diff --git a/src/system/mod.rs b/src/system/mod.rs
index 1da8f5f..2e230fe 100644
--- a/src/system/mod.rs
+++ b/src/system/mod.rs
@@ -1,5 +1,6 @@
 use std::f32::consts::PI;
 use std::ops::Add;
+use num_integer::Integer;
 use rand::Rng;
 use serde::{Serialize, Deserialize, Serializer};
 
@@ -9,10 +10,12 @@ pub mod model;
 pub mod nd;
 
 pub trait GriddedPosition: Add<Output=Self> + Serialize + Clone {
+    const NEIGHBOURS: u32;
+
     fn zero() -> Self;
     fn spawn<R: Rng>(rng: &mut R, radius: f32) -> Self;
     fn abs(&self) -> f32;
-    fn neighbours(&self) -> Vec<Self>;
+    fn neighbour(&self, neighbour_index: u32) -> Self;
     fn linear_index(&self, grid_size: u32) -> usize;
 }
 
@@ -37,6 +40,8 @@ impl Add for Position {
 }
 
 impl GriddedPosition for Position {
+    const NEIGHBOURS: u32 = 4;
+
     fn zero() -> Position {
         Position { x: 0, y: 0 }
     }
@@ -51,13 +56,12 @@ impl GriddedPosition for Position {
         ((self.x.pow(2) + self.y.pow(2)) as f32).powf(0.5)
     }
 
-    fn neighbours(&self) -> Vec<Self> {
-        let a = (0..2).into_iter();
+    fn neighbour(&self, neighbour_index: u32) -> Self {
+        let (dim, sign) = neighbour_index.div_rem(&2);
+        let sign = if sign == 0 { 1 } else { -1 };
+        let offset = Position::in_direction(dim, sign);
 
-        return a.flat_map(|direction| [
-            self.clone() + Position::in_direction(direction, 1),
-            self.clone() + Position::in_direction(direction, -1),
-        ]).collect();
+        self.clone() + offset
     }
 
     fn linear_index(&self, grid_size: u32) -> usize {
diff --git a/src/system/model.rs b/src/system/model.rs
index 8041769..ecbdbb0 100644
--- a/src/system/model.rs
+++ b/src/system/model.rs
@@ -114,8 +114,8 @@ impl<R: Rng, P: GriddedPosition, S: Storage<P>, W: Walker<P>> DLASystem<R, P, S,
     }
 
     fn check_stick(&mut self, position: &P) -> bool {
-        position.neighbours()
-            .iter()
+        (0..P::NEIGHBOURS)
+            .map(|n| position.neighbour(n))
             .any(|neighbour|
                 self.space.at(&neighbour)
                     && self.rng.gen_range(0.0f32..=1.0) < self.stick_probability
diff --git a/src/system/nd.rs b/src/system/nd.rs
index 654a452..1a84b92 100644
--- a/src/system/nd.rs
+++ b/src/system/nd.rs
@@ -1,4 +1,5 @@
 use std::ops::Add;
+use num_integer::Integer;
 use rand::Rng;
 use serde::{Serialize, Serializer};
 use serde::ser::SerializeMap;
@@ -56,6 +57,8 @@ impl<const DIM: usize> Serialize for NDPosition<DIM> {
 }
 
 impl<const DIM: usize> GriddedPosition for NDPosition<DIM> {
+    const NEIGHBOURS: u32 = { 2u32.pow(DIM as u32) } as u32;
+
     fn zero() -> Self {
         NDPosition([0; DIM])
     }
@@ -87,13 +90,12 @@ impl<const DIM: usize> GriddedPosition for NDPosition<DIM> {
         (a as f32).powf(0.5)
     }
 
-    fn neighbours(&self) -> Vec<Self> {
-        let a = (0..DIM).into_iter();
+    fn neighbour(&self, neighbour_index: u32) -> Self {
+        let (dim, sign) = neighbour_index.div_rem(&(DIM as u32));
+        let sign = if sign == 0 { 1 } else { -1 };
+        let offset = Self::in_direction(dim as usize, sign);
 
-        return a.flat_map(|direction| [
-            self.clone() + NDPosition::in_direction(direction, 1),
-            self.clone() + NDPosition::in_direction(direction, -1),
-        ]).collect();
+        self.clone() + offset
     }
 
     fn linear_index(&self, grid_size: u32) -> usize {
diff --git a/src/system/walker.rs b/src/system/walker.rs
index af72685..c563dd4 100644
--- a/src/system/walker.rs
+++ b/src/system/walker.rs
@@ -10,9 +10,7 @@ pub struct LocalRandomWalker;
 
 impl<Position: GriddedPosition> Walker<Position> for LocalRandomWalker {
     fn walk<R: Rng>(&self, rng: &mut R, position: &Position) -> Position {
-        let neighbours = position.neighbours();
-        let index = rng.gen_range(0..(neighbours.len()));
-        neighbours[index].clone()
+        position.neighbour(rng.gen_range(0u32..Position::NEIGHBOURS))
     }
 }