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In this paper we examine functions in the disc algebra $\mathcal{A}(D)$ andthe polydisc algebra $\mathcal{A}(D^I)$, where $I$ is a finite or countablyinfinite set. We prove that, generically, for every $f \in \mathcal{A}(D)$ thecontinuous periodic functions $u=Ref|_{\mathbb{T}}$ and $\tilde{u} =Imf|_{\mathbb{T}}$ are nowhere differentiable on the unit circle $\mathbb{T}$.Afterwards, we generalize this result by proving that, generically, for every$f \in \mathcal{A}(D^I)$, where $I$ is as above, the continuous periodicfunctions $u=Ref|_{\mathbb{T}^I}$ and $\tilde{u} = Imf|_{\mathbb{T}^I}$ have nodirectional derivatives at any point of $\mathbb{T}^I$ and every direction $v\in \mathbb{R}^I$ with $\|v\|_{\infty}=1$.

Topological genericity of nowhere differentiable functions in the disc and polydisc algebras