Thread: Filling graphics in Mathematica

Dear friends hi again,

I am using the following code:

Code:

Manipulate[Plot[{p-Floor[k]^Floor[k]/(Floor[k]+1)^(Floor[k]+1)(Floor[k]-1),1,0},{p,0,2},PlotRange->{{0,2},{0,2}}],{k,1,10}]

The code above gives the following graphic:

My first question is how can I fill the graphic in the following form:

And the second question is how can I plot the following graphic?

Or simply, how can I put the graph of into the first graph?

Thanks.

I could do what I wanted with the following codes, I am giving them below.

Code:

kmax = 10;
Manipulate[
 Show[Graphics[{White, Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
  Graphics[{Cyan, 
    Polygon[{{2, 0}, {k^k/(k + 1)^(k + 1) (k - l), 
       0}, {1 + k^k/(1 + k)^(k + 1) (k - l), 1}, {2, 1}}]}]], {k, 1, 
  kmax, 1}, {l, 0, k - 1, 1}]
Manipulate[
 Show[Graphics[{White, Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
  Graphics[{Magenta, Line[{{1, 1}, {2, 1}}]}]], {k, 1, kmax, 1}, {l, 
  0, k - 1, 1}]
Manipulate[
 Show[Graphics[{White, Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
  Graphics[Table[If[s == k - l, Line[{{1, 1}, {2, 1}}], If[s == 0,
      Line[{{1, 0}, {1, 1}}], 
      Line[{{1, 1}, 
        If[(k - l)/(k - l - s) > 2, {2, (2 s - k + l)/s}, {(k - l)/(
          k - l - s), 0}]}]]], {s, 0, k - l}]]], {k, 1, kmax, 1}, {l, 
  0, k - 1, 1}]
Manipulate[
 Show[Graphics[{White, Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
  Graphics[{Magenta, Polygon[{{2, 0}, {1, 0}, {1, 1}, {2, 1}}]}]], {k,
   1, kmax, 1}, {l, 0, k - 1, 1}]

And all in one version

Code:

kmax = 10;
Manipulate[
 Show[If[c == 1, 
   Show[Graphics[{White, Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
    Graphics[{Cyan, 
      Polygon[{{2, 0}, {k^k/(k + 1)^(k + 1) (k - l), 
         0}, {1 + k^k/(1 + k)^(k + 1) (k - l), 1}, {2, 1}}]}]], 
   If[c == 2, 
    Show[Graphics[{White, Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}],
      Graphics[{Cyan, 
       Polygon[{{2, 0}, {k^k/(k + 1)^(k + 1) (k - l), 
          0}, {1 + k^k/(1 + k)^(k + 1) (k - l), 1}, {2, 1}}]}], 
     Graphics[{Magenta, Line[{{1, 1}, {2, 1}}]}]], 
    If[c == 3, 
     Show[Graphics[{White, 
        Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
      Graphics[{Cyan, 
        Polygon[{{2, 0}, {k^k/(k + 1)^(k + 1) (k - l), 
           0}, {1 + k^k/(1 + k)^(k + 1) (k - l), 1}, {2, 1}}]}], 
      Graphics[
       Table[If[s == k - l, Line[{{1, 1}, {2, 1}}], If[s == 0,
          Line[{{1, 0}, {1, 1}}], 
          Line[{{1, 1}, 
            If[(k - l)/(k - l - s) > 2, {2, (2 s - k + l)/s}, {(
              k - l)/(k - l - s), 0}]}]]], {s, 0, k - l}]]], 
     Show[Graphics[{White, 
        Polygon[{{2, 0}, {0, 0}, {0, 1}, {2, 1}}]}], 
      Graphics[{Cyan, 
        Polygon[{{2, 0}, {k^k/(k + 1)^(k + 1) (k - l), 
           0}, {1 + k^k/(1 + k)^(k + 1) (k - l), 1}, {2, 1}}]}], 
      Graphics[{Magenta, 
        Polygon[{{2, 0}, {1, 0}, {1, 1}, {2, 1}}]}]]]]]], {k, 1, kmax,
   1}, {l, 0, k - 1, 1}, {c, 1, 4, 1}]

Is there a way to simplify the latter code?

Thanks.