This is the graph of a function constructed as follows. Let [math]g(x)= \vert x \vert[/math] on [math]-1\leq x \leq 1[/math] and continue g to the real axis by making it 2-periodic. For [math]n=0,1,2\dots [/math] we now define [math]g_n(x)=\left(\frac{3}{4}\right)^n g(4^n x)[/math]. Finally define [math]f[/math] by [math]f(x)=\sum_{n=0}^{\infty}g_n(x)[/math]. This function is continuous on the real axis but nowhere differentiable.[br]Below you can se the graph of [math]f_N(x)=\sum_{n=0}^{N}g_n(x)[/math]. Change [math]N[/math] to get more summands.