Bypassing dynamical systems: A simple way to get the box-counting dimension of the graph of the Weierstrass function

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In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number x, by W(x)= ∑ₙ₌₀⁺∞ λⁿ (2 πNbⁿx), where λ and Nb are two real numbers such that 0 <λ<1, Nb∈ and λNb > 1, using a sequence a graphs that approximate the studied one.