How to plot this cascaded/waterfall python-type plot using TikZ

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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10
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I would like to make a plot of this equation



P_n = fracn^aa!exp[-n]


for different n. How can I use this cascaded style from the TikZ/PGF examples, to plot P_n (y-axis) with a (x-axis), for different values of n (z-axis: the depth). The x-variable is integers, so I need a bar chart.



This post has received an answer here, but I wanted to resurrect the questions since the image style I would like is shown in this link. Instead of a continuous plot, I would have bar charts, but I would like an enveloping line for each waterfall plot that is tangential to all of the bar charts to clearly show the distributions.




tikz-pgf tikz-styles




share|improve this question
























    up vote
    10
    down vote

    favorite
    3












    I would like to make a plot of this equation



    P_n = fracn^aa!exp[-n]


    for different n. How can I use this cascaded style from the TikZ/PGF examples, to plot P_n (y-axis) with a (x-axis), for different values of n (z-axis: the depth). The x-variable is integers, so I need a bar chart.



    This post has received an answer here, but I wanted to resurrect the questions since the image style I would like is shown in this link. Instead of a continuous plot, I would have bar charts, but I would like an enveloping line for each waterfall plot that is tangential to all of the bar charts to clearly show the distributions.




    tikz-pgf tikz-styles




    share|improve this question






















      up vote
      10
      down vote

      favorite
      3









      up vote
      10
      down vote

      favorite
      3






      3





      I would like to make a plot of this equation



      P_n = fracn^aa!exp[-n]


      for different n. How can I use this cascaded style from the TikZ/PGF examples, to plot P_n (y-axis) with a (x-axis), for different values of n (z-axis: the depth). The x-variable is integers, so I need a bar chart.



      This post has received an answer here, but I wanted to resurrect the questions since the image style I would like is shown in this link. Instead of a continuous plot, I would have bar charts, but I would like an enveloping line for each waterfall plot that is tangential to all of the bar charts to clearly show the distributions.




      tikz-pgf tikz-styles




      share|improve this question












      I would like to make a plot of this equation



      P_n = fracn^aa!exp[-n]


      for different n. How can I use this cascaded style from the TikZ/PGF examples, to plot P_n (y-axis) with a (x-axis), for different values of n (z-axis: the depth). The x-variable is integers, so I need a bar chart.



      This post has received an answer here, but I wanted to resurrect the questions since the image style I would like is shown in this link. Instead of a continuous plot, I would have bar charts, but I would like an enveloping line for each waterfall plot that is tangential to all of the bar charts to clearly show the distributions.





      tikz-pgf tikz-styles





      share|improve this question











      share|improve this question




      share|improve this question










      asked Aug 7 at 17:55









      Sid

      590213




      590213




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          11
          down vote



          accepted










          Thanks for asking a new question! Note also that if you have more rows you'll need to extend the definition of mycolor accordingly.



          EDIT: Simplified the code and made it (as I think) much easier to customize by



          • storing the function in myf. That is, if you have a different function, you'll only to adjust this bit.

          • adding explanations in the code.

          • replacing the single pgfplotsinvokeforeach loop in a double loop over the parameters (a and n in your question).

          Thats the code.



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^X/X!)*exp(-Y);
          defamax5 %<- maximal a
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfmathtruncatemacroNumRows6
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          UPDATE: If you want to go to higher values of a and/or n, it might be worthwhile to rewrite your function, which is in the above of the form



          (huge/large)*small


          in the form 



          (not so huge/large)*((not so huge)*small) .


          Here is an example. I do not claim that it is optimal, that's the first thing that came to my mind. Alternatives include to take the logarithms of subexpressions and taking the exponential at the end. (I compile with lualatex.)



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          Just for fun: if you wish to have bars instead of Gaussians (Gauss was a mathematician and in a bar one gets good drinks ;-), and also do not want the envelop touch the axis, do



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          pgfmathsetmacromyBarWidth0.2
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(1,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black] coordinates (-myBarWidth+X,Y,0)
          (-myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,0); 
          myplot

          xdefmyLstmyLst (amax,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,tension=0.2,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer






















          • You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
            – Sid
            Aug 7 at 18:08










          • Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
            – Sid
            Aug 7 at 18:50










          • image link is broken for me
            – qwr
            Aug 7 at 21:36










          • @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
            – Sid
            Aug 7 at 22:19










          • @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
            – marmot
            Aug 7 at 22:29










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          1 Answer
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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          11
          down vote



          accepted










          Thanks for asking a new question! Note also that if you have more rows you'll need to extend the definition of mycolor accordingly.



          EDIT: Simplified the code and made it (as I think) much easier to customize by



          • storing the function in myf. That is, if you have a different function, you'll only to adjust this bit.

          • adding explanations in the code.

          • replacing the single pgfplotsinvokeforeach loop in a double loop over the parameters (a and n in your question).

          Thats the code.



