We show numerically that the roughness and growth exponents of a wide range of rough surfaces, such as random deposition with relaxation (RDR), ballistic deposition (BD) and restricted solidonsolid model (RSOS), are independent of the underlying regular (square, triangular, honeycomb) or random (Voronoi) lattices. In addition we show that the universality holds also at the level of statistical properties of the isoheight lines on different lattices. This universality is revealed by calculating the fractal dimension, loop correlation exponent and the length distribution exponent of the individual contours. We also indicate that the hyperscaling relations are valid for the isoheight lines of all the studied Gaussian and nonGaussian selfaffine rough surfaces. Finally using the direct method of Langlands et.al we show that the contour lines of the rough surfaces are not conformal invariant except when we have simple Gaussian free field theory with zero roughness exponent.
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