diff --git a/src/common/Graph.js b/src/common/Graph.js
index 822f4dd8..4834b225 100644
--- a/src/common/Graph.js
+++ b/src/common/Graph.js
@@ -1,4 +1,4 @@
-import { PriorityQueue } from "./PriorityQueue.js"
+import { PriorityQueue } from "./PriorityQueue"
 import Victor from "victor"
 
 export const mix = (v1, v2, s) => {
@@ -37,7 +37,9 @@ export const edgeKey = (node1, node2) => {
   return [node1Key, node2Key].sort().toString()
 }
 
-// note: requires string-based nodes to work properly
+// Note: requires string-based nodes to work properly.
+// Path cache is not invalidated on addNode/addEdge for performance.
+// If modifying graph after computing paths, call clearCachedPaths() manually.
 export default class Graph {
   constructor() {
     this.nodeMap = {}
@@ -58,7 +60,6 @@ export default class Graph {
       this.nodeKeys.add(key)
       this.nodeMap[key] = node
       this.adjacencyList[key] = []
-      this.clearCachedPaths()
     }
   }
 
@@ -72,7 +73,6 @@ export default class Graph {
       this.adjacencyList[node2Key].push({ node: node1, weight })
       this.edgeKeys.add(edge12Key)
       this.edgeMap[edge12Key] = [node1.toString(), node2.toString()]
-      this.clearCachedPaths()
     }
   }
 
@@ -93,18 +93,61 @@ export default class Graph {
     return Object.values(this.nodeMap).find(fn)
   }
 
+  // BFS-based shortest path - optimal for uniform edge weights
+  bfsShortestPath(startNode, endNode) {
+    let shortest = this.getCachedShortestPath(startNode, endNode)
+
+    if (shortest === undefined) {
+      const backtrace = {}
+      const visited = new Set()
+      const queue = [startNode]
+
+      visited.add(startNode)
+
+      while (queue.length > 0) {
+        const currentNode = queue.shift()
+
+        if (currentNode === endNode) {
+          break
+        }
+
+        for (const neighbor of this.adjacencyList[currentNode]) {
+          const neighborKey = neighbor.node.toString()
+
+          if (!visited.has(neighborKey)) {
+            visited.add(neighborKey)
+            backtrace[neighborKey] = currentNode
+            queue.push(neighborKey)
+          }
+        }
+      }
+
+      let path = [endNode.toString()]
+      let lastStep = endNode
+
+      while (lastStep !== startNode) {
+        path.unshift(backtrace[lastStep].toString())
+        lastStep = backtrace[lastStep]
+      }
+
+      shortest = path.map((node) => this.nodeMap[node])
+      this.cacheShortestPath(startNode, endNode, shortest)
+    }
+
+    return shortest
+  }
+
+  // Dijkstra's algorithm with binary heap - O((V+E) log V)
   dijkstraShortestPath(startNode, endNode) {
     let shortest = this.getCachedShortestPath(startNode, endNode)
 
     if (shortest === undefined) {
-      let times = {}
-      let backtrace = {}
-      let pq = new PriorityQueue()
-      let nodes = this.nodeKeys
+      const times = {}
+      const backtrace = {}
+      const pq = new PriorityQueue()
 
       times[startNode] = 0
-
-      nodes.forEach((node) => {
+      this.nodeKeys.forEach((node) => {
         if (node !== startNode) {
           times[node] = Infinity
         }
@@ -113,17 +156,18 @@ export default class Graph {
       pq.enqueue([startNode, 0])
 
       while (!pq.isEmpty()) {
-        let shortestStep = pq.dequeue()
-        let currentNode = shortestStep[0]
-        this.adjacencyList[currentNode.toString()].forEach((neighbor) => {
-          let time = times[currentNode] + neighbor.weight
-
-          if (time < times[neighbor.node]) {
-            times[neighbor.node] = time
-            backtrace[neighbor.node] = currentNode
-            pq.enqueue([neighbor.node, time])
+        const [currentNode] = pq.dequeue()
+
+        for (const neighbor of this.adjacencyList[currentNode]) {
+          const neighborKey = neighbor.node.toString()
+          const time = times[currentNode] + neighbor.weight
+
+          if (time < times[neighborKey]) {
+            times[neighborKey] = time
+            backtrace[neighborKey] = currentNode
+            pq.enqueue([neighborKey, time])
           }
-        })
+        }
       }
 
