Htydjtk

So I want to draw a picture like this.

However I can get no where close to it. I have tried following other posts and adapting them which has allowed be to set the axis up correctly but I just cannot get the cubes the same way. Other than putting the location of each cube in manually is there a way to generate all cubes in one go. I don't even need as many cubes as there are in the attatched image, I just want a similar image.

I was able to do this with squares in the 2 dim plane in the following way:

documentclass{article}

usepackage{tikz}

usetikzlibrary{shapes.geometric}



begin{document}

 begin{tikzpicture}[square/.style={regular polygon,regular polygon sides=4}]



% Coordinate axes

begin{scope}[

  semithick,

  ->,

]

  draw (0, 0) -- (0, 9.5);

  draw (0, 0) -- (9.5, 0);



end{scope}



draw[node font=small]

  foreach y in {0, ..., 9} {

    (0, y) +(.25em, 0) -- ++(-.25em, 0)

    node[left] {$y$}

  }      

foreach x in {1, ..., 9} {

    (x,0)  +(0, .25em) -- ++(0, -.25em)

    node[below] {$x$}    

} ;





foreach x in {0, ..., 9} {

 foreach y in {0, ..., 9} { 

node[draw,square,inner sep=5pt,fill] at (x+.5,y+.5) {};                    

                } 

                }    

  end{tikzpicture}

end{document}

I would like to be able to do something similar, if possible.

Edit with closer output to the request, but still the angles needs adjustment (I will not do it)

documentclass{article}

usepackage{tikz}

usetikzlibrary{3d,calc}



begin{document}



xdefdist{0.25}

xdefhdist{0.1}

xdefext{0.5}

xdefout{9.2}

 begin{tikzpicture}[x={(-0.2cm,-0.4cm)}, y={(1cm,0cm)}, z={(0cm,1cm)},

     scale=0.8]





% Coordinate axes

begin{scope}[canvas is xy plane at z=30,rotate around z=30, fill opacity=0.7]

  %draw[->,thick] (0, 0,0) -- (0, 12.7,0)node[below]{Large $mathbf{y}$};

  %draw[->,thick] (0, 0,0) -- (11.5, 0,0) node[left]{Large $mathbf{x}$};

  %draw[->,thick] (0,0,0) -- (0,0,10.5)node[left]{Large $mathbf{z}$};



  foreach x in {0,1,...,9}{

  foreach y in {0,1, ..., 9} {

foreach z in {0,1,...,9}{

   fill[draw=black,blue!75] (x,y,{z+dist}) --({x+dist},y,{z+dist}) --({x+dist},{y+dist},{z+dist})--(x,{y+dist},{z+dist})--cycle; 

   fill[draw=black,brown!40!blue] (x,y,z) --(x,y,{z+dist}) --({x+dist},y,{z+dist})--({x+dist},y,z)--cycle; 

   fill[draw=black,red!45] ({x+dist},y,z) --({x+dist},{y+dist},z) --({x+dist},{y+dist},{z+dist})--({x+dist},y,{z+dist})--cycle; 

 }}}







  draw[thick]({0-ext},{0-ext},{0-ext})--({0-ext},{out+ext},{0-ext})--({out+ext},{out+ext},{0-ext})--({out+ext},{0-ext},{0-ext})--cycle;

  draw[thick]({0-ext},{0-ext},{0-ext})--({0-ext},{0-ext},{out+ext})--({out+ext},{0-ext},{out+ext})--({out+ext},{0-ext},{0-ext})--cycle;

   draw[thick]({0-ext},{out+ext},{0-ext})--({0-ext},{out+ext},{out+ext})--({out+ext},{out+ext},{out+ext})--({out+ext},{out+ext},{0-ext})--cycle;

   draw[thick]({0-ext},{0-ext},{out+ext})--({0-ext},{out+ext},{out+ext})--({out+ext},{out+ext},{out+ext})--({out+ext},{0-ext},{out+ext})--cycle;

%foreach i in {1,...,9}

%{

% draw[-,thin] (i,hdist,0)--(i,-hdist,0) node[left] {i};

% draw[-,thin] (0,hdist,i)--(0,-hdist,i) node[left] {i};

%}







end{scope}



  end{tikzpicture}

end{document}

Old Answer that just shows the basic code needed:

