diff --git a/src/common/Graph.js b/src/common/Graph.js
index 3c1f3ed..b8f0322 100644
--- a/src/common/Graph.js
+++ b/src/common/Graph.js
@@ -13,6 +13,30 @@ export const mix = (v1, v2, s) => {
   return new Victor(result[0], result[1])
 }
 
+export const buildGraph = (nodes) => {
+  const graph = new Graph()
+
+  if (nodes.length > 0) {
+    graph.addNode(nodes[0])
+  }
+
+  for (let i = 0; i < nodes.length - 1; i++) {
+    const node1 = nodes[i]
+    const node2 = nodes[i + 1]
+    graph.addNode(node2)
+    graph.addEdge(node1, node2)
+  }
+
+  return graph
+}
+
+export const edgeKey = (node1, node2) => {
+  const node1Key = node1.toString()
+  const node2Key = node2.toString()
+
+  return [node1Key, node2Key].sort().toString()
+}
+
 // note: requires string-based nodes to work properly
 export default class Graph {
   constructor() {
@@ -42,13 +66,13 @@ export default class Graph {
   addEdge(node1, node2, weight = 1) {
     let node1Key = node1.toString()
     let node2Key = node2.toString()
-    let edgeKey = [node1Key, node2Key].sort().toString()
+    let edge12Key = edgeKey(node1, node2)
 
-    if (!this.edgeKeys.has(edgeKey)) {
+    if (!this.edgeKeys.has(edge12Key)) {
       this.adjacencyList[node1Key].push({ node: node2, weight })
       this.adjacencyList[node2Key].push({ node: node1, weight })
-      this.edgeKeys.add(edgeKey)
-      this.edgeMap[edgeKey] = [node1.toString(), node2.toString()]
+      this.edgeKeys.add(edge12Key)
+      this.edgeMap[edge12Key] = [node1.toString(), node2.toString()]
       this.clearCachedPaths()
     }
   }
@@ -62,6 +86,10 @@ export default class Graph {
     return this.adjacencyList[node.toString()].map((hash) => hash.node)
   }
 
+  getNode(node) {
+    return this.nodeMap[node.toString()]
+  }
+
   dijkstraShortestPath(startNode, endNode) {
     let shortest = this.getCachedShortestPath(startNode, endNode)
 
diff --git a/src/common/lindenmayer.js b/src/common/lindenmayer.js
index 0d10ba1..441b44d 100644
--- a/src/common/lindenmayer.js
+++ b/src/common/lindenmayer.js
@@ -1,5 +1,52 @@
 import Victor from "victor"
 import { vertexRoundP, cloneVertex } from "./geometry"
+import { buildGraph, edgeKey } from "@/common/Graph"
+import { cloneVertices } from "@/common/geometry"
+
+const shortestPath = (nodes) => {
+  const graph = buildGraph(nodes)
+  const path = []
+  const visited = {}
+
+  for (let i = 0; i < nodes.length - 1; i++) {
+    const node1 = nodes[i]
+    const node2 = nodes[i + 1]
+    let node1Key = node1.toString()
+    let edge12Key = edgeKey(node1, node2)
+
+    if (visited[edge12Key]) {
+      const unvisitedNode = nearestUnvisitedNode(i + 1, nodes, visited, graph)
+
+      if (unvisitedNode != null) {
+        const shortestSubPath = graph.dijkstraShortestPath(
+          node1Key,
+          unvisitedNode.toString(),
+        )
+
+        path.push(...cloneVertices(shortestSubPath.slice(1)))
+        i = nodes.indexOf(unvisitedNode) - 1
+      }
+    } else {
+      path.push(node2)
+      visited[edge12Key] = true
+    }
+  }
+
+  return path
+}
+
+const nearestUnvisitedNode = (nodeIndex, nodes, visited, graph) => {
+  for (let i = nodeIndex; i < nodes.length - 1; i++) {
+    const node1 = nodes[i]
+    const node2 = nodes[i + 1]
+
+    if (!visited[edgeKey(node1, node2)]) {
+      return node2
+    }
+  }
+
+  return null // all nodes visited
+}
 
 export const onSubtypeChange = (subtype, changes, attrs) => {
   // if we switch back with too many iterations, the code
@@ -122,3 +169,9 @@ export const lsystemPath = (instructions, config) => {
 