       let path = [endNode.toString()]
diff --git a/src/common/PriorityQueue.js b/src/common/PriorityQueue.js
index 89e96fa6..35359b27 100644
--- a/src/common/PriorityQueue.js
+++ b/src/common/PriorityQueue.js
@@ -1,33 +1,72 @@
+// Binary min-heap priority queue
+// Elements are [value, priority] tuples; lower priority = dequeued first
 export class PriorityQueue {
   constructor() {
-    this.collection = []
+    this.heap = []
   }
 
   enqueue(element) {
-    if (this.isEmpty()) {
-      this.collection.push(element)
-    } else {
-      let added = false
-      for (let i = 1; i <= this.collection.length; i++) {
-        if (element[1] < this.collection[i - 1][1]) {
-          this.collection.splice(i - 1, 0, element)
-          added = true
-          break
-        }
-      }
-
-      if (!added) {
-        this.collection.push(element)
-      }
-    }
+    this.heap.push(element)
+    this.bubbleUp(this.heap.length - 1)
   }
 
   dequeue() {
-    let value = this.collection.shift()
-    return value
+    if (this.heap.length === 0) return undefined
+    if (this.heap.length === 1) return this.heap.pop()
+
+    const min = this.heap[0]
+
+    this.heap[0] = this.heap.pop()
+    this.bubbleDown(0)
+
+    return min
   }
 
   isEmpty() {
-    return this.collection.length === 0
+    return this.heap.length === 0
+  }
+
+  bubbleUp(index) {
+    while (index > 0) {
+      const parentIndex = Math.floor((index - 1) / 2)
+
+      if (this.heap[parentIndex][1] <= this.heap[index][1]) break
+      this.swap(parentIndex, index)
+      index = parentIndex
+    }
+  }
+
+  bubbleDown(index) {
+    const length = this.heap.length
+
+    while (true) {
+      const leftChild = 2 * index + 1
+      const rightChild = 2 * index + 2
+      let smallest = index
+
+      if (
+        leftChild < length &&
+        this.heap[leftChild][1] < this.heap[smallest][1]
+      ) {
+        smallest = leftChild
+      }
+      if (
+        rightChild < length &&
+        this.heap[rightChild][1] < this.heap[smallest][1]
+      ) {
+        smallest = rightChild
+      }
+
+      if (smallest === index) break
+      this.swap(index, smallest)
+      index = smallest
+    }
+  }
+
+  swap(i, j) {
+    const temp = this.heap[i]
+
+    this.heap[i] = this.heap[j]
+    this.heap[j] = temp
   }
 }
diff --git a/src/common/PriorityQueue.spec.js b/src/common/PriorityQueue.spec.js
new file mode 100644
index 00000000..11f0edd8
--- /dev/null
+++ b/src/common/PriorityQueue.spec.js
@@ -0,0 +1,38 @@
+import { PriorityQueue } from "./PriorityQueue"
+
+describe("PriorityQueue", () => {
+  it("dequeues elements in priority order", () => {
+    const pq = new PriorityQueue()
+    pq.enqueue(["c", 3])
+    pq.enqueue(["a", 1])
+    pq.enqueue(["b", 2])
+
+    expect(pq.dequeue()).toEqual(["a", 1])
+    expect(pq.dequeue()).toEqual(["b", 2])
+    expect(pq.dequeue()).toEqual(["c", 3])
+  })
+
+  it("handles empty queue", () => {
+    const pq = new PriorityQueue()
+    expect(pq.isEmpty()).toBe(true)
+    expect(pq.dequeue()).toBeUndefined()
+  })
+
+  it("handles single element", () => {
+    const pq = new PriorityQueue()
+    pq.enqueue(["only", 1])
+    expect(pq.isEmpty()).toBe(false)
+    expect(pq.dequeue()).toEqual(["only", 1])
+    expect(pq.isEmpty()).toBe(true)
+  })
+
+  it("handles duplicate priorities", () => {
+    const pq = new PriorityQueue()
+    pq.enqueue(["first", 1])
+    pq.enqueue(["second", 1])
+
+    const results = [pq.dequeue(), pq.dequeue()]
+    expect(results).toContainEqual(["first", 1])
+    expect(results).toContainEqual(["second", 1])
+  })
+})
diff --git a/src/common/lindenmayer.js b/src/common/lindenmayer.js
index 9911087d..71df1389 100644
--- a/src/common/lindenmayer.js
+++ b/src/common/lindenmayer.js
@@ -17,8 +17,8 @@ const shortestPath = (nodes) => {
     if (visited[edge12Key]) {
       const result = nearestUnvisitedNode(i + 1, nodes, visited, graph)
 
