How do I dynamically draw an image?

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Suppose I have some two dimensional list. For example: 



list = Partition[Range[0, 48], 7];


And I have some function that assigns a colour to each entry of the list, but it takes a long time to execute. For example the following silly function:



f[n_] := With[val = Mod[FactorInteger[n! + 1][[1, 1]], 3], 
val /. 0 -> Blue, 1 -> Green, 2 -> Red]


This function $f$ calculates $p_n pmod3$, where $p_n$ is the smallest prime factor of $n! + 1$. The specific function however does not matter; the point is that it takes some time to be calculated. I want to draw an image of the list after $f$ is applied to every entry of the list. I can do this with the following piece of code: 



Image[Map[f, list, 2]]


On my laptop this takes about $31$ seconds. A resized output of this image is the following (but this picture is irrelevant for the question):



enter image description here



My question is: Is there some way to dynamically draw this picture such that each pixel is immediately drawn after it has been calculated? Maybe such that the pixels that have yet to receive their colour are drawn in another colour, e.g., white, black or grey.



I am interested in this because I am trying to generate images that are quite large for which my function $f$ can take up to hours to completely draw the image. I would like to have some feeling of how much longer it might take and if the correct thing is happening. Ideally the output would change like the following animation.



enter image description here






dynamic image







share|improve this question



























    up vote
    4
    down vote

    favorite












    Suppose I have some two dimensional list. For example: 



    list = Partition[Range[0, 48], 7];


    And I have some function that assigns a colour to each entry of the list, but it takes a long time to execute. For example the following silly function:



    f[n_] := With[val = Mod[FactorInteger[n! + 1][[1, 1]], 3], 
    val /. 0 -> Blue, 1 -> Green, 2 -> Red]


    This function $f$ calculates $p_n pmod3$, where $p_n$ is the smallest prime factor of $n! + 1$. The specific function however does not matter; the point is that it takes some time to be calculated. I want to draw an image of the list after $f$ is applied to every entry of the list. I can do this with the following piece of code: 



    Image[Map[f, list, 2]]


    On my laptop this takes about $31$ seconds. A resized output of this image is the following (but this picture is irrelevant for the question):



    enter image description here



    My question is: Is there some way to dynamically draw this picture such that each pixel is immediately drawn after it has been calculated? Maybe such that the pixels that have yet to receive their colour are drawn in another colour, e.g., white, black or grey.



    I am interested in this because I am trying to generate images that are quite large for which my function $f$ can take up to hours to completely draw the image. I would like to have some feeling of how much longer it might take and if the correct thing is happening. Ideally the output would change like the following animation.



    enter image description here






    dynamic image







    share|improve this question

























      up vote
      4
      down vote

      favorite









      up vote
      4
      down vote

      favorite











      Suppose I have some two dimensional list. For example: 



      list = Partition[Range[0, 48], 7];


      And I have some function that assigns a colour to each entry of the list, but it takes a long time to execute. For example the following silly function:



      f[n_] := With[val = Mod[FactorInteger[n! + 1][[1, 1]], 3], 
      val /. 0 -> Blue, 1 -> Green, 2 -> Red]


      This function $f$ calculates $p_n pmod3$, where $p_n$ is the smallest prime factor of $n! + 1$. The specific function however does not matter; the point is that it takes some time to be calculated. I want to draw an image of the list after $f$ is applied to every entry of the list. I can do this with the following piece of code: 



      Image[Map[f, list, 2]]


      On my laptop this takes about $31$ seconds. A resized output of this image is the following (but this picture is irrelevant for the question):



      enter image description here



      My question is: Is there some way to dynamically draw this picture such that each pixel is immediately drawn after it has been calculated? Maybe such that the pixels that have yet to receive their colour are drawn in another colour, e.g., white, black or grey.



