add minimum spanning trees example, and links from other pages

Author: lee2sman

docs/assets/examples/min-span-tree.webp

@@ -70,3 +70,6 @@ end
 * [Conditions](animation-and-variables-conditions.md) - Use if and else statements to make decisions while your sketch runs.
 * [Copy Image Data](imported-media-copy-image-data.md) - Paint from an image file onto the canvas.
 * [Conway's Game Of Life](conways-life.md) - An implementation of the zero-player game and simulation formulated by mathematician John Conway
+* [Minimum Spanning Tree](min-span-tree.md) - An example of implementing Prim's algorithm for finding the shortest lengths to connect all randomly placed dots
+* [Walking lines](walking-lines.md) - Visualizes randomly drawn lines bouncing around a box with their intersecting points highlighted
+

docs/examples/10print.md

@@ -202,3 +202,12 @@ end
 * [function](/reference/function)
 * [local](/reference/local)
 * [mouseDragged()](/reference/mouseDragged)
+
+## Related Examples
+
+* [10print](10print.md) - An implementaton of the famous 1980s one-liner maze-drawing program
+* [Animation with Events](animation-and-variables-animation-with-events.md) - Pause and resume animation.
+* [Basic Pong](basic-pong.md) - A simple program demonstrating a basic implementation of pong with enemy AI player
+* [Minimum Spanning Tree](min-span-tree.md) - An example of implmenting Prim's algorithm for finding the shortest lengths to connect all randomly placed dots
+* [Walking lines](walking-lines.md) - Visualizes randomly drawn lines bouncing around a box with their intersecting points highlighted
+

docs/examples/conways-life.md

@@ -15,6 +15,7 @@
 * [Walking Lines](walking-lines.md) - Animated intersecting lines
 * [10Print](10print.md) - An implementation of the classic maze-drawing algorithm
 * [Conway's Game Of Life](conways-life.md) - An implementation of the zero-player game and simulation formulated by mathematician John Conway
+* [Minimum Spanning Tree](min-span-tree.md) - An example of implementing Prim's algorithm for finding the shortest lengths to connect all randomly placed dots
 