-      if (result) {
-        const shortestSubPath = graph.dijkstraShortestPath(
+      if (result != null) {
+        const shortestSubPath = graph.bfsShortestPath(
           node1Key,
           result.node.toString(),
         )
diff --git a/src/common/voronoi.js b/src/common/voronoi.js
index f8acd08e..e87ea2e6 100644
--- a/src/common/voronoi.js
+++ b/src/common/voronoi.js
@@ -5,6 +5,7 @@ import seedrandom from "seedrandom"
 import { Delaunay } from "d3-delaunay"
 import PoissonDiskSampling from "poisson-disk-sampling"
 import Victor from "victor"
+import KDBush from "kdbush"
 
 function linearWeight(i, seed, numPoints, options) {
   return 1 + (2 * i) / (numPoints * options.voronoiZoom)
@@ -117,17 +118,33 @@ function wavePatternWeight(points, width, height, options) {
 }
 
 function densityWeight(points, width, height, options) {
-  return points.map((point, i) => {
-    const [x, y] = point
+  // Build spatial index O(n log n)
+  const index = new KDBush(points.length)
+  points.forEach(([x, y]) => index.add(x, y))
+  index.finish()
+
+  // Estimate initial search radius based on average spacing
+  const area = width * height
+  const avgSpacing = Math.sqrt(area / points.length)
+  let searchRadius = avgSpacing * 2
+
+  return points.map(([x, y], i) => {
     let nearestDistance = Infinity
 
-    points.forEach((otherPoint, j) => {
+    // Find nearest neighbor using spatial index O(log n) average
+    let neighbors = index.within(x, y, searchRadius)
+    while (neighbors.length < 2 && searchRadius < Math.max(width, height)) {
+      searchRadius *= 2
+      neighbors = index.within(x, y, searchRadius)
+    }
+
+    for (const j of neighbors) {
       if (i !== j) {
-        const [x2, y2] = otherPoint
+        const [x2, y2] = points[j]
         const distance = Math.sqrt((x - x2) ** 2 + (y - y2) ** 2)
         nearestDistance = Math.min(nearestDistance, distance)
       }
-    })
+    }
 
     const weight = nearestDistance // larger distances (sparser areas) get higher weight
 
@@ -210,7 +227,7 @@ export class VoronoiMixin {
 
       if (!visited) {
         if (prev) {
-          const path = this.graph.dijkstraShortestPath(
+          const path = this.graph.bfsShortestPath(
             prev.toString(),
             neighbor.toString(),
           )
@@ -234,6 +251,7 @@ export class VoronoiMixin {
       voronoiMinDistance,
       voronoiMaxDistance,
       voronoiZoom,
+      voronoiUniformity = 0,
     } = options
     const width =
       voronoiPlacement == "poisson disk sampling"
@@ -270,6 +288,10 @@ export class VoronoiMixin {
       })
     }
 
+    if (voronoiUniformity > 0) {
+      points = this.relaxPoints(points, width, height, voronoiUniformity)
+    }
+
     return points
   }
 
@@ -337,4 +359,44 @@ export class VoronoiMixin {
 
     return graph.findNode(onEdge) || closestNode
   }
+
+  // Lloyd relaxation: move each point to the centroid of its Voronoi cell
+  relaxPoints(points, width, height, iterations) {
+    let relaxedPoints = points
+
+    for (let i = 0; i < iterations; i++) {
+      const delaunay = Delaunay.from(relaxedPoints)
+      const voronoi = delaunay.voronoi([0, 0, width, height])
+
+      relaxedPoints = relaxedPoints.map((point, idx) => {
+        const cell = voronoi.cellPolygon(idx)
+        if (!cell || cell.length < 3) return point
+
+        // Calculate centroid of the cell polygon
+        let cx = 0
+        let cy = 0
+        let area = 0
+
+        for (let j = 0; j < cell.length - 1; j++) {
+          const [x0, y0] = cell[j]
+          const [x1, y1] = cell[j + 1]
+          const cross = x0 * y1 - x1 * y0
+
+          area += cross
+          cx += (x0 + x1) * cross
+          cy += (y0 + y1) * cross
+        }
+
+        area /= 2
+        if (Math.abs(area) < 1e-10) return point
+
+        cx /= 6 * area
+        cy /= 6 * area
+
+        return [cx, cy]
+      })
+    }
+
+    return relaxedPoints
+  }
 }
diff --git a/src/features/effects/Voronoi.js b/src/features/effects/Voronoi.js
index 386f842e..97b29de8 100644
--- a/src/features/effects/Voronoi.js
+++ b/src/features/effects/Voronoi.js
@@ -23,6 +23,12 @@ export const voronoiOptions = {
     type: "togglebutton",
     choices: ["voronoi", "delaunay"],
   },
+  voronoiUniformity: {
+    title: "Uniformity",
+    type: "slider",
+    min: 0,
+    max: 20,
+  },
 }
 