   return currVertices
 }
+
+export const lsystemOptimize = (vertices, config) => {
+  return config.shortestPath >= config.iterations
+    ? shortestPath(vertices)
+    : vertices
+}
diff --git a/src/features/shapes/lsystem/LSystem.js b/src/features/shapes/lsystem/LSystem.js
index df5ace9..d3aa567 100644
--- a/src/features/shapes/lsystem/LSystem.js
+++ b/src/features/shapes/lsystem/LSystem.js
@@ -2,6 +2,7 @@ import Shape from "../Shape"
 import {
   lsystem,
   lsystemPath,
+  lsystemOptimize,
   onSubtypeChange,
   onMinIterations,
   onMaxIterations,
@@ -63,10 +64,10 @@ export default class LSystem extends Shape {
       config.angle = Math.PI / 2
     }
 
-    let curve = lsystemPath(lsystem(config), config)
+    const path = lsystemOptimize(lsystemPath(lsystem(config), config), config)
     const scale = 18.0 // to normalize starting size
 
-    return resizeVertices(curve, scale, scale)
+    return resizeVertices(path, scale, scale)
   }
 
   getOptions() {
diff --git a/src/features/shapes/lsystem/subtypes.js b/src/features/shapes/lsystem/subtypes.js
index 1fa6913..932d2cb 100644
--- a/src/features/shapes/lsystem/subtypes.js
+++ b/src/features/shapes/lsystem/subtypes.js
@@ -106,7 +106,8 @@ export const subtypes = {
     rules: {
       F: "FF-F-F-F-FF",
     },
-    maxIterations: 5,
+    maxIterations: 4,
+    shortestPath: 3,
   },
   // http://algorithmicbotany.org/papers/abop/abop-ch1.pdf
   "Koch Cube 2": {
@@ -115,7 +116,8 @@ export const subtypes = {
     rules: {
       F: "FF-F+F-F-FF",
     },
-    maxIterations: 5,
+    maxIterations: 4,
+    shortestPath: 3,
   },
   // https://onlinemathtools.com/l-system-generator
   "Koch Curve": {
@@ -136,6 +138,7 @@ export const subtypes = {
       F: "FF-F-F-F-F-F+F",
     },
     maxIterations: 4,
+    shortestPath: 3,
   },
   // http://mathforum.org/advanced/robertd/lsys2d.html
   "Koch Island": {
@@ -178,7 +181,8 @@ export const subtypes = {
       9: "--8++++6[+9++++7]--7",
     },
     angle: Math.PI / 5,
-    maxIterations: 6,
+    maxIterations: 5,
+    shortestPath: 5,
   },
   Plusses: {
     axiom: "XYXYXYX+XYXYXYX+XYXYXYX+XYXYXYX",
diff --git a/src/features/shapes/space_filler/SpaceFiller.js b/src/features/shapes/space_filler/SpaceFiller.js
index 7e31437..0371403 100644
--- a/src/features/shapes/space_filler/SpaceFiller.js
+++ b/src/features/shapes/space_filler/SpaceFiller.js
@@ -2,6 +2,7 @@ import Shape from "../Shape"
 import {
   lsystem,
   lsystemPath,
+  lsystemOptimize,
   onSubtypeChange,
   onMinIterations,
   onMaxIterations,
@@ -86,7 +87,7 @@ export default class SpaceFiller extends Shape {
       config.angle = Math.PI / 2
     }
 
-    let curve = lsystemPath(lsystem(config), config)
+    let curve = lsystemOptimize(lsystemPath(lsystem(config), config), config)
     let scale = 1
 
     if (config.iterationsGrow) {
diff --git a/src/features/shapes/space_filler/subtypes.js b/src/features/shapes/space_filler/subtypes.js
index dc54298..521985a 100644
--- a/src/features/shapes/space_filler/subtypes.js
+++ b/src/features/shapes/space_filler/subtypes.js
@@ -58,7 +58,8 @@ export const subtypes = {
       9: "--8++++6[+9++++7]--7",
     },
     angle: Math.PI / 5,
-    maxIterations: 6,
+    maxIterations: 5,
+    shortestPath: 5,
     iterationsGrow: (config) => {
       return 1 + Math.max(1, 3 / config.iterations)
     },