 ## Imported Media
 

docs/examples/index.md

@@ -0,0 +1,126 @@
+# Minimum Spanning Tree
+
+A minimum spanning tree (MST) is an example of a visualization of [Prim's algorithm](https://en.wikipedia.org/wiki/Prim%27s_algorithm) for finding the shortest lengths connecting all randomly placed dots. All of the points are [connected](https://visualgo.net/en/mst) in a tree path with the shortest total edge lengths, with only one path (no 'cycle').
+
+![30 points connected with the shortest total length of lines, forming a tree structure](/assets/examples/min-span-tree.webp "30 points connected with the shortest total length of lines, forming a tree structure")
+
+## How Prim's Algorithm Works
+
+1. Start with any vertex (point) in the graph
+2. Find the shortest edge connecting a visited vertex to an unvisited vertex
+3. Add that edge to the tree and mark the new vertex as visited
+4. Repeat steps 2-3 until all vertices are visited
+
+This algorithm takes a *greedy* approach, always choosing the shortest available edge, which guarantees finding the minimum spanning tree.
+
+## Code
+
+```lua
+require("L5")
+-- Minimum Spanning Tree using Prim's algorithm
+points = {}
+numPoints = 30 -- how many points to draw
+tree = {}  -- Edges in the MST
+visited = {}
+
+function setup()
+  size(800, 600)
+  windowTitle("Minimum Spanning Tree")
+  background(255)
+  
+  -- Generate random points
+  for i = 1, numPoints do
+    points[i] = {
+      x = random(0, width),
+      y = random(0, height)
+    }
+  end
+  
+  -- Build MST using Prim's algorithm
+  buildMST()
+
+  describe("30 points connected with the shortest total length of lines, forming a tree structure.")
+end
+
+function buildMST()
+  -- Start with first point
+  visited[1] = true
+  local numVisited = 1
+  
+  -- Build tree by adding edges one at a time
+  while numVisited < numPoints do
+    local minDist = math.huge --equivalent to infinity in Lua. alternatively, use a large number like 999999
+    local minEdge = nil
+    
+    -- Find shortest edge connecting visited to unvisited
+    for i = 1, numPoints do
+      if visited[i] then
+        for j = 1, numPoints do
+          if not visited[j] then
+            local d = dist(points[i].x, points[i].y, points[j].x, points[j].y)
+            if d < minDist then
+              minDist = d
+              minEdge = {from = i, to = j, dist = d}
+            end
+          end
+        end
+      end
+    end
+    
+    -- Add edge to tree
+    if minEdge then
+      table.insert(tree, minEdge)
+      visited[minEdge.to] = true
+      numVisited = numVisited + 1
+    else
+      break  -- No more edges found
+    end
+  end
+end
+
+function draw()
+  background(255)
+  
+  -- Draw all edges in the MST
+  stroke(100, 100, 255)
+  strokeWeight(2)
+  for _, edge in ipairs(tree) do
+    local p1 = points[edge.from]
+    local p2 = points[edge.to]
+    line(p1.x, p1.y, p2.x, p2.y)
+  end
+  
+  -- Draw all points
+  noStroke()
+  fill(50)
+  for _, point in ipairs(points) do
+    circle(point.x, point.y, 8)
+  end
+end
+```
+
+## More things to try
+
+* You can change `numPoints` to see different densities
+* Modify the point generation to use a grid pattern instead of random
+* Color edges based on their length
+* Animate the MST construction by adding edges one at a time
+
+## Related References
+
+* [if](/reference/if)
+* [line()](/reference/line)
+* [dist()](/reference/dist)
+* [draw()](/reference/draw)
+* [random()](/reference/random)
+* [sqrt()](/reference/sqrt)
+* [table](/reference/table)
+
+## Related Examples
+
+* [10print](10print.md) - An implementaton of the famous 1980s one-liner maze-drawing program
+* [Animation with Events](animation-and-variables-animation-with-events.md) - Pause and resume animation.
+* [Basic Pong](basic-pong.md) - A simple program demonstrating a basic implementation of pong with enemy AI player
+* [Conway's Game of Life](conways-life.md) - An implementation of the zero-player game and simulation formulated by mathematician John Conway
+* [Walking lines](walking-lines.md) - Visualizes randomly drawn lines bouncing around a box with their intersecting points highlighted
+

docs/examples/min-span-tree.md

@@ -123,7 +123,21 @@ function intersectPoint(aX1, aY1, aX2, aY2, bX1, bY1, bX2, bY2)
 end
 ```
 
+## Related References
+
+* [if](/reference/if)
+* [line()](/reference/line)
+* [draw()](/reference/draw)
+* [frameRate()](/reference/frameRate)
+* [random()](/reference/random)
+
 ## Related Examples
 
 * [10print](10print.md) - An implementation of the classic maze-drawing algorithm
-* [Conway's Game of Life](conways-life.md) - An implementation of the zero-player game and simulation formulated by mathematician John Conway
+* [Animation with Events](animation-and-variables-animation-with-events.md) - Pause and resume animation.
+* [Basic Pong](basic-pong.md) - A simple program demonstrating a basic implementation of pong with enemy AI player
+* [Conditions](animation-and-variables-conditions.md) - Use if and else statements to make decisions while your sketch runs.
+* [Copy Image Data](imported-media-copy-image-data.md) - Paint from an image file onto the canvas.
+* [Conway's Game Of Life](conways-life.md) - An implementation of the zero-player game and simulation formulated by mathematician John Conway
+* [Minimum Spanning Tree](min-span-tree.md) - An example of implementing Prim's algorithm for finding the shortest lengths to connect all randomly placed dots
+