2016 Update

Task/Sierpinski-carpet/PowerShell/sierpinski-carpet-1.psh

@@ -0,0 +1,17 @@
+function Draw-SierpinskiCarpet ( [int]$N )
+    {
+    $Carpet = @( '#' ) * [math]::Pow( 3, $N )
+    ForEach ( $i in 1..$N )
+        {
+        $S = [math]::Pow( 3, $i - 1 )
+        ForEach ( $Row in 0..($S-1) )
+            {
+            $Carpet[$Row+$S+$S] = $Carpet[$Row] * 3
+            $Carpet[$Row+$S]    = $Carpet[$Row] + ( " " * $Carpet[$Row].Length ) + $Carpet[$Row]
+            $Carpet[$Row]       = $Carpet[$Row] * 3
+            }
+        }
+    $Carpet
+    }
+
+Draw-SierpinskiCarpet 3

Task/Sierpinski-carpet/PowerShell/sierpinski-carpet-2.psh

@@ -0,0 +1,54 @@
+Function Draw-SierpinskiCarpet ( [int]$N )
+    {
+    #  Define form
+    $Form = [System.Windows.Forms.Form]@{ Size = '300, 300' }
+    $Form.Controls.Add(( $PictureBox = [System.Windows.Forms.PictureBox]@{ Size = $Form.ClientSize; Anchor = 'Top, Bottom, Left, Right' } ))
+
+    #  Main code to draw Sierpinski carpet
+    $Draw = {
+
+        #  Create graphics objects to use
+        $PictureBox.Image = ( $Canvas = New-Object System.Drawing.Bitmap ( $PictureBox.Size.Width, $PictureBox.Size.Height ) )
+        $Graphics = [System.Drawing.Graphics]::FromImage( $Canvas )
+
+        #  Draw single pixel
+        $Graphics.FillRectangle( [System.Drawing.Brushes]::Black, 0, 0, 1, 1 )
+
+        #  If N was not specified, use an N that will fill the form
+        If ( -not $N ) { $N = [math]::Ceiling( [math]::Log( [math]::Max( $PictureBox.Size.Height, $PictureBox.Size.Width ) ) / [math]::Log( 3 ) ) }
+
+        #  Define the shape of the fractal
+        $P  = @( @( 0, 0 ), @( 0, 1 ), @( 0, 2 ) )
+        $P += @( @( 1, 0 ),            @( 1, 2 ) )
+        $P += @( @( 2, 0 ), @( 2, 1 ), @( 2, 2 ) )
+
+        #  For each iteration
+        ForEach ( $i in 0..$N )
+            {
+            #  Copy the result of the previous iteration
+            $Copy = New-Object System.Drawing.TextureBrush ( $Canvas )
+
+            #  Calulate the size of the copy
+            $S = [math]::Pow( 3, $i )
+
+            #  For each position in the next layer of the fractal
+            ForEach ( $i in 1..7 )
+                {
+                #  Adjust the copy for the new location
+                $Copy.TranslateTransform( - $P[$i-1][0] * $S + $P[$i][0] * $S, - $P[$i-1][1] * $S + $P[$i][1] * $S )
+
+                #  Paste the copy of the previous iteration into the new location
+                $Graphics.FillRectangle( $Copy, $P[$i][0] * $S, $P[$i][1] * $S, $S, $S )
+                }
+            }
+        }
+
+    #  Add the main drawing code to the appropriate events to be drawn when the form is first shown and redrawn when the form size is changed
+    $Form.Add_Shown(  $Draw )
+    $Form.Add_Resize( $Draw )
+
+    #  Launch the form
+    $Null = $Form.ShowDialog()
+    }
+
+Draw-SierpinskiCarpet 4

Task/Sierpinski-carpet/PowerShell/sierpinski-carpet.psh

@@ -1,21 +0,0 @@
-function inCarpet($x, $y) {
-    while ($x -ne 0 -and $y -ne 0) {
-        if ($x % 3 -eq 1 -and $y % 3 -eq 1) {
-            return " "
-        }
-        $x = [Math]::Truncate($x / 3)
-        $y = [Math]::Truncate($y / 3)
-    }
-    return "#"
-}
-
-function carpet($n) {
-    for ($y = 0; $y -lt [Math]::Pow(3, $n); $y++) {
-        for ($x = 0; $x -lt [Math]::Pow(3, $n); $x++) {
-            Write-Host -NoNewline (inCarpet $x $y)
-        }
-        Write-Host
-    }
-}
-        #Display the carpet for N=3...
-        carpet 3