      I am interested in this because I am trying to generate images that are quite large for which my function $f$ can take up to hours to completely draw the image. I would like to have some feeling of how much longer it might take and if the correct thing is happening. Ideally the output would change like the following animation.



      enter image description here






      dynamic image







      share|improve this question















      Suppose I have some two dimensional list. For example: 



      list = Partition[Range[0, 48], 7];


      And I have some function that assigns a colour to each entry of the list, but it takes a long time to execute. For example the following silly function:



      f[n_] := With[val = Mod[FactorInteger[n! + 1][[1, 1]], 3], 
      val /. 0 -> Blue, 1 -> Green, 2 -> Red]


      This function $f$ calculates $p_n pmod3$, where $p_n$ is the smallest prime factor of $n! + 1$. The specific function however does not matter; the point is that it takes some time to be calculated. I want to draw an image of the list after $f$ is applied to every entry of the list. I can do this with the following piece of code: 



      Image[Map[f, list, 2]]


      On my laptop this takes about $31$ seconds. A resized output of this image is the following (but this picture is irrelevant for the question):



      enter image description here



      My question is: Is there some way to dynamically draw this picture such that each pixel is immediately drawn after it has been calculated? Maybe such that the pixels that have yet to receive their colour are drawn in another colour, e.g., white, black or grey.



      I am interested in this because I am trying to generate images that are quite large for which my function $f$ can take up to hours to completely draw the image. I would like to have some feeling of how much longer it might take and if the correct thing is happening. Ideally the output would change like the following animation.



      enter image description here






      dynamic image




      dynamic image






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 1 hour ago









      J. M. is computer-less♦

      94.6k10294454




      94.6k10294454










      asked 2 hours ago









      Pjotr5

      349112




      349112




















          2 Answers
          2






          active

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          up vote
          2
          down vote













          If your data is stored as a matrix or an array, constructing a dynamic image of it is as simple as 



          arr = ConstantArray[-1, -1, -1, 40, 40];
          Dynamic[Image[arr, ImageSize -> 400]


          enter image description here



          Then run your program and assign the data to the array you already created. 



          Do[
           Pause @ 0.1;
           Part[arr, Sequence @@ nm] = RandomReal[1, 3];
           ,
           nm, RandomSample @ Tuples[Range @ 40, 2]
           ];


          enter image description here






          share|improve this answer



























            up vote
            2
            down vote













            Additionally to what Jason showed (using Dynamic) it's also possible to use Monitor for this.



            First let's prepare your input list (with a convenience size parameter side) and in addition prepare an extra result array needed for intermediate result and display purposes.



            side = 7;
            list = Partition[Range[0, side^2 - 1], side]
            result = Array[-1 &, side, side]
            Dimensions[result] == Dimensions[list]


            Now define the function we want to apply to each cell



            f[n_] := Mod[FactorInteger[n! + 1][[1, 1]], 3]

            colorfun[n_] := Switch[n, 0, Blue, 1, Green, 2, Red, _, Black]


            Here we split off the part which is used only for coloring as colorfun.



            Monitor[
             Do[result[[j, i]] = f@list[[j, i]], j, side, i, side],
             MatrixPlot[result, ColorFunctionScaling -> False, ColorFunction -> colorfun]
            ]


            This will update the result cells sequentially in a similar way to what you did with Map[,2] before. It's not very beautiful compared to a map but necessary so that Monitor can catch our intermediate results. Monitor will now display a continuously updated MatrixPlot of our result matrix while using our custom ColorFunction.



            Curious Addendum from my side: the updating sadly doesn't seem to work when using ParallelDo instead of Do. Does anybody have an idea to make that happen?






            share|improve this answer




















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              2 Answers
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              active

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              2 Answers
              2






              active

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              oldest

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              active

              oldest

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              up vote
              2
              down vote













              If your data is stored as a matrix or an array, constructing a dynamic image of it is as simple as 



              arr = ConstantArray[-1, -1, -1, 40, 40];
              Dynamic[Image[arr, ImageSize -> 400]


              enter image description here



              Then run your program and assign the data to the array you already created. 



