diff --git a/src/main.rs b/src/main.rs
index 022e41e..78641c8 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -7,7 +7,7 @@ use system::walker::{Walker, LocalRandomWalker};
 use system::storage::{Storage, VectorStorage};
 use num_integer::Integer;
 use rand::rngs::SmallRng;
-use crate::system::{DIM, Position};
+use crate::system::{Position};
 use crate::system::model::DLASystem;
 
 use clap::Parser;
diff --git a/src/system/mod.rs b/src/system/mod.rs
index 7cc21c7..1e5513e 100644
--- a/src/system/mod.rs
+++ b/src/system/mod.rs
@@ -1,11 +1,16 @@
 use std::ops::Add;
-use serde::{Serialize, Deserialize};
+use serde::{Serialize, Deserialize, Serializer};
 
 pub mod walker;
 pub mod storage;
 pub mod model;
 
-pub(crate) const DIM: u32 = 2;
+pub trait GriddedPosition: Add<Output=Self> + Serialize + Clone {
+    fn zero() -> Self;
+    fn abs(&self) -> f32;
+    fn neighbours(&self) -> Vec<Self>;
+    fn linear_index(&self, grid_size: u32) -> usize;
+}
 
 #[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
 pub struct Position {
@@ -14,26 +19,9 @@ pub struct Position {
 }
 
 impl Position {
-    pub fn zero() -> Position {
-        Position { x: 0, y: 0 }
-    }
-
-    pub fn abs(&self) -> f32 {
-        ((self.x.pow(2) + self.y.pow(2)) as f32).powf(0.5)
-    }
-
-    pub fn in_direction(direction: u32, value: i32) -> Self {
+    fn in_direction(direction: u32, value: i32) -> Self {
         if direction == 0 { Position { x: value, y: 0 } } else { Position { x: 0, y: value } }
     }
-
-    pub fn neighbours(&self) -> impl Iterator<Item=Self> + '_ {
-        let a = (0..DIM).into_iter();
-
-        return a.flat_map(|direction| [
-            self.clone() + Position::in_direction(direction, 1),
-            self.clone() + Position::in_direction(direction, -1),
-        ]);
-    }
 }
 
 impl Add for Position {
@@ -43,3 +31,34 @@ impl Add for Position {
         Position { x: self.x + rhs.x, y: self.y + rhs.y }
     }
 }
+
+impl GriddedPosition for Position {
+    fn zero() -> Position {
+        Position { x: 0, y: 0 }
+    }
+
+    fn abs(&self) -> f32 {
+        ((self.x.pow(2) + self.y.pow(2)) as f32).powf(0.5)
+    }
+
+    fn neighbours(&self) -> Vec<Self> {
+        let a = (0..2).into_iter();
+
+        return a.flat_map(|direction| [
+            self.clone() + Position::in_direction(direction, 1),
+            self.clone() + Position::in_direction(direction, -1),
+        ]).collect();
+    }
+
+    fn linear_index(&self, grid_size: u32) -> usize {
+        let grid_size = grid_size as i32;
+
+        assert!(self.x <= grid_size && -(grid_size) <= self.x);
+        assert!(self.y <= grid_size && -(grid_size) <= self.y);
+
+        let x = (self.x + (grid_size) / 2) as usize;
+        let y = (self.y + (grid_size) / 2) as usize;
+
+        return grid_size as usize * y + x;
+    }
+}
diff --git a/src/system/model.rs b/src/system/model.rs
index 1dc4b0b..26855fe 100644
--- a/src/system/model.rs
+++ b/src/system/model.rs
@@ -4,7 +4,7 @@ use std::io::Write;
 use std::io;
 use std::path::Path;
 use rand::prelude::*;
-use crate::system::{DIM, Position};
+use crate::system::{GriddedPosition, Position};
 use crate::system::storage::{Storage, VectorStorage};
 use crate::system::walker::{LocalRandomWalker, Walker};
 use serde::{Serialize, Deserialize};
@@ -38,7 +38,7 @@ impl<R: Rng, S: Storage, W: Walker<R>> DLASystem<R, S, W> {
             running: true,
 
             storage: VectorStorage::new(1600, 2),
-            walker: LocalRandomWalker::new(DIM),
+            walker: LocalRandomWalker::new(2),
             particles: vec![],
             active_particle: None,
 
@@ -89,6 +89,7 @@ impl<R: Rng, S: Storage, W: Walker<R>> DLASystem<R, S, W> {
 
     fn check_stick(&mut self, position: &Position) -> bool {
         position.neighbours()
+            .iter()
             .any(|neighbour|
                 self.storage.at(&neighbour)
                     && self.rng.gen_range(0.0f32..=1.0) < self.stick_probability
diff --git a/src/system/walker.rs b/src/system/walker.rs
index 378f6c3..8f40a4d 100644
--- a/src/system/walker.rs
+++ b/src/system/walker.rs
@@ -1,6 +1,6 @@
 use num_integer::Integer;
 use rand::prelude::Rng;
-use crate::system::{DIM, Position};
+use crate::system::{GriddedPosition, Position};
 
 pub trait Walker<R: Rng> {
     fn walk(&self, rng: &mut R, position: &Position) -> Position;
@@ -16,11 +16,9 @@ impl LocalRandomWalker {
 
 impl<R: Rng> Walker<R> for LocalRandomWalker {
     fn walk(&self, rng: &mut R, position: &Position) -> Position {
-        let (dim, sign) = rng.gen_range(0u32..(DIM * 2)).div_rem(&self.dim);
-        let sign = if sign == 0 { 1 } else { -1 };
-        let offset = Position::in_direction(dim, sign);
-
-        position.clone() + offset
+        let neighbours = position.neighbours();
+        let index = rng.gen_range(0..(neighbours.len()));
+        neighbours[index].clone()
     }
 }