Bsrhrki

Working with path decorations based on this solution provided by marmot I am searching for a possibility to change the decorations amplitude along the graph.

Having this plot

applying the mentioned decoration gives

which is exactly what the decoration is supposed to do.

In fact the required curve should look like this one:

The last output has been created by manually searching the correct positions to manipulate the amplitude which is a "trial and error" method. Changing the dimensions of the tikzpicture will then give a false result, fx

Now the basic idea is to provide a separate path (which can be made visible during development) to control the decorations amplitude along the original (blue) curve. In this case the control path (red) would be quite simple:

The control path could be interpreted as a factor to the decorations amplitude that can be set via decoration=amplitude=.

Assuming this method would be quite handy I'm a bit stunned it is not available in TikZ - or have I overseen it? And if it's not: how can I get the y-value of the control curve within the statestep portion of the decorations definition?

The MWE producing all the above graphs (even if not nicely coded in terms of efficiency and structural beauty):

documentclassarticle
usepackagetikz
usetikzlibrarycalc,decorations.pathmorphing

newcounterrandymark
newcommandamplitudesetter
pgfdeclaredecorationmark random y stepsstart
%
 statestart[width=+0pt,next state=step,persistent precomputation=pgfdecoratepathhascornerstruesetcounterrandymark0]
 stepcounterrandymark
 pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
 %
 statestep[auto end on length=1.5pgfdecorationsegmentlength,
 auto corner on length=1.5pgfdecorationsegmentlength,
 width=+pgfdecorationsegmentlength]
 stepcounterrandymarkamplitudesetter
 pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
 %
 statefinal
 stepcounterrandymark
 pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
 %
%

begindocument
begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 renewcommandamplitudesetter%
 pgfdecorationsegmentamplitude=0.75mm
 ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
 ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
 ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
 ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
 ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
 ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
 ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
 ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
 ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%
 
 draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 renewcommandamplitudesetter%
 pgfdecorationsegmentamplitude=0.75mm
 ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
 ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
 ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
 ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
 ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
 ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
 ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
 ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
 ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%
 
 draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 draw [red,thick,name=amplitudecontrol] (0,1) -- (2,1) -- (2,0) -- (7,0) -- (12,1) -- (25,1);
 draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
endtikzpicture

enddocument

Let me start by saying that I really like that question and am truly impressed by what you have achieved. Here is a proposal to address the scalability. Define a function that governs the amplitude,

varyingamp(x) = whatever you like

where x is the fraction of the decorated path (in order to ensure scalability). (Such a function has been used already here in order to have variable varying line widths. I would not at all be surprised if similar things had been used before.) This is the MWE.

documentclassarticle
usepackagetikz
usetikzlibrarycalc,decorations.pathmorphing

newcounterrandymark
%newcommandamplitudesetter
pgfdeclaredecorationmark random y stepsstart
%
 statestart[width=+0pt,next state=step,persistent precomputation=
 pgfdecoratepathhascornerstruesetcounterrandymark0]
 stepcounterrandymark
 pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
 %
 statestep[auto end on length=1.5pgfdecorationsegmentlength,
 auto corner on length=1.5pgfdecorationsegmentlength,
 width=+pgfdecorationsegmentlength]
 stepcounterrandymark%amplitudesetter
 pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
 %
 statefinal
 stepcounterrandymark
 pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
 %
%

pgfdeclaredecorationmark varying random y stepsstart
%
 statestart[width=+0pt,next state=step,persistent precomputation=
 pgfdecoratepathhascornerstruesetcounterrandymark0]
 stepcounterrandymark
 pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
 %
 statestep[auto end on length=1.5pgfdecorationsegmentlength,
 auto corner on length=1.5pgfdecorationsegmentlength,
 width=+pgfdecorationsegmentlength]
 stepcounterrandymark
 pgfmathsetmacromyfractionthepgfdecorationsegmentlength*valuerandymark/pgfdecoratedpathlength
 pgfmathsetmacromyamplitudevaryingamp(myfraction)
 %typeoutmyfraction,myamplitude
 pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*myamplitude*pgfdecorationsegmentamplitude
 %
 statefinal
 stepcounterrandymark
 pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
 %
%



begindocument
begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark varying random y steps,segment
length=1.5mm,amplitude=0.75mm,declare function=
varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]% 
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 draw[red,thick] plot[variable=x,domain=0:25,samples=101] (x,varyingamp(x/25));
 pgfmathsetseed2
 draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark varying random y
steps,segment length=0.75mm,amplitude=0.75mm,declare function=
varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]
 draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
 pgfmathsetseed2
 draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
 draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture
enddocument

The function is shown in red in the second plot. The third plot shows scalability. (Of course, you also need to rescale the segment lengths. Notice also that this decoration has discrete steps, so if you have a strongly varying function but only a few steps, the function may not be fully "appreciated" since it only gets evaluated at a few points.)