              Do[
               Pause @ 0.1;
               Part[arr, Sequence @@ nm] = RandomReal[1, 3];
               ,
               nm, RandomSample @ Tuples[Range @ 40, 2]
               ];


              enter image description here






              share|improve this answer
























                up vote
                2
                down vote













                If your data is stored as a matrix or an array, constructing a dynamic image of it is as simple as 



                arr = ConstantArray[-1, -1, -1, 40, 40];
                Dynamic[Image[arr, ImageSize -> 400]


                enter image description here



                Then run your program and assign the data to the array you already created. 



                Do[
                 Pause @ 0.1;
                 Part[arr, Sequence @@ nm] = RandomReal[1, 3];
                 ,
                 nm, RandomSample @ Tuples[Range @ 40, 2]
                 ];


                enter image description here






                share|improve this answer






















                  up vote
                  2
                  down vote










                  up vote
                  2
                  down vote









                  If your data is stored as a matrix or an array, constructing a dynamic image of it is as simple as 



                  arr = ConstantArray[-1, -1, -1, 40, 40];
                  Dynamic[Image[arr, ImageSize -> 400]


                  enter image description here



                  Then run your program and assign the data to the array you already created. 



                  Do[
                   Pause @ 0.1;
                   Part[arr, Sequence @@ nm] = RandomReal[1, 3];
                   ,
                   nm, RandomSample @ Tuples[Range @ 40, 2]
                   ];


                  enter image description here






                  share|improve this answer












                  If your data is stored as a matrix or an array, constructing a dynamic image of it is as simple as 



                  arr = ConstantArray[-1, -1, -1, 40, 40];
                  Dynamic[Image[arr, ImageSize -> 400]


                  enter image description here



                  Then run your program and assign the data to the array you already created. 



                  Do[
                   Pause @ 0.1;
                   Part[arr, Sequence @@ nm] = RandomReal[1, 3];
                   ,
                   nm, RandomSample @ Tuples[Range @ 40, 2]
                   ];


                  enter image description here







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 53 mins ago









                  Jason B.

                  46.5k383179




                  46.5k383179




















                      up vote
                      2
                      down vote













                      Additionally to what Jason showed (using Dynamic) it's also possible to use Monitor for this.



                      First let's prepare your input list (with a convenience size parameter side) and in addition prepare an extra result array needed for intermediate result and display purposes.



                      side = 7;
                      list = Partition[Range[0, side^2 - 1], side]
                      result = Array[-1 &, side, side]
                      Dimensions[result] == Dimensions[list]


                      Now define the function we want to apply to each cell



                      f[n_] := Mod[FactorInteger[n! + 1][[1, 1]], 3]

                      colorfun[n_] := Switch[n, 0, Blue, 1, Green, 2, Red, _, Black]


                      Here we split off the part which is used only for coloring as colorfun.



                      Monitor[
                       Do[result[[j, i]] = f@list[[j, i]], j, side, i, side],
                       MatrixPlot[result, ColorFunctionScaling -> False, ColorFunction -> colorfun]
                      ]


                      This will update the result cells sequentially in a similar way to what you did with Map[,2] before. It's not very beautiful compared to a map but necessary so that Monitor can catch our intermediate results. Monitor will now display a continuously updated MatrixPlot of our result matrix while using our custom ColorFunction.



                      Curious Addendum from my side: the updating sadly doesn't seem to work when using ParallelDo instead of Do. Does anybody have an idea to make that happen?






                      share|improve this answer
























                        up vote
                        2
                        down vote













                        Additionally to what Jason showed (using Dynamic) it's also possible to use Monitor for this.



                        First let's prepare your input list (with a convenience size parameter side) and in addition prepare an extra result array needed for intermediate result and display purposes.