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^X/X!)*exp(-Y);
          defamax5 %<- maximal a
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfmathtruncatemacroNumRows6
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          UPDATE: If you want to go to higher values of a and/or n, it might be worthwhile to rewrite your function, which is in the above of the form



          (huge/large)*small


          in the form 



          (not so huge/large)*((not so huge)*small) .


          Here is an example. I do not claim that it is optimal, that's the first thing that came to my mind. Alternatives include to take the logarithms of subexpressions and taking the exponential at the end. (I compile with lualatex.)



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          Just for fun: if you wish to have bars instead of Gaussians (Gauss was a mathematician and in a bar one gets good drinks ;-), and also do not want the envelop touch the axis, do



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          pgfmathsetmacromyBarWidth0.2
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(1,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black] coordinates (-myBarWidth+X,Y,0)
          (-myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,0); 
          myplot

          xdefmyLstmyLst (amax,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,tension=0.2,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer






















          • You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
            – Sid
            Aug 7 at 18:08










          • Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
            – Sid
            Aug 7 at 18:50










          • image link is broken for me
            – qwr
            Aug 7 at 21:36










          • @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
            – Sid
            Aug 7 at 22:19










          • @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
            – marmot
            Aug 7 at 22:29














          up vote
          11
          down vote



          accepted










          Thanks for asking a new question! Note also that if you have more rows you'll need to extend the definition of mycolor accordingly.



          EDIT: Simplified the code and made it (as I think) much easier to customize by



          • storing the function in myf. That is, if you have a different function, you'll only to adjust this bit.

          • adding explanations in the code.

          • replacing the single pgfplotsinvokeforeach loop in a double loop over the parameters (a and n in your question).

          Thats the code.



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^X/X!)*exp(-Y);
          defamax5 %<- maximal a
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfmathtruncatemacroNumRows6
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          UPDATE: If you want to go to higher values of a and/or n, it might be worthwhile to rewrite your function, which is in the above of the form



          (huge/large)*small


          in the form 



          (not so huge/large)*((not so huge)*small) .


          Here is an example. I do not claim that it is optimal, that's the first thing that came to my mind. Alternatives include to take the logarithms of subexpressions and taking the exponential at the end. (I compile with lualatex.)



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          Just for fun: if you wish to have bars instead of Gaussians (Gauss was a mathematician and in a bar one gets good drinks ;-), and also do not want the envelop touch the axis, do



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          pgfmathsetmacromyBarWidth0.2
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(1,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black] coordinates (-myBarWidth+X,Y,0)
          (-myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,0); 
          myplot

          xdefmyLstmyLst (amax,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,tension=0.2,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer






















          • You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
            – Sid
            Aug 7 at 18:08










          • Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
            – Sid
            Aug 7 at 18:50










          • image link is broken for me
            – qwr
            Aug 7 at 21:36










          • @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
            – Sid
            Aug 7 at 22:19










          • @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
            – marmot
            Aug 7 at 22:29












          up vote
          11
          down vote



          accepted







          up vote
          11
          down vote



          accepted






          Thanks for asking a new question! Note also that if you have more rows you'll need to extend the definition of mycolor accordingly.



          EDIT: Simplified the code and made it (as I think) much easier to customize by



          • storing the function in myf. That is, if you have a different function, you'll only to adjust this bit.

          • adding explanations in the code.

          • replacing the single pgfplotsinvokeforeach loop in a double loop over the parameters (a and n in your question).

          Thats the code.



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^X/X!)*exp(-Y);
          defamax5 %<- maximal a
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfmathtruncatemacroNumRows6
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          UPDATE: If you want to go to higher values of a and/or n, it might be worthwhile to rewrite your function, which is in the above of the form



          (huge/large)*small


          in the form 



          (not so huge/large)*((not so huge)*small) .


          Here is an example. I do not claim that it is optimal, that's the first thing that came to my mind. Alternatives include to take the logarithms of subexpressions and taking the exponential at the end. (I compile with lualatex.)



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          Just for fun: if you wish to have bars instead of Gaussians (Gauss was a mathematician and in a bar one gets good drinks ;-), and also do not want the envelop touch the axis, do



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          pgfmathsetmacromyBarWidth0.2
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(1,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black] coordinates (-myBarWidth+X,Y,0)
          (-myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,0); 
          myplot

          xdefmyLstmyLst (amax,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,tension=0.2,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here






          share|improve this answer














          Thanks for asking a new question! Note also that if you have more rows you'll need to extend the definition of mycolor accordingly.



          EDIT: Simplified the code and made it (as I think) much easier to customize by



          • storing the function in myf. That is, if you have a different function, you'll only to adjust this bit.

          • adding explanations in the code.

          • replacing the single pgfplotsinvokeforeach loop in a double loop over the parameters (a and n in your question).

          Thats the code.



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^X/X!)*exp(-Y);
          defamax5 %<- maximal a
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfmathtruncatemacroNumRows6
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          UPDATE: If you want to go to higher values of a and/or n, it might be worthwhile to rewrite your function, which is in the above of the form



          (huge/large)*small


          in the form 



          (not so huge/large)*((not so huge)*small) .


