Added Iterated function system in PowerShell (#895)

* implemented IFS in PowerShell

* fixed typo

Co-authored-by: James Schloss <jrs.schloss@gmail.com>

Author: PaddyKe

contents/IFS/IFS.md

@@ -146,6 +146,8 @@ Here, instead of tracking children of children, we track a single individual tha
 [import:4-16, lang:"coconut"](code/coconut/IFS.coco)
 {% sample lang="java" %}
 [import:16-39, lang:"java"](code/java/IFS.java)
+{% sample lang="ps1" %}
+[import:2-19, lang:"powershell"](code/powershell/IFS.ps1)
 {% endmethod %}
 
 If we set the initial point to the on the equilateral triangle we saw before, we can see the Sierpinski triangle again after a few thousand iterations, as shown below:
@@ -232,6 +234,8 @@ In addition, we have written the chaos game code to take in a set of points so t
 [import, lang:"coconut"](code/coconut/IFS.coco)
 {%sample lang="java" %}
 [import, lang:"java"](code/java/IFS.java)
+{% sample lang="ps1" %}
+[import, lang:"powershell"](code/powershell/IFS.ps1)
 {% endmethod %}
 
 ### Bibliography

contents/IFS/code/powershell/IFS.ps1

@@ -0,0 +1,34 @@
+# This function simulates a "chaos game"
+function Simulate-ChaosGame($n, $shapePoints) {
+    $outputPoints = New-Object System.Collections.ArrayList
+    
+    # Initialize the starting point
+    $point = @($(Get-Random -Minimum 0.0 -Maximum 1.0), $(Get-Random -Minimum 0.0 -Maximum 1.0))
+
+    for ($i = 0; $i -lt $n; $i++) {
+      $outputPoints.add($point) | Out-Null
+      $temp = $shapePoints[$(Get-Random -Maximum $shapePoints.Count)]
+
+      $point = @(
+          0.5 * ($point[0] + $temp[0])
+          0.5 * ($point[1] + $temp[1])
+      )
+    }
+
+    return $outputPoints
+}
+
+
+# This will generate a Sierpinski triangle with a chaos game of n points for an
+# initial triangle with three points on the vertices of an equilateral triangle:
+#     A = (0.0, 0.0)
+#     B = (0.5, sqrt(0.75))
+#     C = (1.0, 0.0)
+# It will output the file sierpinski.dat, which can be plotted after
+$shapePoints = @(
+    @(0.0, 0.0),
+    @(0.5, [math]::sqrt(0.75)),
+    @(1.0, 0.0)
+)
+
+Simulate-ChaosGame -n 10000 -shapePoints $shapePoints | % { "$($_[0])`t$($_[1])" } | Out-File -Path "sierpinski.dat"