                        side = 7;
                        list = Partition[Range[0, side^2 - 1], side]
                        result = Array[-1 &, side, side]
                        Dimensions[result] == Dimensions[list]


                        Now define the function we want to apply to each cell



                        f[n_] := Mod[FactorInteger[n! + 1][[1, 1]], 3]

                        colorfun[n_] := Switch[n, 0, Blue, 1, Green, 2, Red, _, Black]


                        Here we split off the part which is used only for coloring as colorfun.



                        Monitor[
                         Do[result[[j, i]] = f@list[[j, i]], j, side, i, side],
                         MatrixPlot[result, ColorFunctionScaling -> False, ColorFunction -> colorfun]
                        ]


                        This will update the result cells sequentially in a similar way to what you did with Map[,2] before. It's not very beautiful compared to a map but necessary so that Monitor can catch our intermediate results. Monitor will now display a continuously updated MatrixPlot of our result matrix while using our custom ColorFunction.



                        Curious Addendum from my side: the updating sadly doesn't seem to work when using ParallelDo instead of Do. Does anybody have an idea to make that happen?






                        share|improve this answer






















                          up vote
                          2
                          down vote










                          up vote
                          2
                          down vote









                          Additionally to what Jason showed (using Dynamic) it's also possible to use Monitor for this.



                          First let's prepare your input list (with a convenience size parameter side) and in addition prepare an extra result array needed for intermediate result and display purposes.



                          side = 7;
                          list = Partition[Range[0, side^2 - 1], side]
                          result = Array[-1 &, side, side]
                          Dimensions[result] == Dimensions[list]


                          Now define the function we want to apply to each cell



                          f[n_] := Mod[FactorInteger[n! + 1][[1, 1]], 3]

                          colorfun[n_] := Switch[n, 0, Blue, 1, Green, 2, Red, _, Black]


                          Here we split off the part which is used only for coloring as colorfun.



                          Monitor[
                           Do[result[[j, i]] = f@list[[j, i]], j, side, i, side],
                           MatrixPlot[result, ColorFunctionScaling -> False, ColorFunction -> colorfun]
                          ]


                          This will update the result cells sequentially in a similar way to what you did with Map[,2] before. It's not very beautiful compared to a map but necessary so that Monitor can catch our intermediate results. Monitor will now display a continuously updated MatrixPlot of our result matrix while using our custom ColorFunction.



                          Curious Addendum from my side: the updating sadly doesn't seem to work when using ParallelDo instead of Do. Does anybody have an idea to make that happen?






                          share|improve this answer












                          Additionally to what Jason showed (using Dynamic) it's also possible to use Monitor for this.



                          First let's prepare your input list (with a convenience size parameter side) and in addition prepare an extra result array needed for intermediate result and display purposes.



                          side = 7;
                          list = Partition[Range[0, side^2 - 1], side]
                          result = Array[-1 &, side, side]
                          Dimensions[result] == Dimensions[list]


                          Now define the function we want to apply to each cell



                          f[n_] := Mod[FactorInteger[n! + 1][[1, 1]], 3]

                          colorfun[n_] := Switch[n, 0, Blue, 1, Green, 2, Red, _, Black]


                          Here we split off the part which is used only for coloring as colorfun.



                          Monitor[
                           Do[result[[j, i]] = f@list[[j, i]], j, side, i, side],
                           MatrixPlot[result, ColorFunctionScaling -> False, ColorFunction -> colorfun]
                          ]


                          This will update the result cells sequentially in a similar way to what you did with Map[,2] before. It's not very beautiful compared to a map but necessary so that Monitor can catch our intermediate results. Monitor will now display a continuously updated MatrixPlot of our result matrix while using our custom ColorFunction.



                          Curious Addendum from my side: the updating sadly doesn't seem to work when using ParallelDo instead of Do. Does anybody have an idea to make that happen?







                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered 19 mins ago









                          Thies Heidecke

                          6,2662438




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