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This article deals with applications of Voronin's universality theorem forthe Riemann zeta-function $\zeta$. Among other results we prove that everyplane smooth curve appears up to a small error in the curve generated by thevalues $\zeta(\sigma+it)$ for real $t$ where $\sigma\in(1/2,1)$ is fixed. Inthis sense, the values of the zeta-function on any such vertical line providesan atlas for plane curves. In the same framework, we study the curvature ofcurves generated from $\zeta(\sigma+it)$ when $\sigma>1/2$ and we show thatthere is a connection with the zeros of $\zeta'(\sigma+it)$. Moreover, weclarify under which conditions the real and the imaginary part of thezeta-function are jointly universal.

Spirals of Riemann's Zeta-Function --Curvature, Denseness, and Universality--