diff --git a/src/system/spaces/square_grid.rs b/src/system/spaces/square_grid.rs
index d7690cb..823c362 100644
--- a/src/system/spaces/square_grid.rs
+++ b/src/system/spaces/square_grid.rs
@@ -3,7 +3,7 @@ use num_integer::Integer;
 use crate::system::{GriddedPosition, Position};
 use serde::{Serialize, Deserialize};
 
-#[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
+#[derive(Clone, Debug, Hash, PartialEq, Eq, Serialize, Deserialize)]
 pub struct Grid2D {
     pub x: i32,
     pub y: i32,
diff --git a/src/system/walker.rs b/src/system/walker.rs
index bd943c7..5911782 100644
--- a/src/system/walker.rs
+++ b/src/system/walker.rs
@@ -1,6 +1,10 @@
+use std::hash::Hash;
+use bevy::render::render_resource::encase::private::RuntimeSizedArray;
+use itertools::Itertools;
+use rand::distributions::Slice;
 use rand::prelude::Rng;
 use crate::system::{GriddedPosition, Position};
-use crate::system::spaces::square_grid::Grid3D;
+use crate::system::spaces::square_grid::{Grid2D, Grid3D};
 
 pub trait Walker<P: Position> {
     fn walk<R: Rng>(&self, rng: &mut R, position: &P) -> P;
@@ -18,14 +22,131 @@ pub struct DiagonalRandomWalker;
 
 impl Walker<Grid3D> for DiagonalRandomWalker {
     fn walk<R: Rng>(&self, rng: &mut R, position: &Grid3D) -> Grid3D {
-        let a: Vec<i32> = (0..3)
-            .map(|r| rng.gen_range(-1..=1))
-            .collect();
+        static OFFSETS: [Grid3D; 26] = [
+            Grid3D { x: 1, y: 0, z: 0 },
+            Grid3D { x: 1, y: 1, z: 0 },
+            Grid3D { x: 1, y: -1, z: 0 },
+            Grid3D { x: -1, y: 0, z: 0 },
+            Grid3D { x: -1, y: 1, z: 0 },
+            Grid3D { x: -1, y: -1, z: 0 },
+            Grid3D { x: 0, y: 1, z: 0 },
+            Grid3D { x: 0, y: -1, z: 0 },
+            Grid3D { x: 1, y: 0, z: -1 },
+            Grid3D { x: 1, y: 1, z: -1 },
+            Grid3D { x: 1, y: -1, z: -1 },
+            Grid3D { x: -1, y: 0, z: -1 },
+            Grid3D { x: -1, y: 1, z: -1 },
+            Grid3D { x: -1, y: -1, z: -1 },
+            Grid3D { x: 0, y: 1, z: -1 },
+            Grid3D { x: 0, y: -1, z: -1 },
+            Grid3D { x: 0, y: 0, z: -1 },
+            Grid3D { x: 1, y: 0, z: 1 },
+            Grid3D { x: 1, y: 1, z: 1 },
+            Grid3D { x: 1, y: -1, z: 1 },
+            Grid3D { x: -1, y: 0, z: 1 },
+            Grid3D { x: -1, y: 1, z: 1 },
+            Grid3D { x: -1, y: -1, z: 1 },
+            Grid3D { x: 0, y: 1, z: 1 },
+            Grid3D { x: 0, y: -1, z: 1 },
+            Grid3D { x: 0, y: 0, z: 1 },
+        ];
 
-        position.clone() + Grid3D::from_cartesian([a[0] as f32, a[1] as f32, a[2] as f32])
+        position.clone() + OFFSETS[rng.gen_range(0..OFFSETS.len())].clone()
     }
 }
 