 export default class Voronoi extends Effect {
@@ -51,14 +57,16 @@ export default class Voronoi extends Effect {
       ...super.getInitialState(),
       ...{
         voronoiPolygon: "voronoi",
+        voronoiUniformity: 0,
         seed: 1,
       },
     }
   }
 
   getVertices(effect, layer, vertices) {
-    const { seed, voronoiPolygon } = effect
+    const { seed, voronoiPolygon, voronoiUniformity = 0 } = effect
     const { width, height } = dimensions(vertices)
+
     this.rng = seedrandom(seed)
     noise.seed(seed)
 
@@ -68,7 +76,12 @@ export default class Voronoi extends Effect {
       ),
       (vertex) => vertex.toString(),
     )
-    const points = this.generatePointsFromVertices(mappedVertices)
+    let points = this.generatePointsFromVertices(mappedVertices)
+
+    if (voronoiUniformity > 0) {
+      points = this.relaxPoints(points, width, height, voronoiUniformity)
+    }
+
     this.graph = this.buildGraph(points, voronoiPolygon, width, height)
 
     this.vertices = []
diff --git a/src/features/effects/effectFactory.js b/src/features/effects/effectFactory.js
index 9626ea21..811abb96 100644
--- a/src/features/effects/effectFactory.js
+++ b/src/features/effects/effectFactory.js
@@ -9,7 +9,7 @@ import ProgramCode from "./ProgramCode"
 import Track from "./Track"
 import Transformer from "./Transformer"
 import Warp from "./Warp"
-// import Voronoi from "./Voronoi"
+import Voronoi from "./Voronoi"
 
 export const effectFactory = {
   loop: Loop,
@@ -21,8 +21,7 @@ export const effectFactory = {
   noise: Noise,
   track: Track,
   warp: Warp,
-  // too slow; disabling until we implement worker-based vertex computation
-  // voronoi: Voronoi
+  voronoi: Voronoi,
 }
 
 export const getEffect = (type, ...args) => {
diff --git a/src/features/shapes/Voronoi.js b/src/features/shapes/Voronoi.js
index 55b9d4ea..bfd95be2 100644
--- a/src/features/shapes/Voronoi.js
+++ b/src/features/shapes/Voronoi.js
@@ -77,6 +77,12 @@ export const voronoiOptions = {
       )
     },
   },
+  voronoiUniformity: {
+    title: "Uniformity",
+    type: "slider",
+    min: 0,
+    max: 20,
+  },
   seed: {
     title: "Random seed",
     min: 1,
@@ -107,6 +113,7 @@ export default class Voronoi extends Shape {
         voronoiMinDistance: 30,
         voronoiMaxDistance: 50,
         voronoiFrequency: 5,
+        voronoiUniformity: 0,
         seed: 1,
       },
     }
diff --git a/src/features/shapes/tessellation_twist/TessellationTwist.js b/src/features/shapes/tessellation_twist/TessellationTwist.js
index c497e901..208dd70b 100644
--- a/src/features/shapes/tessellation_twist/TessellationTwist.js
+++ b/src/features/shapes/tessellation_twist/TessellationTwist.js
@@ -200,7 +200,7 @@ export default class TessellationTwist extends Shape {
       if (prevKey) {
         if (!graph.hasEdge(key, prevKey)) {
           // non-eulerian move, so we'll walk the shortest valid path between them
-          let path = graph.dijkstraShortestPath(prevKey, key)
+          let path = graph.bfsShortestPath(prevKey, key)
           path.shift()
           path.forEach((node) => walkedVertices.push(node))
           walkedVertices.push(vertex)