Plot a function defined on terms on its value on an interval

Question

Besicovitch-Ursell family of fractal functions uses the following auxiliary definition:
$phi(x) = 2x$ on $[0,1/2]$.
$phi(-x) = phi(x+1)$ otherwise.
Is there a way to plot this in Mathematica?

Ulrich Neumann · Accepted Answer

Perhaps

[Phi][x_] :=Which[0 <= x <= 1/2, 2 x, x < 0, [Phi][1 + x], True, [Phi][1 -x]]
Plot[[Phi][x], {x, -2, 2}]

is what you are looking for?

Roger Bagula · Answer

Also called Knopp function in Edgar's other book:
f[x_] := 2*x /; 0 <= x <= 1/2
f[x_] := 2 - 2*x /; 1/2 < x <= 1

ff[x_] = f[Mod[Abs[x], 1]];
Plot[f[Mod[Abs[x], 1]], {x, 0, 2}]

Plot a function defined on terms on its value on an interval

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