionals and shapefinders

For a given surface the four Minkowski functionals (from the first to the fourth) are proportional to the enclosed volume V, the area of the surface S, the integrated mean curvature C, and the integrated Gaussian curvature χ. Consider an excursion set F_φ0 of a field φ(x) (the set of all points where the density is higher than a given limit, φ(x) ≥ φ₀). Then, the first Minkowski functional is the volume of this region (the excursion set): (B.1)The second Minkowski functional is proportional to the surface area of the boundary δF_φ of the excursion set: (B.2)The third Minkowski functional is proportional to the integrated mean curvature C of the boundary: (B.3)where R₁(x) and R₂(x) are the principal radii of curvature of the boundary. The fourth Minkowski functional is proportional to the integrated Gaussian curvature (the Euler characteristic) of the boundary: (B.4)At high (low) densities this functional gives us the number of isolated clumps (void cavities) in the sample (Martínez & Saar 2002; Saar et al. 2007): (B.5)The first three functionals were used to calculate the shapefinders K₁ (planarity) and K₂ (filamentarity) (Sahni et al. 1998; Shandarin et al. 2004; Saar 2009) and their ratio, the shape parameter K₁/K₂. The smaller the shape parameter, the more elongated a supercluster is. We used morphological information about superclusters, and their visual appearance to classify them as filaments and spiders. As an example, we present in Fig. B.1 the sky distribution of galaxies in one filament-type and one spider-type supercluster (SCL 001 and SCL 019, respectively).

	Fig. B.1 Sky distribution of galaxies for the supercluster SCl 001 of filament morphology (upper panel), and for the supercluster SCl 019 of spider morphology (lower panel). Red dots correspond to galaxies with low SFR, log   SFR < −0.5, and blue dots to galaxies with high SFR, log   SFR ≥ −0.5.
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Appendix C: Quantiles of galaxy parameters in different samples.

© ESO, 2014