+impl Walker<Grid2D> for DiagonalRandomWalker {
+    fn walk<R: Rng>(&self, rng: &mut R, position: &Grid2D) -> Grid2D {
+        static OFFSETS: [Grid2D; 8] = [
+            Grid2D { x: 1, y: 0 },
+            Grid2D { x: 1, y: 1 },
+            Grid2D { x: 1, y: -1 },
+            Grid2D { x: -1, y: 0 },
+            Grid2D { x: -1, y: 1 },
+            Grid2D { x: -1, y: -1 },
+            Grid2D { x: 0, y: 1 },
+            Grid2D { x: 0, y: -1 },
+        ];
+
+        position.clone() + OFFSETS[rng.gen_range(0..OFFSETS.len())].clone()
+    }
+}
+
+fn test_uniformity_and_range<W: Walker<P>, P>(walker: W, expected: &[P], n: usize, tolerance: f32) where P: GriddedPosition + Hash + Eq {
+    use rand::thread_rng;
+    let mut rng = thread_rng();
+    let origin = &P::zero();
+
+    let results: Vec<P> = (0..n)
+        .map(|_| walker.walk(&mut rng, origin))
+        .collect();
+
+    let groups = results.iter()
+        .into_group_map_by(|a| (*a).clone());
+
+    assert_eq!(groups.len(), expected.len(), "Wrong number of walk positions generated");
+    assert!(results.iter().unique().all(|a| expected.contains(a)), "Contains unexpected walk position");
+
+    for group in groups.values() {
+        let proportion = group.len() as f32 / n as f32;
+        assert!((proportion - (1.0 / expected.len() as f32)).abs() < tolerance, "Failed tolerance check");
+    }
+}
+
+#[test]
+fn uniformity_direct_grid2d() {
+    test_uniformity_and_range(LocalRandomWalker, &[
+        Grid2D { x: 1, y: 0 },
+        Grid2D { x: -1, y: 0 },
+        Grid2D { x: 0, y: 1 },
+        Grid2D { x: 0, y: -1 },
+    ], 1_000_000, 0.001);
+}
+
+#[test]
+fn uniformity_direct_grid3d() {
+    test_uniformity_and_range(LocalRandomWalker, &[
+        Grid3D { x: 1, y: 0, z: 0 },
+        Grid3D { x: -1, y: 0, z: 0 },
+        Grid3D { x: 0, y: 1, z: 0 },
+        Grid3D { x: 0, y: -1, z: 0 },
+        Grid3D { x: 0, y: 0, z: 1 },
+        Grid3D { x: 0, y: 0, z: -1 },
+    ], 1_000_000, 0.001);
+}
+
+#[test]
+fn diagonal_grid2d() {
+    let mut expected = Vec::new();
+
+    for x in -1..=1 {
+        for y in -1..=1 {
+            if !(x == 0 && y == 0) {
+                expected.push(Grid2D { x,  y })
+            }
+        }
+    }
+
+    test_uniformity_and_range(DiagonalRandomWalker, &expected, 1_000_000, 0.001);
+}
+
+#[test]
+fn diagonal_grid3d() {
+    let mut expected = Vec::new();
+
+    for x in -1..=1 {
+        for y in -1..=1 {
+            for z in -1..=1 {
+                if !(x == 0 && y == 0 && z == 0) {
+                    expected.push(Grid3D { x,  y, z })
+                }
+            }
+        }
+    }
+
+    test_uniformity_and_range(DiagonalRandomWalker, &expected, 1_000_000, 0.001);
+}
+
 mod test {
     use rand::rngs::SmallRng;
     use rand::{SeedableRng, thread_rng};
@@ -33,42 +154,6 @@ mod test {
     use crate::system::spaces::square_grid::{Grid2D, Grid3D};
     use crate::system::walker::{DiagonalRandomWalker, LocalRandomWalker, Walker};
 
-    #[test]
-    fn uniformity() {
-        let walker = LocalRandomWalker;
-        let mut rng = SmallRng::from_rng(thread_rng()).unwrap();
-        let mut results: Vec<Grid2D> = vec![];
-
-        let origin = &Grid2D::zero();
-
-        let x: u32 = (1_000_000);
-        for i in 0..x {
-            results.push(walker.walk(&mut rng, origin));
-        }
-
-        let a = results
-            .iter()
-            .filter(|a| **a == Grid2D { x: 0, y: 1 })
-            .count();
-
-        let b = results
-            .iter()
-            .filter(|a| **a == Grid2D { x: 0, y: -1 })
-            .count();
-
-        let c = results
-            .iter()
-            .filter(|a| **a == Grid2D { x: 1, y: 0 })
-            .count();
-
-        let d = results
-            .iter()
-            .filter(|a| **a == Grid2D { x: -1, y: 0 })
-            .count();
-
-        println!("{} {} {} {}", a as f32 / x as f32, b as f32 / x as f32, c as f32 / x as f32, d as f32 / x as f32);
-    }
-
     #[test]
     fn diagonal() {
         let drw = DiagonalRandomWalker;