To implement datenwolfdatenwolf's suggestion to perturb curves with Perlin noise to give that "hand-drawn" look and feel, here's one way to use one-dimensional Perlin noise for the perturbation:
fBm = With[{permutations = Apply[Join, ConstantArray[RandomSample[Range[0, 255]], 2]]}, Compile[{{x, _Real}}, Module[{xf = Floor[x], xi, xa, u, i, j}, xi = Mod[xf, 16] + 1; xa = x - xf; u = xa*xa*xa*(10.0 + xa*(xa*6.0 - 15.0)); i = permutations[[permutations[[xi]] + 1]]; j = permutations[[permutations[[xi + 1]] + 1]]; (2 Boole[OddQ[i]] - 1)*xa*(1.0 - u) + (2 Boole[OddQ[j]] - 1)*(xa - 1)*u], "CompilationTarget" -> "WVM", RuntimeAttributes -> {Listable}]]; handdrawn[fun_, fr_, divisor_, color_, at_] := Graphics[{Directive[color, AbsoluteThickness[at]], BSplineCurve[Table[fun@x + fBm[fr x]/(5 divisor), {x, 0.01, 10, .1}]]}] I had previously used the one-dimensional Perlin noise routine in this answerthis answer.
In any event, here's a stripped-down version of chris's plot:
Show[ handdrawn[{#, 1.5 + 10 (Sin[#]^2/Sqrt[#]) Exp[-(# - 5)^2/2]} &, 30, 3, Darker[Cyan, 0.3], 3], handdrawn[{#, 3 + 10 (Sin[#]^2/Sqrt[#]) Exp[-(# - 7)^2/2]} &, 30, 3, White, 8], handdrawn[{#, 3 + 10 (Sin[#]^2/Sqrt[#]) Exp[-(# - 7)^2/2]} &, 30, 3, Darker[Red, 0.3], 3], handdrawn[{1, #} &, 30, 4, Black, 3], handdrawn[{#, 1} &, 30, 4, Black, 3], PlotRange -> All] 
As a bonus, here's a "hand-drawn" arrow routine you can use:
hArrow[{p_, q_}, fr_, divisor_] := Arrow[BSplineCurve[Table[p (1 - u) + q u + RotationMatrix[Arg[#1 + I #2] & @@ (p - q)].{u, fBm[fr u]/(5 divisor)}, {u, 0, 1, 1/50}]]] Replicating the comic strip in the OP with these routines (along with using the "Humor Sans" font) is left as an exercise.
