I have this graphic: 
But I would like this:
without the yellow curve, of course.
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2 2 Answers
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There are likely other ways, but this is one of the simplest:
curve = {x, Sqrt[x^2 + 1]}; nv = Normalize[Cross[D[curve, x]]]; With[{n = 30, h = 1/10}, ParametricPlot[{curve, curve + h Sin[n x] nv} // Evaluate, {x, -2, 2}]] 
answered Mar 5, 2018 at 7:52
J. M.'s missing motivation
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This is another simple way. The idea is to plot a $\cos$ function, by changing its frequency and amplitude, you can adjust the twisting needed
f1[x_]:=Sqrt[x^2+1] data=Table[z0= 1/10 Cos[50 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; Show[Plot[f1[x],{x,-2,2},AxesOrigin->{0,.7}], ListLinePlot[data,PlotStyle->Red]] 
This one has smaller frequency
data=Table[z0=1/10 Cos[20 x];z1=f1[x];{x,z0+z1},{x,-2,2,.02}]; 
Manipulate[ data = Table[z0 = h Cos[w x]; z1 = f1[x]; {x, z0 + z1}, {x, -2, 2, .02}]; Show[Plot[f1[x], {x, -2, 2}, AxesOrigin -> {0, .7}], ListLinePlot[data, PlotStyle -> Red]], {{h, .1, "amplitude"}, 0, .5, .01, Appearance -> "Labeled"}, {{w, 20, "frequency"}, 1, 100, 1, Appearance -> "Labeled"}, TrackedSymbols :> {h, w}, Initialization :> ( f1[x_] := Sqrt[x^2 + 1]; ) ] 
PlotStyleto change, e.g, line colors... $\endgroup$