Here is a way:

documentclass{article}

usepackage{tikz}

usetikzlibrary{3d,calc}



begin{document}



xdefdist{0.2}

xdefhdist{0.1}

 begin{tikzpicture}[x={(-0.2cm,-0.4cm)}, y={(1cm,0cm)}, z={(0cm,1cm)}, 

     scale=0.8,

     fill opacity=0.4,

     color={gray},bottom color=white,top color=black]



 tikzset{xyplane/.style={canvas is xy plane at z=#1}}



% Coordinate axes

begin{scope}[xyplane=0,rotate around z=28]

  draw[->,thick] (0, 0,0) -- (0, 12.7,0)node[below]{Large $mathbf{y}$};

  draw[->,thick] (0, 0,0) -- (11.5, 0,0) node[left]{Large $mathbf{x}$};

  draw[->,thick] (0,0,0) -- (0,0,10.5)node[left]{Large $mathbf{z}$};

foreach i in {1,...,9}

{

 draw[-,thin] (i,hdist,0)--(i,-hdist,0) node[left] {i};

 draw[-,thin] (0,hdist,i)--(0,-hdist,i) node[left] {i};

}



foreach x in {0,1,...,9}{

  foreach y in {0,1, ..., 9} {

foreach z in {0,...,9}{

   fill[draw=black,blue!75] (x,y,{z+dist}) --({x+dist},y,{z+dist}) --({x+dist},{y+dist},{z+dist})--(x,{y+dist},{z+dist})--cycle; 

   fill[draw=black,brown!80] (x,y,z) --(x,y,{z+dist}) --({x+dist},y,{z+dist})--({x+dist},y,z)--cycle; 

   fill[draw=black,red!45] ({x+dist},y,z) --({x+dist},{y+dist},z) --({x+dist},{y+dist},{z+dist})--({x+dist},y,{z+dist})--cycle; 

 }}}



end{scope}



  end{tikzpicture}

end{document}

Just for fun!

documentclass{standalone}

usepackage{tikz,tikz-3dplot}

usepackage{amsmath}

defl{0.15}

tikzset{

  cube/.pic={

    draw (0,0,0) -- (0,l,0) -- (l,l,0) -- (l,0,0) -- cycle;

    %draw the back-right of the cube

    draw (0,0,0) -- (0,l,0) -- (0,l,l) -- (0,0,l) -- cycle;

    %draw the back-left of the cube

    draw (0,0,0) -- (l,0,0) -- (l,0,l) -- (0,0,l) -- cycle;

    %draw the front-right of the cube

    draw[fill=red] (l,0,0) -- (l,l,0) -- (l,l,l) -- (l,0,l)-- cycle;

    %draw the front-left of the cube

    draw[fill=orange] (0,l,0) -- (l,l,0) -- (l,l,l) -- (0,l,l) -- cycle;

    %draw the top of the cube

    draw[fill=blue] (0,0,l) -- (0,l,l) -- (l,l,l) -- (l,0,l) -- cycle;        

            }

        }





begin{document}

   tdplotsetmaincoords{60}{135}

begin{tikzpicture}

    [tdplot_main_coords,scale=1,

        axis/.style={-latex,thick},

        cube/.style={thin,opacity=.5}]



    %draw the axes

    draw[axis] (0,0,0) -- (6,0,0) node[above]{$x$};

    draw[axis] (0,0,0) -- (0,6,0) node[anchor=west]{$y$};

    draw[axis] (0,0,0) -- (0,0,6) node[anchor=west]{$z$};



    foreach x in {0,0.5,...,5}{

    foreach y in {0,0.5,...,5}{

    foreach z in {0,0.5,...,5}{

    pic at (x,y,z) {cube};

   }}}





    end{tikzpicture}

end{document}

This is just to comment that pgfplots has these cubes built in, and that you might want to have a look at this great answer if you want a perspective view.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

begin{document}

begin{tikzpicture}

edefCoords{}

pgfmathtruncatemacro{Nmax}{10}

foreach X in {1,...,Nmax}

 {foreach Y in {1,...,Nmax}

  {foreach Z in {1,...,Nmax}

   {xdefCoords{Coords (X,Y,Z)}}

  }

 }

 begin{axis}[

        view={120}{40},

        width=220pt,

        height=220pt,

       % z buffer=sort,

        xmin=-1,xmax=Nmax+1,

        ymin=-1,ymax=Nmax+1,

        zmin=-1,zmax=Nmax+1,

        enlargelimits=upper,

        xtick=empty,ytick=empty,ztick=empty,

        ]

   addplot3 [only marks,scatter,mark=cube*,mark size=4]

            coordinates {Coords};

 end{axis}

end{tikzpicture}

end{document}