          Here is an example. I do not claim that it is optimal, that's the first thing that came to my mind. Alternatives include to take the logarithms of subexpressions and taking the exponential at the end. (I compile with lualatex.)



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(0,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black,smooth,
          domain=-0.4:0.4] (x+X,Y,myf(X,Y)*exp(-SteepNess*x^2));
           
          myplot

          xdefmyLstmyLst (amax+1,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here



          Just for fun: if you wish to have bars instead of Gaussians (Gauss was a mathematician and in a bar one gets good drinks ;-), and also do not want the envelop touch the axis, do



          documentclass[border=3.14mm]standalone
          usepackagepgfplots
          % if you plot more than 6 rows, you'll need to extend the following 
          % definition accordingly. alternatively you could work with color maps here.
          newcommandmycolor[1]ifcase#1
          white%0
          or
          blue%1
          or
          red%2
          or
          green!50!black%3
          or
          yellow%4
          or
          purple%5
          or
          orange%6
          or
          cyan%7
          or
          brown%8
          or
          red!50!black%9
          or
          blue!50!black%10
          fi
          pgfplotssetcompat=1.16
          begindocument
          tikzsetdeclare function=myf(X,Y)=((Y)^(X/2)/X!)*((Y)^(X/2)*exp(-Y));
          defamax7 %<- maximal a
          pgfmathtruncatemacroNumRows7
          pgfmathsetmacromyBarWidth0.2
          defSteepNess48 % <- this value determines the shape of the Gaussians. if 
          % you have different function myf, you may need to adjust it
          begintikzpicture
          beginaxis[width=9cm,
           set layers=standard,
           domain=0:amax+1,
           samples y=1,
           view=4020,
           xmin=-1,ymax=amax+3,
           %hide axis,
           %xtick=empty, ytick=empty, ztick=empty,
           clip=false
          ]
          pgfplotsinvokeforeachNumRows,...,1 % your n will now be stored in #1
           draw [on layer=background, gray!20] (axis cs:0,#1,0) -- (axis cs:amax+1,#1,0);

          pgfmathtruncatemacroXmaxNumRows*amax
          foreach Y in 1,...,NumRows
          xdefmyLst(1,Y,0) % initialize the list for envelopes
          foreach X in 1,...,amax

          pgfmathsetmacromymaxmyf(X,Y) %<- this is not absolutely necessary
          xdefmyLstmyLst (X,Y,mymax) % build up the list
          edefmyplotnoexpandaddplot3 [fill=mycolorY,fill opacity=0.4,
          line width=0.7pt,on layer=main,draw=black] coordinates (-myBarWidth+X,Y,0)
          (-myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,myf(X,Y)*exp(-SteepNess*0^2))
          (myBarWidth+X,Y,0); 
          myplot

          xdefmyLstmyLst (amax,Y,0) % complete the list
          edefmyplotnoexpandaddplot3[smooth,tension=0.2,fill=mycolorY,fill opacity=0.1] coordinatesmyLst;
          % if you do not want to have the envelope, just comment the following out
          myplot

          endaxis
          endtikzpicture
          enddocument


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Aug 7 at 23:23

























          answered Aug 7 at 18:03









          marmot

          54.6k459117




          54.6k459117











          • You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
            – Sid
            Aug 7 at 18:08










          • Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
            – Sid
            Aug 7 at 18:50










          • image link is broken for me
            – qwr
            Aug 7 at 21:36










          • @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
            – Sid
            Aug 7 at 22:19










          • @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
            – marmot
            Aug 7 at 22:29
















          • You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
            – Sid
            Aug 7 at 18:08










          • Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
            – Sid
            Aug 7 at 18:50










          • image link is broken for me
            – qwr
            Aug 7 at 21:36










          • @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
            – Sid
            Aug 7 at 22:19










          • @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
            – marmot
            Aug 7 at 22:29















          You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
          – Sid
          Aug 7 at 18:08




          You're welcome. This looks great! Is it possible to add a waveform that envelopes each of the coloured distributions?
          – Sid
          Aug 7 at 18:08












          Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
          – Sid
          Aug 7 at 18:50




          Fantastic! These waterfall plots are quite common in python's matplotlib package. Hopefully, many others can make use of this for a more native plot to LaTeX!
          – Sid
          Aug 7 at 18:50












          image link is broken for me
          – qwr
          Aug 7 at 21:36




          image link is broken for me
          – qwr
          Aug 7 at 21:36












          @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
          – Sid
          Aug 7 at 22:19




          @marmot, if you look closely, some of the envelopes have some kink along the waveform. Also if you change a for, say, 10, then the waveforms don't follow the height of the bars.
          – Sid
          Aug 7 at 22:19












          @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
          – marmot
          Aug 7 at 22:29




          @Sid You can adjust the tension of these plots. Or one would have to resort to more elaborate means, at the moment it is really just a smooth interpolation of the maxima with tension=1. And I cannot plot your function to amax=10, how do you compile it? I get an ! Arithmetic overflow. error.
          – marmot
          Aug 7 at 22:29

















           

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